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Electron quantum optics in graphene

Published 8 Jan 2024 in cond-mat.mes-hall | (2401.04233v1)

Abstract: In the last decade, graphene has become an exciting platform for electron optical experiments, in many aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states, \eg, snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers.

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References (350)
  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field in atomically thin carbon films,” Science, vol. 306, pp. 666–669, oct 2004.
  2. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature, vol. 556, pp. 43–50, Apr. 2018.
  3. R. Hanbury Brown and R. Q. Twiss, “A new type of interferometer for use in radio astronomy,” Philosophical Magazine, vol. 45, no. 366, pp. 663–682, 1954.
  4. R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature, vol. 177, no. 4497, pp. 27–29, 1956.
  5. B. Huard, J. Sulpizio, N. Stander, K. Todd, B. Yang, and D. Goldhaber-Gordon, “Transport measurements across a tunable potential barrier in graphene,” Physical review letters, vol. 98, no. 23, p. 236803, 2007.
  6. M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Letters, vol. 28, no. 4, pp. 282–284, 2007.
  7. J. Williams, L. DiCarlo, and C. Marcus, “Quantum hall effect in a gate-controlled pn junction of graphene,” Science, vol. 317, no. 5838, pp. 638–641, 2007.
  8. D. Abanin and L. Levitov, “Quantized transport in graphene pn junctions in a magnetic field,” Science, vol. 317, no. 5838, pp. 641–643, 2007.
  9. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nature Phsics, vol. 2, pp. 620–625, sep 2006.
  10. V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a veselago lens in graphene p-n junctions,” Science, vol. 315, pp. 1252–1255, mar 2007.
  11. V. V. Cheianov and V. I. Fal’ko, “Selective transmission of Dirac electrons and ballistic magnetoresistance of np junctions in graphene,” Physical Review B, vol. 74, p. 041403, jul 2006.
  12. P. Silvestrov and K. Efetov, “Quantum dots in graphene,” Physical Review Letters, vol. 98, no. 1, p. 016802, 2007.
  13. R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegmann, “Electron mobilities in modulation‐doped semiconductor heterojunction superlattices,” Applied Physics Letters, vol. 33, pp. 665–667, oct 1978.
  14. A. Ketterson, F. Ponse, T. Henderson, J. Klem, and H. Morkoç, “Extremely low contact resistances for AlGaAs/GaAs modulation‐doped field‐effect transistor structures,” Journal of Applied Physics, vol. 57, pp. 2305–2307, mar 1985.
  15. J. Y. Chung, A. Gupta, K. W. Baldwin, K. W. West, M. Shayegan, and L. N. Pfeiffer, “Understanding limits to mobility in ultrahigh-mobility gaas two-dimensional electron systems: 100100100100 million cm22{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT/vs and beyond,” Phys. Rev. B, vol. 106, p. 075134, aug 2022.
  16. B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, and C. T. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Physical Review Letters, vol. 60, pp. 848–850, feb 1988.
  17. K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Communications, vol. 146, pp. 351–355, jun 2008.
  18. X. Du, I. Skachko, A. Barker, and E. Y. Andrei, “Approaching ballistic transport in suspended graphene,” Nature Nanotechnology 2008 3:8, vol. 3, pp. 491–495, jul 2008.
  19. C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nature Nanotechnology, vol. 5, pp. 722–726, oct 2010.
  20. L. Wang, Z. Chen, C. R. Dean, T. Taniguchi, K. Watanabe, L. E. Brus, and J. Hone, “Negligible environmental sensitivity of graphene in a hexagonal boron nitride/graphene/h-bn sandwich structure,” ACS Nano, vol. 6, pp. 9314–9319, oct 2012.
  21. L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, “One-dimensional electrical contact to a two-dimensional material,” Science, vol. 342, pp. 614–617, Nov. 2013.
  22. A. F. Young and P. Kim, “Quantum interference and Klein tunnelling in graphene heterojunctions,” Nature Physics, vol. 5, pp. 222–226, mar 2009.
  23. P. Rickhaus, R. Maurand, M.-H. Liu, M. Weiss, K. Richter, and C. Schönenberger, “Ballistic interferences in suspended graphene,” Nat Commun, vol. 4, p. 2342, Aug. 2013.
  24. L. Banszerus, M. Schmitz, S. Engels, M. Goldsche, K. Watanabe, T. Taniguchi, B. Beschoten, and C. Stampfer, “Ballistic Transport Exceeding 28 μ𝜇\muitalic_μm in CVD Grown Graphene,” Nano Letters, vol. 16, pp. 1387–1391, Feb. 2016.
  25. A. V. Shytov, M. S. Rudner, and L. S. Levitov, “Klein backscattering and Fabry-Pérot interference in graphene heterojunctions,” Phys. Rev. Lett., vol. 101, p. 156804, Oct 2008.
  26. J. R. Williams, “Electron optics with graphene p-n junctions,” in 2D Materials: Properties and Devices, pp. 141–158, Cambridge University Press, 2017.
  27. P. Rickhaus, P. Makk, M.-H. Liu, E. Tóvári, M. Weiss, R. Maurand, K. Richter, and C. Schönenberger, “Snake trajectories in ultraclean graphene p–n junctions,” Nature Communications 2015 6:1, vol. 6, pp. 1–6, mar 2015.
  28. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature, vol. 438, pp. 197–200, nov 2005.
  29. Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature, vol. 438, pp. 201–204, nov 2005.
  30. Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for Coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Perot interferometers,” Physical Review B, vol. 79, no. 24, p. 241304, 2009.
  31. Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, “An electronic Mach–Zehnder interferometer,” Nature, vol. 422, pp. 415–418, Mar. 2003.
  32. G. Fève, A. Mahe’, J.-M. Berroir, T. Kontos, B. Plaçais, D. C. Glattli, A. Cavanna, B. Etienne, and Y. Jin, “An on-demand coherent single-electron source,” Science, vol. 316, pp. 1169–1172, May 2007.
  33. J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau, and D. C. Glattli, “Minimal-excitation states for electron quantum optics using levitons,” Nature, vol. 502, pp. 659–663, Oct. 2013.
  34. M. Henny, S. Oberholzer, C. Strunk, T. Heinzel, K. Ensslin, M. Holland, and C. Schönenberger, “The fermionic Hanbury Brown and Twiss experiment,” Science, vol. 284, pp. 296–298, apr 1999.
  35. W. D. Oliver, J. Kim, R. C. Liu, and Y. Yamamoto, “Hanbury Brown and Twiss-type experiment with electrons,” Science, vol. 284, pp. 299–301, apr 1999.
  36. E. Bocquillon, F. D. Parmentier, C. Grenier, J.-M. Berroir, P. Degiovanni, D. C. Glattli, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, “Electron quantum optics: Partitioning electrons one by one,” Physical Review Letters, vol. 108, p. 196803, may 2012.
  37. E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, “Coherence and indistinguishability of single electrons emitted by independent sources,” Science, vol. 339, pp. 1054–1057, Mar. 2013.
  38. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, “Direct observation of anyonic braiding statistics,” Nat Phys, vol. 16, pp. 931–936, Sept. 2020.
  39. H. Bartolomei, M. Kumar, R. Bisognin, A. Marguerite, J.-M. Berroir, E. Bocquillon, B. Plaçais, A. Cavanna, Q. Dong, U. Gennser, Y. Jin, and G. Fève, “Fractional statistics in anyon collisions,” Science, vol. 368, pp. 173–177, Apr. 2020.
  40. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys., vol. 80, pp. 1083–1159, Sept. 2008.
  41. M. O. Goerbig, “Electronic properties of graphene in a strong magnetic field,” Reviews of Modern Physics, vol. 83, pp. 1193–1243, nov 2011.
  42. A. F. Young, C. R. Dean, L. Wang, H. Ren, P. Cadden-Zimansky, K. Watanabe, T. Taniguchi, J. Hone, K. L. Shepard, and P. Kim, “Spin and valley quantum Hall ferromagnetism in graphene,” Nature Physics, vol. 8, pp. 550–556, July 2012.
  43. M. Kharitonov, “Phase diagram for the ν=0𝜈0\nu=0italic_ν = 0 quantum hall state in monolayer graphene,” Phys. Rev. B, vol. 85, p. 155439, Apr 2012.
  44. M. Kharitonov, “Canted antiferromagnetic phase of the ν=0𝜈0\nu\mathbf{=}0italic_ν = 0 quantum hall state in bilayer graphene,” Phys. Rev. Lett., vol. 109, p. 046803, Jul 2012.
  45. A. Knothe and T. Jolicoeur, “Phase diagram of a graphene bilayer in the zero-energy landau level,” Phys. Rev. B, vol. 94, p. 235149, Dec 2016.
  46. M. T. Allen, J. Martin, and A. Yacoby, “Gate-defined quantum confinement in suspended bilayer graphene,” Nature Communications, vol. 3, p. 934, July 2012.
  47. S. Dröscher, C. Barraud, K. Watanabe, T. Taniguchi, T. Ihn, and K. Ensslin, “Electron flow in split-gated bilayer graphene,” New Journal of Physics, vol. 14, no. 10, p. 103007, 2012.
  48. A. S. M. Goossens, S. C. M. Driessen, T. A. Baart, K. Watanabe, T. Taniguchi, and L. M. K. Vandersypen, “Gate-defined confinement in bilayer graphene-hexagonal boron nitride hybrid devices,” Nano Letters, vol. 12, pp. 4656–4660, Sept. 2012.
  49. H. Overweg, H. Eggimann, X. Chen, S. Slizovskiy, M. Eich, R. Pisoni, Y. Lee, P. Rickhaus, K. Watanabe, T. Taniguchi, V. Fal’ko, T. Ihn, and K. Ensslin, “Electrostatically induced quantum point contacts in bilayer graphene,” Nano Letters, vol. 18, pp. 553–559, Jan. 2018.
  50. F. Guinea, A. K. Geim, M. I. Katsnelson, and K. S. Novoselov, “Generating quantizing pseudomagnetic fields by bending graphene ribbons,” Phys. Rev. B, vol. 81, p. 035408, Jan 2010.
  51. S.-M. Choi, S.-H. Jhi, and Y.-W. Son, “Effects of strain on electronic properties of graphene,” Physical Review B, vol. 81, feb 2010.
  52. D. Grassano, M. D’Alessandro, O. Pulci, S. G. Sharapov, V. P. Gusynin, and A. A. Varlamov, “Work function, deformation potential, and collapse of landau levels in strained graphene and silicene,” Phys. Rev. B, vol. 101, p. 245115, Jun 2020.
  53. L. Wang, A. Baumgartner, P. Makk, S. Zihlmann, B. S. Varghese, D. I. Indolese, K. Watanabe, T. Taniguchi, and C. Schönenberger, “Global strain-induced scalar potential in graphene devices,” Communications Physics, vol. 4, jun 2021.
  54. A. F. Young, J. D. Sanchez-Yamagishi, B. Hunt, S. H. Choi, K. Watanabe, T. Taniguchi, R. C. Ashoori, and P. Jarillo-Herrero, “Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state,” Nature, vol. 505, pp. 528–532, jan 2014.
  55. L. Veyrat, A. Jordan, K. Zimmermann, F. Gay, K. Watanabe, T. Taniguchi, H. Sellier, and B. Sacépé, “Low-magnetic-field regime of a gate-defined constriction in high-mobility graphene,” Nano Letters, vol. 19, pp. 635–642, feb 2019.
  56. A. Knothe and T. Jolicoeur, “Edge structure of graphene monolayers in the N𝑁Nitalic_N=0 quantum Hall state,” Phys. Rev. B, vol. 92, p. 165110, 2015.
  57. E. McCann and V. I. Fal’ko, “Landau-level degeneracy and quantum Hall effect in a graphite bilayer,” Physical Review Letters, vol. 96, p. 086805, Mar. 2006.
  58. E. McCann, D. S. Abergel, and V. I. Fal’ko, “The low energy electronic band structure of bilayer graphene,” The European Physical Journal Special Topics, vol. 148, pp. 91–103, Sept. 2007.
  59. E. McCann and M. Koshino, “The electronic properties of bilayer graphene,” Reports on Progress in Physics, vol. 76, no. 5, p. 056503, 2013.
  60. M.-C. Chang and Q. Niu, “Berry phase, hyperorbits, and the Hofstadter spectrum,” Phys. Rev. Lett., vol. 75, pp. 1348–1351, Aug 1995.
  61. N. W. Ashcroft and N. D. Mermin, Solid State Physics. New York: Holt, Rinehart and Winston, 1976.
  62. M.-H. Liu, J. Bundesmann, and K. Richter, “Spin-dependent Klein tunneling in graphene: Role of Rashba spin-orbit coupling,” Phys. Rev. B, vol. 85, p. 085406, Feb 2012.
  63. C. Handschin, Quantum-Transport in Encapsulated Graphene P-N junctions. PhD thesis, Department of Physics, University of Basel, Basel, Mar 2017. Magna Cum Laude.
  64. O. Klein, “Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac,” Zeitschrift für Physik, vol. 53, pp. 157–165, Mar. 1929.
  65. C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Reviews Of Modern Physics, vol. 80, pp. 1337–1354, oct 2008.
  66. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys., vol. 81, p. 109, 2009.
  67. P. Allain and J. Fuchs, “Klein tunneling in graphene: optics with massless electrons,” Eur. Phys. J. B, vol. 83, pp. 301–317, 2011.
  68. S. Datta, Electronic Transport in Mesoscopic Systems. Cambridge University Press, 1995.
  69. P. Rickhaus, Electron optics in ballistic graphene. PhD thesis, University of Basel, 2015.
  70. P. Rickhaus, Electron Optics in Ballistic Graphene. PhD thesis, Department of Physics, University of Basel, Basel, Sep 2015.
  71. M. Wimmer, Quantum transport in nanostructures: From computational concepts to spintronics in graphene and magnetic tunnel junctions. PhD thesis, Universität Regensburg, 2008.
  72. C. H. Lewenkopf and E. R. Mucciolo, “The recursive Green’s function method for graphene,” Journal of Computational Electronics, vol. 12, pp. 203–231, may 2013.
  73. S. Luryi, “Quantum capacitance devices,” Appl. Phys. Lett., vol. 52, no. 6, pp. 501–503, 1988.
  74. T. Fang, A. Konar, H. Xing, and D. Jena, “Carrier statistics and quantum capacitance of graphene sheets and ribbons,” Appl. Phys. Lett., vol. 91, no. 9, p. 092109, 2007.
  75. S. Dröscher, P. Roulleau, F. Molitor, P. Studerus, C. Stampfer, K. Ensslin, and T. Ihn, “Quantum capacitance and density of states of graphene,” Applied Physics Letters, vol. 96, no. 15, p. 152104, 2010.
  76. M.-H. Liu, “Theory of carrier density in multigated doped graphene sheets with quantum correction,” Phys. Rev. B, vol. 87, p. 125427, Mar 2013.
  77. C. Multiphysics, “Introduction to comsol multiphysics®,” COMSOL Multiphysics, Burlington, MA, accessed Feb, vol. 9, p. 2018, 1998.
  78. Springer, 2012.
  79. M.-H. Liu, P. Rickhaus, P. Makk, E. Tóvári, R. Maurand, F. Tkatschenko, M. Weiss, C. Schönenberger, and K. Richter, “Scalable tight-binding model for graphene,” Physical Review Letters, vol. 114, p. 036601, Jan 2015.
  80. P. Rickhaus, M.-H. Liu, P. Makk, R. Maurand, S. Hess, S. Zihlmann, M. Weiss, K. Richter, and C. Schönenberger, “Guiding of electrons in a few-mode ballistic graphene channel,” Nano Letters, vol. 15, pp. 5819–5825, sep 2015.
  81. P. Rickhaus, P. Makk, M.-H. Liu, K. Richter, and C. Schönenberger, “Gate tuneable beamsplitter in ballistic graphene,” Applied Physics Letters, vol. 107, dec 2015.
  82. B. Terres, L. A. Chizhova, F. Libisch, J. Peiro, D. Joerger, S. Engels, A. Girschik, K. Watanabe, T. Taniguchi, S. V. Rotkin, J. Burgdoerfer, and C. Stampfer, “Size quantization of dirac fermions in graphene constrictions,” Nature Communications, vol. 7, p. 11528, may 2016.
  83. S. Xiang, A. Mreńca-Kolasińska, V. Miseikis, S. Guiducci, K. Kolasiński, C. Coletti, B. Szafran, F. Beltram, S. Roddaro, and S. Heun, “Interedge backscattering in buried split-gate-defined graphene quantum point contacts,” Physical Review B, vol. 94, no. 15, p. 155446, 2016.
  84. M.-H. Liu, C. Gorini, and K. Richter, “Creating and steering highly directional electron beams in graphene,” Phys. Rev. Lett., vol. 118, p. 066801, Feb 2017.
  85. L. Bours, S. Guiducci, A. Mreńca-Kolasińska, B. Szafran, J. C. Maan, and S. Heun, “Manipulating quantum Hall edge channels in graphene through scanning gate microscopy,” Physical Review B, vol. 96, p. 195423, nov 2017.
  86. K. Kolasinski, A. Mrenca-Kolasinska, and B. Szafran, “Imaging snake orbits at graphene n−p𝑛𝑝n-pitalic_n - italic_p junctions,” Phys. Rev. B, vol. 95, p. 045304, jan 2017.
  87. P. Makk, C. Handschin, E. Tóvári, K. Watanabe, T. Taniguchi, K. Richter, M.-H. Liu, and C. Schönenberger, “Coexistence of classical snake states and Aharonov-Bohm oscillations along graphene p n junctions,” Physical Review B, vol. 98, p. 035413, jul 2018.
  88. Q. Ma, F. D. Parmentier, P. Roulleau, and G. Fleury, “Graphene n−p𝑛𝑝n-pitalic_n - italic_p junctions in the quantum Hall regime: Numerical study of incoherent scattering effects,” Phys Rev B, vol. 97, p. 205445, May 2018.
  89. B. Brun, N. Moreau, S. Somanchi, V.-H. Nguyen, K. Watanabe, T. Taniguchi, J.-C. Charlier, C. Stampfer, and B. Hackens, “Imaging dirac fermions flow through a circular veselago lens,” Phys. Rev. B, vol. 100, p. 041401, Jul 2019.
  90. T. L. M. Lane, A. Knothe, and V. I. Fal’ko, “Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene,” Physical Review B, vol. 100, p. 115427, Sept. 2019.
  91. R. Kraft, M.-H. Liu, P. B. Selvasundaram, S.-C. Chen, R. Krupke, K. Richter, and R. Danneau, “Anomalous cyclotron motion in graphene superlattice cavities,” Physical Review Letters, vol. 125, p. 217701, Nov. 2020.
  92. W.-H. Kang, S.-C. Chen, and M.-H. Liu, “Cloning of zero modes in one-dimensional graphene superlattices,” Phys. Rev. B, vol. 102, p. 195432, Nov 2020.
  93. N. Moreau, B. Brun, S. Somanchi, K. Watanabe, T. Taniguchi, C. Stampfer, and B. Hackens, “Upstream modes and antidots poison graphene quantum Hall effect,” Nat Commun, vol. 12, pp. 1–7, July 2021.
  94. N. Moreau, B. Brun, S. Somanchi, K. Watanabe, T. Taniguchi, C. Stampfer, and B. Hackens, “Contacts and upstream modes explain the electron-hole asymmetry in the graphene quantum Hall regime,” Phys Rev B, vol. 104, p. L201406, Nov. 2021.
  95. J.-K. Schrepfer, S.-C. Chen, M.-H. Liu, K. Richter, and M. Hentschel, “Dirac fermion optics and directed emission from single- and bilayer graphene cavities,” Phys. Rev. B, vol. 104, p. 155436, Oct 2021.
  96. A. Mreńca-Kolasińska, P. Rickhaus, G. Zheng, K. Richter, T. Ihn, K. Ensslin, and M.-H. Liu, “Quantum capacitive coupling between large-angle twisted graphene layers,” 2D Materials, vol. 9, p. 025013, Feb 2022.
  97. B. Brun, V.-H. Nguyen, N. Moreau, S. Somanchi, K. Watanabe, T. Taniguchi, J.-C. Charlier, C. Stampfer, and B. Hackens, “Graphene whisperitronics: Transducing whispering gallery modes into electronic transport,” Nano Letters, vol. 22, pp. 128–134, Jan. 2022.
  98. S.-B. Chiu, A. Mreńca-Kolasińska, K. L. Lei, C.-H. Chiu, W.-H. Kang, S.-C. Chen, and M.-H. Liu, “Manipulating electron waves in graphene using carbon nanotube gating,” Phys. Rev. B, vol. 105, p. 195416, May 2022.
  99. Y. Zhumagulov, T. Frank, and J. Fabian, “Edge states in proximitized graphene ribbons and flakes in a perpendicular magnetic field: Emergence of lone pseudohelical pairs and pure spin-current states,” Phys. Rev. B, vol. 105, may 2022.
  100. Q. Rao, W.-H. Kang, H. Xue, Z. Ye, X. Feng, K. Watanabe, T. Taniguchi, N. Wang, M.-H. Liu, and D.-K. Ki, “Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT,” Nature Communications, vol. 14, p. 6124, mar 2023.
  101. R. Du, M.-H. Liu, J. Mohrmann, F. Wu, R. Krupke, H. von Löhneysen, K. Richter, and R. Danneau, “Tuning anti-Klein to Klein tunnelingin bilayer graphene,” Physical Review Letters, vol. 121, p. 127706, Sept. 2018.
  102. M.-H. Liu and K. Richter, “Efficient quantum transport simulation for bulk graphene heterojunctions,” Phys. Rev. B, vol. 86, p. 115455, Sep 2012.
  103. M. Drienovsky, F.-X. Schrettenbrunner, A. Sandner, D. Weiss, J. Eroms, M.-H. Liu, F. Tkatschenko, and K. Richter, “Towards superlattices: Lateral bipolar multibarriers in graphene,” Physical Review B, vol. 89, p. 115421, Mar. 2014.
  104. A. Varlet, M.-H. Liu, V. Krueckl, D. Bischoff, P. Simonet, K. Watanabe, T. Taniguchi, K. Richter, K. Ensslin, and T. Ihn, “Fabry-Pérot interference in gapped bilayer graphene with broken anti-Klein tunneling,” Phys. Rev. Lett., vol. 113, p. 116601, Sep 2014.
  105. P. Rickhaus, M.-H. Liu, M. Kurpas, A. Kurzmann, Y. Lee, H. Overweg, M. Eich, R. Pisoni, T. Taniguchi, K. Watanabe, K. Richter, K. Ensslin, and T. Ihn, “The electronic thickness of graphene,” Science Advances, 2020.
  106. A. S. Mayorov, R. V. Gorbachev, S. V. Morozov, L. Britnell, R. Jalil, L. A. Ponomarenko, P. Blake, K. S. Novoselov, K. Watanabe, T. Taniguchi, and A. K. Geim, “Micrometer-scale ballistic transport in encapsulated graphene at room temperature,” Nano Letters, vol. 11, pp. 2396–2399, jun 2011.
  107. T. Taychatanapat, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, “Electrically tunable transverse magnetic focusing in graphene,” Nature Physics 2013 9:4, vol. 9, pp. 225–229, feb 2013.
  108. S. Bhandari, G.-H. Lee, A. Klales, K. Watanabe, T. Taniguchi, E. Heller, P. Kim, and R. M. Westervelt, “Imaging cyclotron orbits of electrons in graphene,” Nano letters, 2016.
  109. M. Lee, J. R. Wallbank, P. Gallagher, K. Watanabe, T. Taniguchi, V. I. Fal’ko, and D. Goldhaber-Gordon, “Ballistic miniband conduction in a graphene superlattice,” Science, vol. 353, pp. 1526–1529, Sept. 2016.
  110. J. H. Chen, C. Jang, S. Xiao, M. Ishigami, and M. S. Fuhrer, “Intrinsic and extrinsic performance limits of graphene devices on SiO2,” Nature Nanotechnology 2008 3:4, vol. 3, pp. 206–209, mar 2008.
  111. A. M. Goossens, V. E. Calado, A. Barreiro, K. Watanabe, T. Taniguchi, and L. M. Vandersypen, “Mechanical cleaning of graphene,” Applied Physics Letters, vol. 100, p. 73110, feb 2012.
  112. N. Lindvall, A. Kalabukhov, and A. Yurgens, “Cleaning graphene using atomic force microscope,” Journal of Applied Physics, vol. 111, mar 2012.
  113. N. Tombros, A. Veligura, J. Junesch, J. Jasper Van Den Berg, P. J. Zomer, M. Wojtaszek, I. J. Vera Marun, H. T. Jonkman, and B. J. Van Wees, “Large yield production of high mobility freely suspended graphene electronic devices on a polydimethylglutarimide based organic polymer,” Journal of Applied Physics, vol. 109, may 2011.
  114. R. Maurand, P. Rickhaus, P. Makk, S. Hess, E. Tóvári, C. Handschin, M. Weiss, and C. Schönenberger, “Fabrication of ballistic suspended graphene with local-gating,” Carbon, vol. 79, pp. 486–492, nov 2014.
  115. S. J. Haigh, A. Gholinia, R. Jalil, S. Romani, L. Britnell, D. C. Elias, K. S. Novoselov, L. A. Ponomarenko, A. K. Geim, and R. Gorbachev, “Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices,” Nature Materials 2012 11:9, vol. 11, pp. 764–767, jul 2012.
  116. P. J. Zomer, M. H. Guimarães, J. C. Brant, N. Tombros, and B. J. Van Wees, “Fast pick up technique for high quality heterostructures of bilayer graphene and hexagonal boron nitride,” Applied Physics Letters, vol. 105, jul 2014.
  117. A. V. Kretinin, Y. Cao, J. S. Tu, G. L. Yu, R. Jalil, K. S. Novoselov, S. J. Haigh, A. Gholinia, A. Mishchenko, M. Lozada, T. Georgiou, C. R. Woods, F. Withers, P. Blake, G. Eda, A. Wirsig, C. Hucho, K. Watanabe, T. Taniguchi, A. K. Geim, and R. V. Gorbachev, “Electronic properties of graphene encapsulated with different two-dimensional atomic crystals,” Nano Letters, vol. 14, pp. 3270–3276, jun 2014.
  118. F. Pizzocchero, L. Gammelgaard, B. S. Jessen, J. M. Caridad, L. Wang, J. Hone, P. Bøggild, and T. J. Booth, “The hot pick-up technique for batch assembly of van der Waals heterostructures,” Nature Communications 2016 7:1, vol. 7, pp. 1–10, jun 2016.
  119. D. G. Purdie, N. M. Pugno, T. Taniguchi, K. Watanabe, A. C. Ferrari, and A. Lombardo, “Cleaning interfaces in layered materials heterostructures,” Nature Communications 2018 9:1, vol. 9, pp. 1–12, dec 2018.
  120. A. A. Zibrov, C. Kometter, H. Zhou, E. M. Spanton, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, “Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level,” Nature 2017 549:7672, vol. 549, pp. 360–364, sep 2017.
  121. Y. Zeng, J. I. Li, S. A. Dietrich, O. M. Ghosh, K. Watanabe, T. Taniguchi, J. Hone, and C. R. Dean, “High-quality magnetotransport in graphene using the edge-free corbino geometry,” Physical Review Letters, vol. 122, p. 137701, apr 2019.
  122. H. Polshyn, H. Zhou, E. M. Spanton, T. Taniguchi, K. Watanabe, and A. F. Young, “Quantitative transport measurements of fractional quantum Hall energy gaps in edgeless graphene devices,” Physical Review Letters, vol. 121, p. 226801, nov 2018.
  123. M. Yankowitz, Q. Ma, P. Jarillo-Herrero, and B. J. LeRoy, “van der Waals heterostructures combining graphene and hexagonal boron nitride,” Nature Reviews Physics 2018 1:2, vol. 1, pp. 112–125, jan 2019.
  124. W. Wang, N. Clark, M. Hamer, A. Carl, E. Tovari, S. Sullivan-Allsop, E. Tillotson, Y. Gao, H. de Latour, F. Selles, J. Howarth, E. G. Castanon, M. Zhou, H. Bai, X. Li, A. Weston, K. Watanabe, T. Taniguchi, C. Mattevi, T. H. Bointon, P. V. Wiper, A. J. Strudwick, L. A. Ponomarenko, A. Kretinin, S. J. Haigh, A. Summerfield, and R. Gorbachev, “Ultra-clean assembly of van der Waals heterostructures,” Nature Electronics, pp. 1–10, aug 2023.
  125. J. Barrier, P. Kumaravadivel, R. Krishna Kumar, L. A. Ponomarenko, N. Xin, M. Holwill, C. Mullan, M. Kim, R. V. Gorbachev, M. D. Thompson, J. R. Prance, T. Taniguchi, K. Watanabe, I. V. Grigorieva, K. S. Novoselov, A. Mishchenko, V. I. Fal’ko, A. K. Geim, and A. I. Berdyugin, “Long-range ballistic transport of Brown-Zak fermions in graphene superlattices,” Nature Communications 2020 11:1, vol. 11, pp. 1–7, nov 2020.
  126. Y. Nam, D. K. Ki, D. Soler-Delgado, and A. F. Morpurgo, “Electron–hole collision limited transport in charge-neutral bilayer graphene,” Nature Physics 2017 13:12, vol. 13, pp. 1207–1214, aug 2017.
  127. S. Zihlmann, Spin and charge relaxation in graphene. PhD thesis, Department of Physics, University of Basel, Basel, Mar 2018.
  128. A. Coissard, D. Wander, H. Vignaud, A. G. Grushin, C. Repellin, K. Watanabe, T. Taniguchi, F. Gay, C. B. Winkelmann, H. Courtois, H. Sellier, and B. Sacépé, “Imaging tunable quantum Hall broken-symmetry orders in graphene,” Nature 2022 605:7908, vol. 605, pp. 51–56, may 2022.
  129. X. Liu, Z. Wang, K. Watanabe, T. Taniguchi, O. Vafek, and J. I. Li, “Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening,” Science, vol. 371, pp. 1261–1265, mar 2021.
  130. M. Kim, S. G. Xu, A. I. Berdyugin, A. Principi, S. Slizovskiy, N. Xin, P. Kumaravadivel, W. Kuang, M. Hamer, R. Krishna Kumar, R. V. Gorbachev, K. Watanabe, T. Taniguchi, I. V. Grigorieva, V. I. Fal’ko, M. Polini, and A. K. Geim, “Control of electron-electron interaction in graphene by proximity screening,” Nat Commun, vol. 11, pp. 1–6, May 2020.
  131. P. Stepanov, I. Das, X. Lu, A. Fahimniya, K. Watanabe, T. Taniguchi, F. H. Koppens, J. Lischner, L. Levitov, and D. K. Efetov, “Untying the insulating and superconducting orders in magic-angle graphene,” Nature 2020 583:7816, vol. 583, pp. 375–378, jul 2020.
  132. L. Wang, P. Makk, S. Zihlmann, A. Baumgartner, D. I. Indolese, K. Watanabe, T. Taniguchi, and C. Schönenberger, “Mobility enhancement in graphene by in situ reduction of random strain fluctuations,” Physical Review Letters, vol. 124, p. 157701, apr 2020.
  133. N. J. Couto, D. Costanzo, S. Engels, D. K. Ki, K. Watanabe, T. Taniguchi, C. Stampfer, F. Guinea, and A. F. Morpurgo, “Random strain fluctuations as dominant disorder source for high-quality on-substrate graphene devices,” Physical Review X, vol. 4, p. 041019, oct 2014.
  134. S. Morikawa, Z. Dou, S. W. Wang, C. G. Smith, K. Watanabe, T. Taniguchi, S. Masubuchi, T. Machida, and M. R. Connolly, “Imaging ballistic carrier trajectories in graphene using scanning gate microscopy,” Applied Physics Letters, vol. 107, dec 2015.
  135. S. Bhandari, G. H. Lee, K. Watanabe, T. Taniguchi, P. Kim, and R. M. Westervelt, “Imaging Andreev reflection in graphene,” Nano Letters, vol. 20, pp. 4890–4894, jul 2020.
  136. J. Ingla-Aynés, A. L. R. Manesco, T. S. Ghiasi, S. Volosheniuk, K. Watanabe, T. Taniguchi, and H. S. van der Zant, “Specular electron focusing between gate-defined quantum point contacts in bilayer graphene,” Nano Letters, vol. 23, p. 5453–5459, jun 2023.
  137. S. Chen, Z. Han, M. M. Elahi, K. M. M. Habib, L. Wang, B. Wen, Y. Gao, T. Taniguchi, K. Watanabe, J. Hone, A. W. Ghosh, and C. R. Dean, “Electron optics with p-n junctions in ballistic graphene,” Science, vol. 353, pp. 1522–1525, sep 2016.
  138. A. I. Berdyugin, B. Tsim, P. Kumaravadivel, S. G. Xu, A. Ceferino, A. Knothe, R. K. Kumar, T. Taniguchi, K. Watanabe, A. K. Geim, I. V. Grigorieva, and V. I. Fal’ko, “Minibands in twisted bilayer graphene probed by magnetic focusing,” Science Advances, vol. 6, p. eaay7838, Apr. 2020.
  139. H. Graef, Q. Wilmart, M. Rosticher, D. Mele, L. Banszerus, C. Stampfer, T. Taniguchi, K. Watanabe, J. M. Berroir, E. Bocquillon, G. Fève, E. H. Teo, and B. Plaçais, “A corner reflector of graphene Dirac fermions as a phonon-scattering sensor,” Nature Communications 2019 10:1, vol. 10, pp. 1–9, jun 2019.
  140. K. Wang, M. M. Elahi, L. Wang, K. M. Habib, T. Taniguchi, K. Watanabe, J. Hone, A. W. Ghosh, G. H. Lee, and P. Kim, “Graphene transistor based on tunable Dirac fermion optics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 116, pp. 6575–6579, apr 2019.
  141. M. M. Elahi, K. M. Masum Habib, K. Wang, G. H. Lee, P. Kim, and A. W. Ghosh, “Impact of geometry and non-idealities on electron ”optics” based graphene p-n junction devices,” Applied Physics Letters, vol. 114, jan 2019.
  142. S. Morikawa, Q. Wilmart, S. Masubuchi, K. Watanabe, T. Taniguchi, B. Plaçais, and T. Machida, “Dirac fermion reflector by ballistic graphene sawtooth-shaped npn junctions,” Semiconductor Science and Technology, vol. 32, p. 045010, mar 2017.
  143. G. H. Lee, G. H. Park, and H. J. Lee, “Observation of negative refraction of Dirac fermions in graphene,” Nature Physics 2015 11:11, vol. 11, pp. 925–929, sep 2015.
  144. A. W. Barnard, A. Hughes, A. L. Sharpe, K. Watanabe, T. Taniguchi, and D. Goldhaber-Gordon, “Absorptive pinhole collimators for ballistic Dirac fermions in graphene,” Nature Communications 2017 8:1, vol. 8, pp. 1–6, may 2017.
  145. G. Liu, J. Velasco, Jr., W. Bao, and C. N. Lau, “Fabrication of graphene p-n-p junctions with contactless top gates,” Applied Physics Letters, vol. 92, may 2008.
  146. C. Handschin, B. Fülöp, P. Makk, S. Blanter, M. Weiss, K. Watanabe, T. Taniguchi, S. Csonka, and C. Schönenberger, “Point contacts in encapsulated graphene,” Applied Physics Letters, vol. 107, p. 183108, Nov 2015.
  147. C. Gold, A. Knothe, A. Kurzmann, A. Garcia-Ruiz, K. Watanabe, T. Taniguchi, V. Fal’ko, K. Ensslin, and T. Ihn, “Coherent jetting from a gate-defined channel in bilayer graphene,” Physical Review Letters, vol. 127, p. 046801, July 2021.
  148. X. Zhang, W. Ren, E. Bell, Z. Zhu, K. T. Tsai, Y. Luo, K. Watanabe, T. Taniguchi, E. Kaxiras, M. Luskin, and K. Wang, “Gate-tunable Veselago interference in a bipolar graphene microcavity,” Nature Communications 2022 13:1, vol. 13, pp. 1–6, nov 2022.
  149. Bischoff Dominik, Simonet Pauline, Varlet Anastasia, Overweg Hiske C., Eich Marius, Ihn Thomas, and Ensslin Klaus, “The importance of edges in reactive ion etched graphene nanodevices,” physica status solidi (RRL) – Rapid Research Letters, vol. 10, pp. 68–74, Aug. 2015.
  150. D. Bischoff, F. Libisch, J. Burgdörfer, T. Ihn, and K. Ensslin, “Characterizing wave functions in graphene nanodevices: Electronic transport through ultrashort graphene constrictions on a boron nitride substrate,” Physical Review B, vol. 90, p. 115405, Sept. 2014.
  151. T. Ihn, J. Güttinger, F. Molitor, S. Schnez, E. Schurtenberger, A. Jacobsen, S. Hellmüller, T. Frey, S. Dröscher, C. Stampfer, and K. Ensslin, “Graphene single-electron transistors,” Materials Today, vol. 13, pp. 44–50, Mar. 2010.
  152. H. Overweg, A. Knothe, T. Fabian, L. Linhart, P. Rickhaus, L. Wernli, K. Watanabe, T. Taniguchi, D. Sánchez, J. Burgdörfer, F. Libisch, V. I. Fal’ko, K. Ensslin, and T. Ihn, “Topologically nontrivial valley states in bilayer graphene quantum point contacts,” Physical Review Letters, vol. 121, p. 257702, Dec. 2018.
  153. Y. Lee, A. Knothe, H. Overweg, M. Eich, C. Gold, A. Kurzmann, V. Klasovika, T. Taniguchi, K. Wantanabe, V. Fal’ko, T. Ihn, K. Ensslin, and P. Rickhaus, “Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts,” Physical Review Letters, vol. 124, p. 126802, Mar. 2020.
  154. L. Banszerus, B. Frohn, T. Fabian, S. Somanchi, A. Epping, M. Müller, D. Neumaier, K. Watanabe, T. Taniguchi, F. Libisch, B. Beschoten, F. Hassler, and C. Stampfer, “Observation of the spin-orbit gap in bilayer graphene by one-dimensional ballistic transport,” Physical Review Letters, vol. 124, p. 177701, May 2020.
  155. A. Knothe and V. Fal’ko, “Influence of minivalleys and Berry curvature on electrostatically induced quantum wires in gapped bilayer graphene,” Physical Review B, vol. 98, p. 155435, Oct. 2018.
  156. R. Kraft, I. V. Krainov, V. Gall, A. P. Dmitriev, R. Krupke, I. V. Gornyi, and R. Danneau, “Valley subband splitting in bilayer graphene quantum point contacts,” Physical Review Letters, vol. 121, p. 257703, Dec. 2018.
  157. M. Eich, R. Pisoni, H. Overweg, A. Kurzmann, Y. Lee, P. Rickhaus, T. Ihn, K. Ensslin, F. Herman, M. Sigrist, K. Watanabe, and T. Taniguchi, “Spin and valley states in gate-defined bilayer graphene quantum dots,” Physical Review X, vol. 8, p. 031023, July 2018.
  158. M. Eich, R. Pisoni, A. Pally, H. Overweg, A. Kurzmann, Y. Lee, P. Rickhaus, K. Watanabe, T. Taniguchi, K. Ensslin, and T. Ihn, “Coupled quantum dots in bilayer graphene,” Nano Letters, vol. 18, pp. 5042–5048, Aug. 2018.
  159. L. Banszerus, B. Frohn, A. Epping, D. Neumaier, K. Watanabe, T. Taniguchi, and C. Stampfer, “Gate-defined electron hole double dots in bilayer graphene,” Nano Letters, vol. 18, pp. 4785–4790, Aug. 2018.
  160. S. Möller, L. Banszerus, A. Knothe, C. Steiner, E. Icking, S. Trellenkamp, F. Lentz, K. Watanabe, T. Taniguchi, L. I. Glazman, V. I. Fal’ko, C. Volk, and C. Stampfer, “Probing Two-Electron Multiplets in Bilayer Graphene Quantum Dots,” Physical Review Letters, vol. 127, p. 256802, Dec. 2021.
  161. C. Tong, R. Garreis, A. Knothe, M. Eich, A. Sacchi, K. Watanabe, T. Taniguchi, V. Fal’ko, T. Ihn, K. Ensslin, and A. Kurzmann, “Tunable valley splitting and bipolar operation in graphene quantum dots,” Nano Letters, vol. 21, pp. 1068–1073, Jan. 2021.
  162. C. Tong, A. Kurzmann, R. Garreis, W. W. Huang, S. Jele, M. Eich, L. Ginzburg, C. Mittag, K. Watanabe, T. Taniguchi, K. Ensslin, and T. Ihn, “Pauli blockade of tunable two-electron spin and valley states in graphene quantum dots,” Physical Review Letters, vol. 128, p. 067702, Feb. 2022.
  163. A. Knothe and V. Fal’ko, “Quartet states in two-electron quantum dots in bilayer graphene,” Physical Review B, vol. 101, p. 235423, June 2020.
  164. L. Banszerus, A. Rothstein, T. Fabian, S. Möller, E. Icking, S. Trellenkamp, F. Lentz, D. Neumaier, K. Watanabe, T. Taniguchi, F. Libisch, C. Volk, and C. Stampfer, “Electron hole crossover in gate-controlled bilayer graphene quantum dots,” Nano Letters, vol. 20, pp. 7709–7715, Oct. 2020.
  165. A. Kurzmann, Y. Kleeorin, C. Tong, R. Garreis, A. Knothe, M. Eich, C. Mittag, C. Gold, F. K. de Vries, K. Watanabe, T. Takashi, F. Vladimir, M. Yigal, I. Thomas, and E. Klaus, “Kondo effect and spin–orbit coupling in graphene quantum dots,” Nature communications, vol. 12, no. 1, p. 6004, 2021.
  166. R. Garreis, A. Knothe, C. Tong, M. Eich, C. Gold, K. Watanabe, T. Taniguchi, V. Fal’ko, T. Ihn, K. Ensslin, and A. Kurzmann, “Shell filling and trigonal warping in graphene quantum dots,” Physical Review Letters, vol. 126, p. 147703, Apr. 2021.
  167. L. Banszerus, K. Hecker, S. Möller, E. Icking, K. Watanabe, T. Taniguchi, C. Volk, and C. Stampfer, “Spin relaxation in a single-electron graphene quantum dot,” Nature Communications, vol. 13, p. 3637, June 2022.
  168. L. Banszerus, S. Möller, E. Icking, K. Watanabe, T. Taniguchi, C. Volk, and C. Stampfer, “Single-electron double quantum dots in bilayer graphene,” Nano Letters, vol. 20, pp. 2005–2011, Mar. 2020.
  169. L. Banszerus, S. Möller, C. Steiner, E. Icking, S. Trellenkamp, F. Lentz, K. Watanabe, T. Taniguchi, C. Volk, and C. Stampfer, “Spin-valley coupling in single-electron bilayer graphene quantum dots,” Nature communications, vol. 12, no. 1, p. 5250, 2021.
  170. A. Knothe, L. I. Glazman, and V. I. Fal’ko, “Tunneling theory for a bilayer graphene quantum dot’s single- and two-electron states,” New Journal of Physics, vol. 24, p. 043003, Apr. 2022.
  171. L. Banszerus, S. Möller, K. Hecker, E. Icking, K. Watanabe, T. T. …, and C. Stampfer, “Particle–hole symmetry protects spin-valley blockade in graphene quantum dots,” Nature, pp. 1–6, 2023.
  172. D. Mayer and A. Knothe, “Tuning‐Confined States and Valley G‐Factors by Quantum Dot Design in Bilayer Graphene,” physica status solidi (b), p. 2300395, Nov. 2023.
  173. S. Iwakiri, F. K. de Vries, E. Portolés, G. Zheng, T. Taniguchi, K. Watanabe, T. Ihn, and K. Ensslin, “Gate-defined electron interferometer in bilayer graphene,” Nano Letters, vol. 22, pp. 6292–6297, Aug. 2022.
  174. H. L. Fu, K. Huang, K. Watanabe, T. Taniguchi, M. Kayyalha, and J. Zhu, “Aharonov-bohm oscillations in bilayer graphene quantum hall edge state fabry-perot interferometers,” Nano Letters, vol. 23, pp. 718–725, jan 2023.
  175. M. Mirzakhani, N. Myoung, F. M. Peeters, and H. C. Park, “Electronic mach-zehnder interference in a bipolar hybrid monolayer-bilayer graphene junction,” Carbon, vol. 201, pp. 734–744, oct 2023.
  176. J. Ingla-Aynés, A. L. R. Manesco, T. S. Ghiasi, K. Watanabe, T. Taniguchi, and H. S. J. van der Zant, “A ballistic electron source with magnetically-controlled valley polarization in bilayer graphene,” arXiv, 2023.
  177. L. Seemann, A. Knothe, and M. Hentschel, “Gate-tunable regular and chaotic electron dynamics in ballistic bilayer graphene cavities,” Physical Review B, vol. 107, p. 205404, May 2023.
  178. C. G. Péterfalvi, L. Oroszlány, C. J. Lambert, and J. Cserti, “Intraband electron focusing in bilayer graphene,” New Journal of Physics, vol. 14, p. 063028, June 2012.
  179. S. Xu, M. M. Al Ezzi, N. Balakrishnan, A. Garcia-Ruiz, B. Tsim, C. Mullan, J. Barrier, N. Xin, B. A. Piot, T. Taniguchi, K. Watanabe, A. Carvalho, A. Mishchenko, A. K. Geim, V. I. Fal’ko, S. Adam, A. H. C. Neto, K. S. Novoselov, and Y. Shi, “Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene,” Nature Physics, vol. 17, pp. 619–626, May 2021.
  180. R. Huber, M.-H. Liu, S.-C. Chen, M. Drienovsky, A. Sandner, K. Watanabe, T. Taniguchi, K. Richter, D. Weiss, and J. Eroms, “Band conductivity oscillations in a gate-tunable graphene superlattice,” Nano Lett., vol. 20, no. 11, pp. 8046–8052, 2020.
  181. R. Huber, M.-N. Steffen, M. Drienovsky, A. Sandner, K. Watanabe, T. Taniguchi, D. Pfannkuche, D. Weiss, and J. Eroms, “Band conductivity oscillations in a gate-tunable graphene superlattice,” Nature Communications, vol. 13, p. 2856, May 2022.
  182. M. Drienovsky, J. Joachimsmeyer, A. Sandner, M.-H. Liu, T. Taniguchi, K. Watanabe, K. Richter, D. Weiss, and J. Eroms, “Commensurability oscillations in one-dimensional graphene superlattices,” Phys. Rev. Lett., vol. 121, p. 026806, Jul 2018.
  183. A. Mreńca-Kolasińska, S.-C. Chen, and M.-H. Liu, “Probing miniband structure and hofstadter butterfly in gated graphene superlattices via magnetotransport,” npj 2D Materials and Applications, vol. 7, p. Article number: 64, sep 2023.
  184. C. Moulsdale, A. Knothe, and V. Fal’ko, “Engineering of the topological magnetic moment of electrons in bilayer graphene using strain and electrical bias,” Physical Review B, vol. 101, p. 085118, Feb. 2020.
  185. A. Varlet, M. Mucha-Kruczyński, D. Bischoff, P. Simonet, T. Taniguchi, K. Watanabe, V. Fal’ko, T. Ihn, and K. Ensslin, “Tunable Fermi surface topology and Lifshitz transition in bilayer graphene,” Synthetic Metals, vol. 210, pp. 19–31, Dec. 2015.
  186. Y. Zhao, J. Wyrick, F. D. Natterer, J. F. Rodriguez-Nieva, C. Lewandowski, K. Watanabe, T. Taniguchi, L. S. Levitov, N. B. Zhitenev, and J. A. Stroscio, “Creating and probing electron whispering-gallery modes in graphene,” Science, vol. 348, no. 6235, pp. 672–675, 2015.
  187. Z. Ge, D. Wong, J. Lee, F. Joucken, E. A. Quezada-Lopez, S. Kahn, H.-Z. Tsai, T. Taniguchi, K. Watanabe, F. Wang, A. Zettl, M. F. Crommie, and J. J. Velasco, “Imaging quantum interference in stadium-shaped monolayer and bilayer graphene quantum dots,” Nano Letters, vol. 21, pp. 8993–8998, Nov. 2021.
  188. J. F. Rodriguez-Nieva and L. S. Levitov, “Berry phase jumps and giant nonreciprocity in dirac quantum dots,” Physical Review B, vol. 94, Dec 2016.
  189. J. Wurm, A. Rycerz, I. Adagideli, M. Wimmer, K. Richter, and H. U. Baranger, “Symmetry classes in graphene quantum dots: Universal spectral statistics, weak localization, and conductance fluctuations,” Physical Review Letters, vol. 102, FEB 6 2009.
  190. J. H. Bardarson, M. Titov, and P. W. Brouwer, “Electrostatic confinement of electrons in an integrable graphene quantum dot,” Phys. Rev. Lett., vol. 102, p. 226803, Jun 2009.
  191. J. Wurm, M. Wimmer, H. U. Baranger, and K. Richter, “Graphene rings in magnetic fields: Aharonov-Bohm effect and valley splitting,” Semiconductor Science and technology, vol. 25, MAR 4 2010.
  192. M. Schneider and P. W. Brouwer, “Resonant scattering in graphene with a gate-defined chaotic quantum dot,” Physical Review B, vol. 84, p. 115440, Sept. 2011.
  193. J. Heinl, M. Schneider, and P. W. Brouwer, “Interplay of Aharonov-Bohm and Berry phases in gate-defined graphene quantum dots,” Physical Review B, vol. 87, p. 245426, June 2013.
  194. M. Schneider and P. W. Brouwer, “Density of states as a probe of electrostatic confinement in graphene,” Physical Review B, vol. 89, p. 205437, May 2014.
  195. J. Wurm, K. Richter, and i. d. I. Adagideli, “Edge effects in graphene nanostructures: From multiple reflection expansion to density of states,” Phys. Rev. B, vol. 84, p. 075468, Aug 2011.
  196. J. Wurm, K. Richter, and I. Adagideli, “Edge effects in graphene nanostructures: Semiclassical theory of spectral fluctuations and quantum transport,” Physical review B, vol. 84, NOV 14 2011.
  197. H.-Y. Xu, G.-L. Wang, L. Huang, and Y.-C. Lai, “Chaos in Dirac electron optics: Emergence of a relativistic quantum chimera,” Phys. Rev. Lett., vol. 120, p. 124101, Mar 2018.
  198. D. Bercioux, D. Frustaglia, and A. D. Martino, “Chiral spin channels in curved graphene p⁢n𝑝𝑛pnitalic_p italic_n junctions,” Phys. Rev. B, vol. 108, p. 115140, Sep 2023.
  199. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature, vol. 385, p. 45–47, Jan 1997.
  200. M. Hentschel and K. Richter, “Quantum chaos in optical systems: The annular billiard,” Physical Review E, vol. 66, no. 5, 2002.
  201. J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett., vol. 100, p. 033901, Jan 2008.
  202. C.-D. Han, C.-Z. Wang, H.-Y. Xu, D. Huang, and Y.-C. Lai, “Decay of semiclassical massless Dirac fermions from integrable and chaotic cavities,” Phys. Rev. B, vol. 98, p. 104308, Sep 2018.
  203. A. Varlet, M.-H. Liu, D. Bischoff, P. Simonet, T. Taniguchi, K. Watanabe, K. Richter, T. Ihn, and K. Ensslin, “Band gap and broken chirality in single-layer and bilayer graphene,” Physics statis solidi rapid research letters, vol. 10, pp. 46–57, JAN 2016.
  204. M. M. Elahi, Y. Zeng, C. R. Dean, and A. W. Ghosh, “Direct evidence of Klein-antiKlein tunneling of graphitic electrons in a Corbino geometry,” arXiv, Oct. 2022.
  205. C. Handschin, P. Makk, P. Rickhaus, M.-H. Liu, K. Watanabe, T. Taniguchi, K. Richter, and C. Schönenberger, “Fabry-Perot resonances in a graphene/hbn moire superlattice,” Nano Letters, vol. 17, pp. 328–333, jan 2017.
  206. P. Divari and G. Kliros, “Modeling the thermopower of ballistic graphene ribbons,” Physica E: Low-dimensional Systems and Nanostructures, vol. 42, no. 9, pp. 2431–2435, 2010.
  207. L. C. Campos, A. F. Young, K. Surakitbovorn, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, “Quantum and classical confinement of resonant states in a trilayer graphene Fabry-Perot interferometer,” Nature Communications, vol. 3, p. 1239, DEC 2012.
  208. M. Oksanen, A. Uppstu, A. Laitinen, D. J. Cox, M. F. Craciun, S. Russo, A. Harju, and P. Hakonen, “Single-mode and multimode Fabry-Pérot interference in suspended graphene,” Physical Review B, vol. 89, p. 121414, Mar 2014.
  209. V. E. Calado, S. Goswami, G. Nanda, M. Diez, A. R. Akhmerov, K. Watanabe, T. Taniguchi, T. M. Klapwijk, and L. M. K. Vandersypen, “Ballistic josephson junctions in edge-contacted graphene,” Nature Nanotechnology, vol. 10, p. 761, sep 2015.
  210. T. Taychatanapat, J. Y. Tan, Y. Yeo, K. Watanabe, T. Taniguchi, and B. Oezyilmaz, “Conductance oscillations induced by ballistic snake states in a graphene heterojunction,” Nature Communications, vol. 6, p. 6093, feb 2015.
  211. M. Ben Shalom, M. J. Zhu, V. I. Fal’ko, A. Mishchenko, A. V. Kretinin, K. S. Novoselov, C. R. Woods, K. Watanabe, T. Taniguchi, A. K. Geim, and J. R. Prance, “Quantum oscillations of the critical current and high-field superconducting proximity in ballistic graphene,” Nature Physics, vol. 12, pp. 318–322, APR 2016.
  212. M. T. Allen, O. Shtanko, I. C. Fulga, J. I. J. Wang, D. Nurgaliev, K. Watanabe, T. Taniguchi, A. R. Akhmerov, P. Jarillo-Herrero, L. S. Leyitov, and A. Yacoby, “Observation of electron coherence and Fabry-Perot standing waves at a graphene edge,” Nano Letters, vol. 17, no. 12, pp. 7380–7386, 2017.
  213. G. Nanda, J. L. Aguilera-Servin, P. Rakyta, A. Kormanyos, R. Kleiner, D. Koelle, K. Watanabe, T. Taniguchi, L. M. K. Vandersypen, and S. Goswami, “Current-phase relation of ballistic graphene Josephson junctions,” Nano Letters, vol. 17, pp. 3396–3401, jun 2017.
  214. M. Zhu, M. Ben Shalom, A. Mishchsenko, V. I. Fal’ko, K. Novoselov, and A. Geim, “Supercurrent and multiple Andreev reflections in micrometer-long ballistic graphene josephson junctions,” Nanoscale, vol. 10, pp. 3020–3025, feb 2018.
  215. P. Pandey, R. Kraft, R. Krupke, D. Beckmann, and R. Danneau, “Andreev reflection in ballistic normal metal/graphene/superconductor junctions,” Physical Review B, vol. 100, p. 165416, cct 2019.
  216. M. Jung, P. Rickhaus, S. Zihlmann, P. Makk, and C. Schönenberger, “Microwave photodetection in an ultraclean suspended bilayer graphene p–n junction,” Nano Letters, vol. 16, no. 11, pp. 6988–6993, 2016.
  217. P. Rickhaus, G. Zheng, J. L. Lado, Y. Lee, A. Kurzmann, M. Eich, R. Pisoni, C. Tong, R. Garreis, C. Gold, M. Masseroni, T. Taniguchi, K. Wantanabe, T. Ihn, and K. Ensslin, “Gap opening in twisted double bilayer graphene by crystal fields,” Nano Letters, vol. 19, no. 12, pp. 8821–8828, 2019.
  218. M. Mueller, M. Braeuninger, and B. Trauzettel, “Temperature dependence of the conductivity of ballistic graphene,” Physical Review Letters, vol. 103, p. 196801, Nov 6 2009.
  219. T. Ideue and Y. Iwasa, “Symmetry breaking and nonlinear electric transport in van der waals nanostructures,” in Annual Review Of Condensed Matter Physics, vol 12, 2021 (A. P. Mackenzie and M. C. Marchetti, eds.), vol. 12 of Annual Review of Condensed Matter Physics, pp. 201–223, Thomson Reuters, 2021.
  220. L. Huang, Y.-C. Lai, D. K. Ferry, R. Akis, and S. M. Goodnick, “Transmission and scarring in graphene quantum dots,” Journal of Physics-Condensed Matter, vol. 21, aug 2009.
  221. T. K. Ghosh, A. De Martino, W. Häusler, L. Dell’Anna, and R. Egger, “Conductance quantization and snake states in graphene magnetic waveguides,” Phys. Rev. B, vol. 77, p. 081404, Feb 2008.
  222. L. Oroszlány, P. Rakyta, A. Kormányos, C. J. Lambert, and J. Cserti, “Theory of snake states in graphene,” Phys. Rev. B, vol. 77, p. 081403, Feb 2008.
  223. S. P. Milovanovic, M. R. Masir, and F. M. Peeters, “Interplay between snake and quantum edge states in a graphene hall bar with a pn-junction,” Applied Physics Letters, vol. 105, p. 123507, sep 2014.
  224. L. Cohnitz, A. De Martino, W. Häusler, and R. Egger, “Chiral interface states in graphene p−n𝑝𝑛p\text{$-$}nitalic_p - italic_n junctions,” Physical Review B, vol. 94, p. 165443, Oct 2016.
  225. D. Bercioux and A. De Martino, “Spin-orbit interaction and snake states in a graphene p-n junction,” Phys. Rev. B, vol. 100, p. 115407, Sep 2019.
  226. H.-S. Sim, K.-H. Ahn, K. J. Chang, G. Ihm, N. Kim, and S. J. Lee, “Magnetic edge states in a magnetic quantum dot,” Phys. Rev. Lett., vol. 80, pp. 1501–1504, Feb 1998.
  227. A. Nogaret, S. J. Bending, and M. Henini, “Resistance resonance effects through magnetic edge states,” Phys. Rev. Lett., vol. 84, pp. 2231–2234, Mar 2000.
  228. J. Reijniers and F. M. Peeters, “Snake orbits and related magnetic edge states,” Journal of Physics: Condensed Matter, vol. 12, p. 9771, Nov 2000.
  229. J. Reijniers, A. Matulis, K. Chang, F. M. Peeters, and P. Vasilopoulos, “Confined magnetic guiding orbit states,” Europhysics Letters, vol. 59, p. 749, sep 2002.
  230. B. I. Halperin, “Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential,” Phys. Rev. B, vol. 25, pp. 2185–2190, Feb 1982.
  231. A. H. MacDonald and P. Streda, “Quantized Hall effect and edge currents,” Phys. Rev. B, vol. 29, pp. 1616–1619, Feb 1984.
  232. B. E. Kane, D. C. Tsui, and G. Weimann, “Evidence for edge currents in the integral quantum Hall effect,” Phys. Rev. Lett., vol. 59, pp. 1353–1356, Sep 1987.
  233. M. Büttiker, “Absence of backscattering in the quantum Hall effect in multiprobe conductors,” Phys. Rev. B, vol. 38, pp. 9375–9389, Nov 1988.
  234. S. Washburn, A. B. Fowler, H. Schmid, and D. Kern, “Quantized Hall effect in the presence of backscattering,” Phys. Rev. Lett., vol. 61, pp. 2801–2804, Dec 1988.
  235. S. W. McDonald and A. N. Kaufman, “Spectrum and eigenfunctions for a hamiltonian with stochastic trajectories,” Phys. Rev. Lett., vol. 42, pp. 1189–1191, Apr 1979.
  236. N. Davies, A. A. Patel, A. Cortijo, V. Cheianov, F. Guinea, and V. I. Fal’ko, “Skipping and snake orbits of electrons: Singularities and catastrophes,” Phys. Rev. B, vol. 85, p. 155433, apr 2012.
  237. J.-C. Chen, X. C. Xie, and Q.-F. Sun, “Current oscillation of snake states in graphene p𝑝pitalic_p-n𝑛nitalic_n junction,” Phys. Rev. B, vol. 86, p. 035429, Jul 2012.
  238. S. P. Milovanovic, M. R. Masir, and F. M. Peeters, “Spectroscopy of snake states using a graphene Hall bar,” Applied Physics Letters, vol. 103, p. 233502, dec 2013.
  239. M. Büttiker, “Chapter 4: The quantum hall effect in open conductors,” in Semiconductors and Semimetals (M. Reed, ed.), vol. 35 of Semiconductors and Semimetals, pp. 191–277, Elsevier, 1992.
  240. T. Christen and M. Büttiker, “Low-frequency admittance of quantized Hall conductors,” Phys. Rev. B, vol. 53, pp. 2064–2072, Jan 1996.
  241. D. Sánchez and M. Büttiker, “Magnetic-field asymmetry of nonlinear mesoscopic transport,” Phys. Rev. Lett., vol. 93, p. 106802, Sep 2004.
  242. D. Sánchez and R. López, “Scattering theory of nonlinear thermoelectric transport,” Phys. Rev. Lett., vol. 110, p. 026804, Jan 2013.
  243. C. Gorini, D. Weinmann, and R. A. Jalabert, “Scanning-gate-induced effects in nonlinear transport through nanostructures,” Phys. Rev. B, vol. 89, p. 115414, Mar 2014.
  244. C. Texier and J. Mitscherling, “Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry,” Phys. Rev. B, vol. 97, p. 075306, Feb 2018.
  245. M. Moskalets and M. Büttiker, “Floquet scattering theory of quantum pumps,” Phys. Rev. B, vol. 66, p. 205320, Nov 2002.
  246. P. Samuelsson and M. Büttiker, “Dynamic generation of orbital quasiparticle entanglement in mesoscopic conductors,” Phys. Rev. B, vol. 71, p. 245317, Jun 2005.
  247. A. E. and M. G., Mesoscopic physics of electrons and photons. Cambridge University Press, 2007.
  248. I. Y., Introduction to Mesoscopic Physics. Oxford University Press, 2008.
  249. P. Samuelsson, E. V. Sukhorukov, and M. Büttiker, “Two-particle Aharonov-Bohm effect and entanglement in the electronic Hanbury Brown–Twiss setup,” Phys. Rev. Lett., vol. 92, p. 026805, Jan 2004.
  250. V. S.-W. Chung, P. Samuelsson, and M. Büttiker, “Visibility of current and shot noise in electrical Mach-Zehnder and Hanbury Brown Twiss interferometers,” Phys. Rev. B, vol. 72, p. 125320, Sep 2005.
  251. C. W. J. Beenakker, “Edge channels for the fractional quantum Hall effect,” Phys. Rev. Lett., vol. 64, pp. 216–219, Jan 1990.
  252. A. Chang, “A unified transport theory for the integral and fractional quantum Hall effects: Phase boundaries, edge currents, and transmission/reflection probabilities,” Solid State Communications, vol. 74, no. 9, pp. 871–876, 1990.
  253. D. B. Chklovskii, B. I. Shklovskii, and L. I. Glazman, “Electrostatics of edge channels,” Phys. Rev. B, vol. 46, pp. 4026–4034, Aug 1992.
  254. D. B. Chklovskii, K. A. Matveev, and B. I. Shklovskii, “Ballistic conductance of interacting electrons in the quantum Hall regime,” Phys. Rev. B, vol. 47, p. 12605, 1993.
  255. P. Armagnat and X. Waintal, “Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor,” Journal of Physics: Materials, vol. 3, p. 02LT01, mar 2020.
  256. I. M. Flór, A. Lacerda-Santos, G. Fleury, P. Roulleau, and X. Waintal, “Positioning of edge states in a quantum Hall graphene p n junction,” Physical Review B, vol. 105, p. L241409, jun 2022.
  257. C. d. C. Chamon and X. G. Wen, “Sharp and smooth boundaries of quantum Hall liquids,” Phys. Rev. B, vol. 49, pp. 8227–8241, Mar 1994.
  258. N. Paradiso, S. Heun, S. Roddaro, L. Sorba, F. Beltram, G. Biasiol, L. N. Pfeiffer, and K. W. West, “Imaging fractional incompressible stripes in integer quantum Hall systems,” Phys. Rev. Lett., vol. 108, p. 246801, Jun 2012.
  259. R. Bhattacharyya, M. Banerjee, M. Heiblum, D. Mahalu, and V. Umansky, “Melting of interference in the fractional quantum Hall effect: Appearance of neutral modes,” Phys. Rev. Lett., vol. 122, p. 246801, Jun 2019.
  260. U. Khanna, M. Goldstein, and Y. Gefen, “Fractional edge reconstruction in integer quantum Hall phases,” Phys. Rev. B, vol. 103, p. L121302, Mar 2021.
  261. U. Khanna, M. Goldstein, and Y. Gefen, “Emergence of neutral modes in Laughlin-like fractional quantum Hall phases,” Phys. Rev. Lett., vol. 129, p. 146801, Sep 2022.
  262. G. Li, A. Luican-Mayer, D. Abanin, L. Levitov, and E. Y. Andrei, “Evolution of Landau levels into edge states in graphene,” Nature communications, vol. 4, no. 1, p. 1744, 2013.
  263. A. Coissard, A. G. Grushin, C. Repellin, L. Veyrat, K. Watanabe, T. Taniguchi, F. Gay, H. Courtois, H. Sellier, and B. Sacépé, “Absence of edge reconstruction for quantum Hall edge channels in graphene devices,” Science Advances, vol. 9, p. eadf7220, Sep 2023.
  264. Y.-T. Cui, B. Wen, E. Y. Ma, G. Diankov, Z. Han, F. Amet, T. Taniguchi, K. Watanabe, D. Goldhaber-Gordon, C. R. Dean, and Z.-X. Shen, “Unconventional correlation between quantum hall transport quantization and bulk state filling in gated graphene devices,” Phys. Rev. Lett., vol. 117, p. 186601, Oct 2016.
  265. A. Seredinski, A. W. Draelos, E. G. Arnault, M.-T. Wei, H. Li, T. Fleming, K. Watanabe, T. Taniguchi, F. Amet, and G. Finkelstein, “Quantum hall–based superconducting interference device,” Science advances, vol. 5, no. 9, p. eaaw8693, 2019.
  266. C. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid. Cambridge, England, UK: Cambridge University Press, 2005.
  267. T. Giamarchi, Quantum Physics in One Dimension. Oxford University Press, 2003.
  268. F. D. M. Haldane, “Luttinger liquid theory of one-dimensional quantum fluids. i. properties of the Luttinger model and their extension to the general 1d interacting spinless fermi gas,” Journal of Physics C: Solid State Physics, vol. 14, p. 2585, jul 1981.
  269. J. von Delft and H. Schoeller, “Bosonization for beginners — refermionization for experts,” Annalen der Physik, vol. 510, no. 4, pp. 225–305, 1998.
  270. A. Imambekov, T. L. Schmidt, and L. I. Glazman, “One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm,” Rev. Mod. Phys., vol. 84, pp. 1253–1306, Sep 2012.
  271. A. Levchenko and T. Micklitz, “Kinetic processes in Fermi–Luttinger liquids,” JETP, vol. 132, p. 675, 2021.
  272. D. Ferraro, B. Roussel, C. Cabart, E. Thibierge, G. Fève, C. Grenier, and P. Degiovanni, “Real-Time Decoherence of Landau and Levitov Quasiparticles in Quantum Hall Edge Channels,” Physical Review Letters, vol. 113, p. 166403, oct 2014.
  273. T. Fujisawa, “Nonequilibrium charge dynamics of Tomonaga–Luttinger liquids in quantum hall edge channels,” Annalen der Physik, vol. 534, no. 4, p. 2100354, 2022.
  274. H. Förster, S. Pilgram, and M. Büttiker, “Decoherence and full counting statistics in a Mach-Zehnder interferometer,” Phys. Rev. B, vol. 72, p. 075301, Aug 2005.
  275. F. Marquardt, “Fermionic Mach-Zehnder interferometer subject to a quantum bath,” Europhysics Letters, vol. 72, p. 788, nov 2005.
  276. A. M. Lunde, S. E. Nigg, and M. Büttiker, “Interaction-induced edge channel equilibration,” Phys. Rev. B, vol. 81, p. 041311, Jan 2010.
  277. J. T. Chalker, Y. Gefen, and M. Y. Veillette, “Decoherence and interactions in an electronic Mach-Zehnder interferometer,” Phys. Rev. B, vol. 76, p. 085320, Aug 2007.
  278. D. E. Feldman and B. I. Halperin, “Robustness of quantum Hall interferometry,” Phys. Rev. B, vol. 105, p. 165310, Apr 2022.
  279. I. P. Levkivskyi and E. V. Sukhorukov, “Dephasing in the electronic Mach-Zehnder interferometer at filling factor ν=2𝜈2\nu=2italic_ν = 2,” Phys Rev B, vol. 78, p. 045322, July 2008.
  280. I. Neder, M. Heiblum, Y. Levinson, D. Mahalu, and V. Umansky, “Unexpected behavior in a two-path electron interferometer,” Physical Review Letters, vol. 9, no. 1, p. 016804, 2023.
  281. P. Roulleau, F. Portier, D. Glattli, P. Roche, A. Cavanna, G. Faini, U. Gennser, and D. Mailly, “Finite bias visibility of the electronic Mach-Zehnder interferometer,” Physical Review B, vol. 76, p. 161309, oct 2007.
  282. P. Roulleau, F. Portier, P. Roche, A. Cavanna, G. Faini, U. Gennser, and D. Mailly, “Direct measurement of the coherence length of edge states in the integer quantum Hall regime,” Phys Rev Lett, vol. 100, p. 126802, Mar. 2008.
  283. C. Altimiras, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly, and F. Pierre, “Tuning energy relaxation along quantum hall channels,” Phys. Rev. Lett., vol. 105, p. 226804, Nov 2010.
  284. H. le Sueur, C. Altimiras, U. Gennser, A. Cavanna, D. Mailly, and F. Pierre, “Energy Relaxation in the Integer Quantum Hall Regime,” Physical Review Letters, vol. 105, p. 056803, jul 2010.
  285. W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys., vol. 75, pp. 715–775, May 2003.
  286. I. Safi and H. Saleur, “One-channel conductor in an ohmic environment: Mapping to a Tomonaga-Luttinger liquid and full counting statistics,” Phys. Rev. Lett., vol. 93, p. 126602, Sep 2004.
  287. P. Degiovanni, C. Grenier, and G. Fève, “Decoherence and relaxation of single-electron excitations in quantum Hall edge channels,” Physical Review B, vol. 80, p. 241307, dec 2009.
  288. C. Neuenhahn and F. Marquardt, “Universal dephasing in a chiral 1d interacting fermion system,” Phys. Rev. Lett., vol. 102, p. 046806, Jan 2009.
  289. S. Komiyama, H. Hirai, S. Sasa, and S. Hiyamizu, “Violation of the integral quantum hall effect: Influence of backscattering and the role of voltage contacts,” Phys. Rev. B, vol. 40, pp. 12566–12569, Dec 1989.
  290. L. Chirolli, F. Taddei, R. Fazio, and V. Giovannetti, “Interactions in electronic Mach-Zehnder interferometers with copropagating edge channels,” Phys. Rev. Lett., vol. 111, p. 036801, Jul 2013.
  291. M. Büttiker, “Role of quantum coherence in series resistors,” Phys. Rev. B, vol. 33, pp. 3020–3026, Mar 1986.
  292. M. Jo, J.-Y. M. Lee, A. Assouline, P. Brasseur, K. Watanabe, T. Taniguchi, P. Roche, D. Glattli, N. Kumada, F. Parmentier, et al., “Scaling behavior of electron decoherence in a graphene Mach-Zehnder interferometer,” Nature Communications, vol. 13, no. 1, p. 5473, 2022.
  293. S. Morikawa, S. Masubuchi, R. Moriya, K. Watanabe, T. Taniguchi, and T. Machida, “Edge-channel interferometer at the graphene quantum Hall pn junction,” Applied Physics Letters, vol. 106, no. 18, p. 183101, 2015.
  294. D. S. Wei, T. van der Sar, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, B. I. Halperin, and A. Yacoby, “Mach-Zehnder interferometry using spin- and valley-polarized quantum Hall edge states in graphene,” Sci Adv, vol. 3, p. e1700600, Aug. 2017.
  295. C. Handschin, P. Makk, P. Rickhaus, R. Maurand, K. Watanabe, T. Taniguchi, K. Richter, M.-H. Liu, and C. Schönenberger, “Giant valley-isospin conductance oscillations in ballistic graphene,” Nano Letters, vol. 17, pp. 5389–5393, sep 2017.
  296. M. Jo, P. Brasseur, A. Assouline, G. Fleury, H.-S. Sim, K. Watanabe, T. Taniguchi, W. Dumnernpanich, P. Roche, D. Glattli, et al., “Quantum Hall valley splitters and a tunable Mach-Zehnder interferometer in graphene,” Physical Review Letters, vol. 126, no. 14, p. 146803, 2021.
  297. J. Tworzydło, I. Snyman, A. R. Akhmerov, and C. W. J. Beenakker, “Valley-isospin dependence of the quantum Hall effect in a graphene p𝑝pitalic_p-n𝑛nitalic_n junction,” Phys. Rev. B, vol. 76, p. 035411, Jul 2007.
  298. L. Trifunovic and P. W. Brouwer, “Valley isospin of interface states in a graphene p⁢n𝑝𝑛pnitalic_p italic_n junction in the quantum Hall regime,” Phys. Rev. B, vol. 99, p. 205431, May 2019.
  299. M. K. Rehmann, Y. B. Kalyoncu, M. Kisiel, N. Pascher, F. J. Giessibl, F. Müller, K. Watanabe, T. Taniguchi, E. Meyer, M.-H. Liu, and D. M. Zumbühl, “Characterization of hydrogen plasma defined graphene edges,” Carbon, vol. 150, pp. 417–424, 2019.
  300. D. S. Wei, T. van der Sar, S. H. Lee, K. Watanabe, T. Taniguchi, B. I. Halperin, and A. Yacoby, “Electrical generation and detection of spin waves in a quantum Hall ferromagnet,” Science, vol. 362, pp. 229–233, Oct. 2018.
  301. A. Assouline, L. Pugliese, H. Chakraborti, S. Lee, L. Bernabeu, M. Jo, K. Watanabe, T. Taniguchi, D. Glattli, N. Kumada, et al., “Emission and coherent control of levitons in graphene,” Science, vol. 382, no. 6676, pp. 1260–1264, 2023.
  302. G. Seelig and M. Büttiker, “Charge-fluctuation-induced dephasing in a gated mesoscopic interferometer,” Physical Review B, vol. 64, no. 24, p. 245313, 2001.
  303. S.-C. Youn, H.-W. Lee, and H.-S. Sim, “Nonequilibrium dephasing in an electronic Mach-Zehnder interferometer,” Physical review letters, vol. 100, no. 19, p. 196807, 2008.
  304. P. Roulleau, F. Portier, P. Roche, A. Cavanna, G. Faini, U. Gennser, and D. Mailly, “Noise dephasing in edge states of the integer quantum Hall regime,” Physical Review Letters, vol. 101, no. 18, p. 186803, 2008.
  305. E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, “Separation of neutral and charge modes in one-dimensional chiral edge channels,” Nature communications, vol. 4, no. 1, p. 1839, 2013.
  306. E. Sukhorukov and V. Cheianov, “Resonant Dephasing in the Electronic Mach-Zehnder Interferometer,” Physical Review Letters, vol. 99, p. 156801, oct 2007.
  307. L. V. Litvin, A. Helzel, H.-P. Tranitz, W. Wegscheider, and C. Strunk, “Edge-channel interference controlled by Landau level filling,” Physical Review B, vol. 78, p. 075303, aug 2008.
  308. C. Altimiras, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly, and F. Pierre, “Non-equilibrium edge-channel spectroscopy in the integer quantum Hall regime,” Nature Physics, vol. 6, pp. 34–39, oct 2009.
  309. P. Degiovanni, C. Grenier, G. Fève, C. Altimiras, H. le Sueur, and F. Pierre, “Plasmon scattering approach to energy exchange and high-frequency noise in ν𝜈\nuitalic_ν = 2 quantum Hall edge channels,” Physical Review B, vol. 81, p. 121302, mar 2010.
  310. P.-A. Huynh, F. Portier, H. le Sueur, G. Faini, U. Gennser, D. Mailly, F. Pierre, W. Wegscheider, and P. Roche, “Quantum Coherence Engineering in the Integer Quantum Hall Regime,” Physical Review Letters, vol. 108, p. 256802, jun 2012.
  311. V. Freulon, A. Marguerite, J.-M. Berroir, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, “Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization,” Nat. Commun., vol. 6, pp. 1–6, Apr 2015.
  312. A. M. Lunde and S. E. Nigg, “Statistical theory of relaxation of high-energy electrons in quantum Hall edge states,” Physical Review B, vol. 94, p. 045409, jul 2016.
  313. A. Marguerite, C. Cabart, C. Wahl, B. Roussel, V. Freulon, D. Ferraro, C. Grenier, J.-M. Berroir, B. Plaçais, T. Jonckheere, J. Rech, T. Martin, P. Degiovanni, A. Cavanna, Y. Jin, and G. Fève, “Decoherence and relaxation of a single electron in a one-dimensional conductor,” Physical Review B, vol. 94, p. 115311, sep 2016.
  314. I. Gurman, R. Sabo, M. Heiblum, V. Umansky, and D. Mahalu, “Dephasing of an electronic two-path interferometer,” Physical Review B, vol. 93, p. 121412, mar 2016.
  315. S. Tewari, P. Roulleau, C. Grenier, F. Portier, A. Cavanna, U. Gennser, D. Mailly, and P. Roche, “Robust quantum coherence above the Fermi sea,” Physical Review B, vol. 93, p. 035420, jan 2016.
  316. A. Marguerite, E. Bocquillon, J.-M. Berroir, B. Plaçais, A. Cavanna, Y. Jin, P. Degiovanni, and G. Fève, “Two-particle interferometry in quantum Hall edge channels,” Physica Status Solidi (b), vol. 254, p. 1600618, mar 2017.
  317. K. Itoh, R. Nakazawa, T. Ota, M. Hashisaka, K. Muraki, and T. Fujisawa, “Signatures of a Nonthermal Metastable State in Copropagating Quantum Hall Edge Channels,” Physical Review Letters, vol. 120, p. 197701, may 2018.
  318. C. Cabart, B. Roussel, G. Fève, and P. Degiovanni, “Taming electronic decoherence in one-dimensional chiral ballistic quantum conductors,” Physical Review B, vol. 98, p. 155302, oct 2018.
  319. H. Duprez, E. Sivre, A. Anthore, A. Aassime, A. Cavanna, A. Ouerghi, U. Gennser, and F. Pierre, “Macroscopic Electron Quantum Coherence in a Solid-State Circuit,” Phys Rev X, vol. 9, p. 021030, May 2019.
  320. R. H. Rodriguez, F. D. Parmentier, D. Ferraro, P. Roulleau, U. Gennser, A. Cavanna, M. Sassetti, F. Portier, D. Mailly, and P. Roche, “Relaxation and revival of quasiparticles injected in an interacting quantum Hall liquid,” Nat. Commun., vol. 11, pp. 1–8, May 2020.
  321. D. S. Wei, T. Van Der Sar, S. H. Lee, K. Watanabe, T. Taniguchi, B. I. Halperin, and A. Yacoby, “Electrical generation and detection of spin waves in a quantum hall ferromagnet,” Science, vol. 362, no. 6411, pp. 229–233, 2018.
  322. A. Assouline, M. Jo, P. Brasseur, K. Watanabe, T. Taniguchi, T. Jolicoeur, D. Glattli, N. Kumada, P. Roche, F. Parmentier, et al., “Excitonic nature of magnons in a quantum hall ferromagnet,” Nature Physics, vol. 17, no. 12, pp. 1369–1374, 2021.
  323. S. Nakaharai, J. R. Williams, and C. M. Marcus, “Gate-defined graphene quantum point contact in the quantum Hall regime,” Phys. Rev. Lett., vol. 107, p. 036602, July 2011.
  324. K. Zimmermann, A. Jordan, F. Gay, K. Watanabe, T. Taniguchi, Z. Han, V. Bouchiat, H. Sellier, and B. Sacépé, “Tunable transmission of quantum Hall edge channels with full degeneracy lifting in split-gated graphene devices,” Nat. Commun., vol. 8, pp. 1–7, Apr. 2017.
  325. L. A. Cohen, N. L. Samuelson, T. Wang, K. Klocke, C. C. Reeves, T. Taniguchi, K. Watanabe, S. Vijay, M. P. Zaletel, and A. F. Young, “Nanoscale electrostatic control in ultraclean van der Waals heterostructures by local anodic oxidation of graphite gates,” Nature Physics, vol. –, no. –, pp. –, 2023.
  326. X. Liu, G. Farahi, C. L. Chiu, Z. Papic, K. Watanabe, T. . Taniguchi, and A. Yazdani, “Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet,” Science, vol. 375, no. 6578, pp. 321–326, 2022.
  327. N. F. Ahmad, T. Iwasaki, K. Komatsu, K. Watanabe, T. Taniguchi, H. Mizuta, Y. Wakayama, A. M. Hashim, Y. Morita, S. Moriyama, and S. Nakaharai, “Effect of gap width on electron transport through quantum point contact in hBN/graphene/hBN in the quantum Hall regime,” Applied Physics Letters, vol. 114, p. 023101, jan 2019.
  328. Y. Ronen, T. Werkmeister, D. Haie Najafabadi, A. T. Pierce, L. E. Anderson, Y. J. Shin, S. Y. Lee, Y. H. Lee, B. Johnson, K. Watanabe, et al., “Aharonov–bohm effect in graphene-based Fabry–Pérot quantum Hall interferometers,” Nature nanotechnology, vol. 16, no. 5, pp. 563–569, 2021.
  329. L. A. Cohen, N. L. Samuelson, T. Wang, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, “Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact,” Science, vol. 382, pp. 542–547, Dec. 2023.
  330. J. Li, H. Wen, K. Watanabe, T. Taniguchi, and J. Zhu, “Gate-controlled transmission of quantum Hall edge states in bilayer graphene,” Physical Review Letters, vol. 120, p. 057701, jan 2018.
  331. C. Déprez, L. Veyrat, H. Vignaud, G. Nayak, K. Watanabe, T. Taniguchi, F. Gay, H. Sellier, and B. Sacépé, “A tunable Fabry–Pérot quantum Hall interferometer in graphene,” Nat Nanotechnol, vol. 16, pp. 555–562, May 2021.
  332. S. Biswas, R. Bhattacharyya, H. K. Kundu, A. Das, M. Heiblum, V. Umansky, M. Goldstein, and Y. Gefen, “Shot noise does not always provide the quasiparticle charge,” Nature physics, vol. 18, no. 12, pp. 1476–1481, 2022.
  333. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, “Half-integer conductance plateau at the ν𝜈\nuitalic_ν= 2/3 fractional quantum Hall state in a quantum point contact,” Physical Review Letters, vol. 130, no. 7, p. 076205, 2023.
  334. N. Schiller, Y. Oreg, and K. Snizhko, “Extracting the scaling dimension of quantum Hall quasiparticles from current correlations,” Physical Review B, vol. 105, no. 16, p. 165150, 2022.
  335. L. Zhao, E. G. Arnault, T. F. Larson, Z. Iftikhar, A. Seredinski, T. Fleming, K. Watanabe, T. Taniguchi, F. Amet, and G. Finkelstein, “Graphene-based quantum hall interferometer with self-aligned side gates,” Nano Letters, vol. 22, no. 23, pp. 9645–9651, 2022.
  336. D. E. Feldman and B. I. Halperin, “Fractional charge and fractional statistics in the quantum Hall effects,” Reports on Progress in Physics, vol. 84, no. 7, p. 076501, 2021.
  337. B. I. Halperin, A. Stern, I. Neder, and B. Rosenow, “Theory of the Fabry-Perot quantum Hall interferometer,” Physical Review B, vol. 83, no. 15, p. 155440, 2011.
  338. B. Van Wees, L. P. Kouwenhoven, C. Harmans, J. Williamson, C. Timmering, M. Broekaart, C. Foxon, and J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Physical Review Letters, vol. 62, no. 21, p. 2523, 1989.
  339. N. Ofek, A. Bid, M. Heiblum, A. Stern, V. Umansky, and D. Mahalu, “Role of interactions in an electronic Fabry–Perot interferometer operating in the quantum Hall effect regime,” Proceedings of the National Academy of Sciences, vol. 107, no. 12, pp. 5276–5281, 2010.
  340. D. McClure, W. Chang, C. M. Marcus, L. Pfeiffer, and K. West, “Fabry-Perot interferometry with fractional charges,” Physical Review Letters, vol. 108, no. 25, p. 256804, 2012.
  341. I. Sivan, R. Bhattacharyya, H. Choi, M. Heiblum, D. Feldman, D. Mahalu, and V. Umansky, “Interaction-induced interference in the integer quantum Hall effect,” Physical Review B, vol. 97, no. 12, p. 125405, 2018.
  342. J. Nakamura, S. Fallahi, H. Sahasrabudhe, R. Rahman, S. Liang, G. C. Gardner, and M. J. Manfra, “Aharonov–Bohm interference of fractional quantum Hall edge modes,” Nature Physics, vol. 15, no. 6, pp. 563–569, 2019.
  343. H. Choi, I. Sivan, A. Rosenblatt, M. Heiblum, V. Umansky, and D. Mahalu, “Robust electron pairing in the integer quantum Hall effect regime,” Nature communications, vol. 6, no. 1, p. 7435, 2015.
  344. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, “Fabry-Perot interferometry at the ν𝜈\nuitalic_ν= 2/5 fractional quantum Hall state,” Phys. Rev. X, vol. 13, p. 041012, Oct 2023.
  345. C. de C. Chamon, D. E. Freed, S. A. Kivelson, S. L. Sondhi, and X. G. Wen, “Two point-contact interferometer for quantum Hall systems,” Physical Review B, vol. 55, pp. 2331–2343, jan 1997.
  346. J. Li, C. Tan, S. Chen, Y. Zeng, T. Taniguchi, K. Watanabe, J. Hone, and C. Dean, “Even-denominator fractional quantum Hall states in bilayer graphene,” Science, vol. 358, no. 6363, pp. 648–652, 2017.
  347. T. Werkmeister, J. R. Ehrets, Y. Ronen, M. E. Wesson, D. Najafabadi, Z. Wei, K. Watanabe, T. Taniguchi, D. E. Feldman, B. I. Halperin, A. Yacoby, and P. Kim, “Strongly coupled edge states in a graphene quantum Hall interferometer,” arXiv:2312.03150, 2023.
  348. W. Yang, D. Perconte, C. Déprez, K. Watanabe, T. Taniguchi, S. Dumont, E. Wagner, F. Gay, I. Safi, H. Sellier, and B. Sacépé, “Evidence for correlated electron pairs and triplets in quantum hall interferometers,” arXiv:2312.14767, 2023.
  349. S. Biswas, H. K. Kundu, V. Umansky, and M. Heiblum, “Electron Pairing of Interfering Interface-Based Edge Modes,” Physical Review Letters, vol. 131, 2023.
  350. G. A. Frigeri and B. Rosenow, “Electron pairing in the quantum Hall regime due to neutralon exchange,” Phys. Rev. Res., vol. 2, p. 043396, Dec 2020.

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