Landau levels in twisted bilayer graphene and semiclassical orbits

Abstract

Twisted bilayer graphene has been argued theoretically to host exceptionally flat bands when the angle between the two layers falls within a magic range near 1.1 • . This is now strongly supported by experiment, which furthermore reveals dramatic correlation effects in the magic range due to the relative dominance of interactions when the bandwidth is suppressed. Experimentally, quantum oscillations exhibit different Landau level degeneracies when the angles fall in or outside the magic range; these observations can contain crucial information about the low energy physics. In this paper, we report a thorough theoretical study of the Landau level structure of the non-interacting continuum model for twisted bilayer graphene as the magnetic field and the twist angle are tuned. We first show that a discernible difference exists in the butterfly spectra when twist angle falls in and outside the magic range. Next, we carry out semiclassical analysis in detail, which quantitatively determines the origin of the low energy Landau levels from the zero field band structure. We find that the Landau level degeneracy predicted in the above analyses is capable of partially explaining features of the quantum oscillation experiments in a natural way. Finally, topological aspects, validity, and other subtle points of the model are discussed. arXiv:1903.11563v1 [cond-mat.str-el]

Fractional Chern insulators in magic-angle twisted bilayer graphene

“…We obtain the Hofstadter spectrum following refs. [40][41][42] , which is shown in Extended Data Fig. 5.…”

Topological flat bands and correlated states in twisted monolayer-bilayer graphene

“…In order to quantify this effect, we computed the spectrum of tMBG in the presence of a magnetic field. Previous works [40][41][42][43] have developed complementary approaches to study the behavior of tBG in a magnetic field. We used the method introduced by Ref.…”

“…We used the method introduced by Ref. [42], which amounts to projecting the interlayer coupling onto a basis set of single-layer Landau level wave functions. The details of our method are outlined in Appendix A.…”

Correlation-driven topological phases in magic-angle twisted bilayer graphene

“…This is largely due to difficulties in band structure calculations that incorporate all relevant effects such as electronic correlations [30][31][32] , strain 33 , and atomic reconstruction 34 . In particular, several mechanisms were proposed to explain the origin of four-fold LLs formed at charge neutrality 33,35,36 but to date there is no general consensus.…”