Band gap formation in commensurate twisted bilayer graphene/hBN moiré lattices
Abstract: We report on the investigation of periodic superstructures in twisted bilayer graphene (tBLG) van-der-Waals heterostructures, where one of the graphene layers is aligned to hexagonal boron nitride (hBN). Our theoretical simulations reveal that if the ratio of the resulting two moir\'e unit cell areas is a simple fraction, the graphene/hBN moir\'e lattice acts as a staggered potential, breaking the degeneracy between tBLG AA sites. This leads to additional band gaps at energies where a subset of tBLG AA sites is fully occupied. These gaps manifest as Landau fans in magnetotransport, which we experimentally observe in an aligned tBLG/hBN heterostructure. Our study demonstrates the identification of commensurate tBLG/hBN van-der-Waals heterostructures by magnetotransport, highlights the persistence of moir\'e effects on length scales of tens of nanometers, and represents an interesting step forward in the ongoing effort to realise designed quantum materials with tailored properties.
- F. Bloch, Über die Quantenmechanik der Elektronen in Kristallgittern, Z. Phys. 52, 555 (1929).
- T. Cea, P. A. Pantaleón, and F. Guinea, Band structure of twisted bilayer graphene on hexagonal boron nitride, Phys. Rev. B 102, 155136 (2020).
- J. Shi, J. Zhu, and A. H. MacDonald, Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride, Phys. Rev. B 103, 075122 (2021).
- X. Lin and J. Ni, Symmetry breaking in the double moir\’e superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride, Phys. Rev. B 102, 035441 (2020).
- N. Bultinck, S. Chatterjee, and M. P. Zaletel, Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene, Phys. Rev. Lett. 124, 166601 (2020).
- Y. Zhang, D. Mao, and T. Senthil, Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous Hall effect and a lattice model, Phys. Rev. Res. 1, 033126 (2019).
- N. N. T. Nam and M. Koshino, Lattice relaxation and energy band modulation in twisted bilayer graphene, Phys. Rev. B 96, 075311 (2017).
- R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. U.S.A. 108, 12233 (2011).
- L. A. Chizhova, F. Libisch, and J. Burgdörfer, Graphene quantum dot on boron nitride: Dirac cone replica and hofstadter butterfly, Phys. Rev. B 90, 165404 (2014).
- W. Albrecht, J. Moers, and B. Hermanns, HNF - Helmholtz Nano Facility, Journal of Large-Scale Research Facilities 3, 112 (2017).
- A. Laturia, M. L. Van de Put, and W. G. Vandenberghe, Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: from monolayer to bulk, npj 2D Mater. Appl. 2, 1 (2018).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- I. Souza, N. Marzari, and D. Vanderbilt, Maximally localized wannier functions for entangled energy bands, Phys. Rev. B 65, 035109 (2001).
- N. Marzari and D. Vanderbilt, Maximally localized generalized wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
- P. Moon and M. Koshino, Electronic properties of graphene/hexagonal-boron-nitride moiré superlattice, Phys. Rev. B 90, 155406 (2014).
- C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, Journal of Research of the National Bureau of Standards 45, 255 (1950).
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.