Phase transitions out of quantum Hall states in moiré materials
Abstract: Motivated by the recent experimental breakthroughs in observing Fractional Quantum Anomalous Hall (FQAH) states in moir\'e materials, we propose and study various unconventional phase transitions between quantum Hall phases and Fermi liquids or charge ordered phases upon tuning the bandwidth. At a fixed rational lattice filling $\nu$, we describe a quantum Ginzburg-Landau theory to describe the intertwinement between the FQAH and Charge Density Wave (CDW) orders. We use this theory to describe phase transitions between the FQAH and a CDW insulator. The critical theory for a direct second order transition resembles that of the familiar deconfined quantum critical point (DQCP) but with an additional Chern-Simons term. At filling -1/2, we study the possibility of a continuous transition between the composite Fermi liquid (CFL) and the Fermi liquid (FL) building on and refining previous work by Barkeshli and McGreevy. Crucially we show that filling constraints ignored in that work ensure that translation symmetry alone is enough to enable a second order CFL-FL transition. We argue that there must be critical CDW fluctuations though neither phase has long range CDW order. We present experimental signatures the most striking of which is a universal jump of both longitudinal and Hall resistivities at the critical point. With disorder, we argue that the CDW order gets pinned and the CFL-FL evolution happens through an intermediate electrically insulating phase with mobile neutral fermions. A clean analog of this insulating phase with long range CDW order and a neutral fermi surface can potentially also exist. We also present a critical theory for the CFL to FL transition at filling -3/4. Our work opens up a new avenue to realize deconfined criticality and fractionalized phases beyond familiar Landau level physics in the moire Chern band system.
- J. K. Jain, Physical review letters 63, 199 (1989).
- N. Regnault and B. A. Bernevig, Physical Review X 1, 021014 (2011).
- E. J. Bergholtz and Z. Liu, International Journal of Modern Physics B 27, 1330017 (2013).
- C. Repellin and T. Senthil, Physical Review Research 2, 023238 (2020).
- V. Crépel and L. Fu, Phys. Rev. B 107, L201109 (2023).
- M. Barkeshli and J. McGreevy, Physical Review B 89, 235116 (2014).
- M. Barkeshli and J. McGreevy, Physical Review B 86, 075136 (2012).
- T. Senthil, Physical Review B 78, 045109 (2008).
- Our theory incorporates lattice translation and filling constraints as crucial ingredients but does not respect C3subscript𝐶3C_{3}italic_C start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT symmetry. Thus it could potentially describe the CFL-FL evolution if the experimental system breaks C3subscript𝐶3C_{3}italic_C start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT, as seems possible due to strain that is likely present.
- T. Senthil, arXiv preprint arXiv:2306.12638 (2023).
- X.-G. Wen and Y.-S. Wu, Physical review letters 70, 1501 (1993).
- A. Burkov and L. Balents, Physical Review B 72, 134502 (2005).
- The electron operator is a product of a monopole operator of α𝛼\alphaitalic_α and three ϕvsubscriptitalic-ϕ𝑣\phi_{v}italic_ϕ start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT operators. Though the monopole scaling dimension is not known, each ϕvsubscriptitalic-ϕ𝑣\phi_{v}italic_ϕ start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT has a mean field scaling dimension of 1/2121/21 / 2. Hence we might expect ΔesubscriptΔ𝑒\Delta_{e}roman_Δ start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT is at least equal to 3232\frac{3}{2}divide start_ARG 3 end_ARG start_ARG 2 end_ARG).
- X.-Y. Song and Y.-H. Zhang, SciPost Phys. 15, 215 (2023).
- Actually a spinc𝑐{}_{c}start_FLOATSUBSCRIPT italic_c end_FLOATSUBSCRIPT connection. Also strictly speaking this parton representation introduces an SU(2)𝑆𝑈2SU(2)italic_S italic_U ( 2 ) gauge redundancy but we assume that the mean field states of interest break the SU(2)𝑆𝑈2SU(2)italic_S italic_U ( 2 ) gauge structure to U(1)𝑈1U(1)italic_U ( 1 ).
- This is definitely true in the free Dirac theory without any gauge field.
- C. Wang and T. Senthil, Phys. Rev. B 93, 085110 (2016).
- Similar phenomena are found at other deconfined critical pointsSenthil et al. (2004b).
- The random pinning of the CDW will occur on a length scale that grows as a power of the disorder strength while the localization length will be exponentially large in the disorder strength. Hence for weak disorder it is legitimate to ignore localization effects.
- O. I. Motrunich, Physical Review B 73, 155115 (2006).
- D. F. Mross and T. Senthil, Physical Review B 84, 041102 (2011).
- N. Read, Phys. Rev. B 58, 16262?16290 (1998).
- Z. Dong and T. Senthil, Physical Review B 102, 205126 (2020).
- Z. Dong and T. Senthil, Physical Review B 105, 085301 (2022).
- H. Goldman and T. Senthil, Physical Review B 105, 075130 (2022).
- K. K. Ma and K. Yang, Physical Review B 105, 035132 (2022).
- The projective translation symmetry T1T2=−T2T1subscript𝑇1subscript𝑇2subscript𝑇2subscript𝑇1T_{1}T_{2}=-T_{2}T_{1}italic_T start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = - italic_T start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT does not have one dimensional representation.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.