Abstract
Monolayer graphene placed with a twist on top of AB-stacked bilayer graphene hosts topological flat bands in a wide range of twist angles. The dispersion of these bands and gaps between them can be efficiently controlled by a perpendicular electric field, which induces topological transitions accompanied by changes of the Chern numbers. In the regime where the applied electric field induces gaps between the flat bands, we find a relatively uniform distribution of the Berry curvature. Consequently, interaction-induced valley- and/or spin-polarized states at integer filling factors are energetically favorable. In particular, we predict a quantum anomalous Hall state at filling factor $\nu=1$ for a range of twist angles $1^\circ<\theta <1.4^\circ$. Furthermore, to characterize the response of the system to magnetic field, we computed the Hofstadter butterfly and the Wannier plot, which can be used to probe the dispersion and topology of the flat bands in this material.
Highlights
Studies of twisted two-dimensional materials have gained an enormous boost after the discovery of correlated insulator states and superconductivity in twisted bilayer graphene [1,2,3,4,5,6]. tBG has been predicted [7] to be a natural platform for interaction physics due to the presence of magic angles where nearly flat bands near charge neutrality are formed
Theoretical Hartree-Fock studies [21,22,23] complemented with exact diagonalization studies [24] have argued that such a state may arise in tBG as a combined effect of alignment with the hBN substrate and Coulomb interaction, via a mechanism reminiscent of quantum Hall ferromagnetism
This is clearly seen for twisted monolayer-bilayer graphene (tMBG), where the density of states is significantly higher close to ν = −4, washing out the Landau fans originating from other integer fillings
Summary
Studies of twisted two-dimensional materials have gained an enormous boost after the discovery of correlated insulator states and superconductivity in twisted bilayer graphene (tBG) [1,2,3,4,5,6]. tBG has been predicted [7] to be a natural platform for interaction physics due to the presence of magic angles where nearly flat bands near charge neutrality are formed. TBG has been predicted [7] to be a natural platform for interaction physics due to the presence of magic angles where nearly flat bands near charge neutrality are formed. Following these results, a variety of related stacked materials with flat bands have been proposed and experimentally studied, including twisted double graphene bilayers [8], trilayer graphene on hBN [9,10,11], and twisted transition-metal dichalcogenides [12].
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