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We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moire superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures, but show different valley Chern numbers of the flat bands. These differences between the AB-AB and AB-BA configurations of TDBG clearly manifest as different Landau level sequences in the Hofstadter butterfly spectra calculated using the tight-binding model. The Landau level sequences are explained from the point of view of the distribution of orbital magnetization in momentum space that is governed by the rotational $C_2$ and time-reversal $mathcal{T}$ symmetries. Our results can be readily extended to other twisted graphene multilayers and $h$-BN/graphene heterostructures thus establishing the Hofstadter butterfly spectra as a powerful tool for detecting the non-trivial valley band topology.
A number of moire graphene systems have nearly flat topological bands where electron motion is strongly correlated. Though microscopically these systems are only quasiperiodic, they can typically be treated as translation invariant to an excellent ap
Recently twisted bilayer graphene (t-BLG) emerges as a new strongly correlated physical platform near a magic twist angle, which hosts many exciting phenomena such as the Mott-like insulating phases, unconventional superconducting behavior and emerge
We study RKKY interactions for magnetic impurities on graphene in situations where the electronic spectrum is in the form of Landau levels. Two such situations are considered: non-uniformly strained graphene, and graphene in a real magnetic field. RK
In graphene moire superlattices, electronic interactions between layers are mostly hidden as band structures get crowded because of folding, making their interpretation cumbersome. Here, the evolution of the electronic band structure as a function of
Two-dimensional systems with $C_{2}mathcal{T}$ ($Pmathcal{T}$) symmetry exhibit the Euler class topology $Einmathbb{N}$ in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying the energy level