Landau Levels as a Probe for Band Topology in Graphene Moiré Superlattices

Generalized Peierls substitution for the tight-binding model of twisted multilayer graphene in a magnetic field

“…Up to now, the most studied TLG, namely twisted bilayer graphene (TBLG) and twisted double bilayer graphene (TDBLG), have been synthesized successfully by nanotechnology fabrication methods [1]. Notably, TLG exhibit various intriguing physical properties, such as superconductivity at the magic angle [2][3][4], the nontrivial topology of flat bands [5,6], the anomalous Hall effect [7,8], the unique magnetic quantization [9][10][11][12][13] and the quantum Hall effect (QHE) [14][15][16][17][18][19][20]. These make TLG a prominent candidate for potential applications in new-generation devices with new advanced functionalities [21].…”

“…Their band structures have been presented from a theoretical perspective by using densityfunctional theory (DFT) [22,23] and modeling [24][25][26][27][28][29][30][31][32]. Additionally, band structures have also been obtained experimentally by utilizing scanning-tunneling microscopy (STM) and spectroscopy (STS) techniques [9,[32][33][34][35][36][37][38][39]. Besides electronic structures, the magnetic quantization which provides important dynamical information of materials has been identified experimentally [10,11] and predicted theoretically [9,12,13] for TBLG and TDBLG.…”

“…Additionally, band structures have also been obtained experimentally by utilizing scanning-tunneling microscopy (STM) and spectroscopy (STS) techniques [9,[32][33][34][35][36][37][38][39]. Besides electronic structures, the magnetic quantization which provides important dynamical information of materials has been identified experimentally [10,11] and predicted theoretically [9,12,13] for TBLG and TDBLG. It has been shown for TBLG that its quantum Hall conductivity (QHC) exhibits a step structure, in which the plateau series (in the unit e 2 /h) are ±4, ±8, ±12 • • • [14][15][16][17].…”

“…Meanwhile, the studies for QHE in TDBLG with small twist angles have also been carried out. However, their filling factors are responsive to the stacking configuration and magnetic field [18][19][20]. Though remarkable efforts have been devoted to studies of the transport properties of TLG, a deep understanding of the QHC step formation, as well as its connection to the quantized Landau levels (LLs), still remain a mystery.…”

An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration

“…We utilize a geometric method to study the physics of TBG. This method is in principle valid for arbitrary twist angle, which is mainly inspired by considering the twist as a kind of deformation [15] and attributing the approximate zero energy flat band to the effective SU(2) gauge field (pseudo magnetic vector potential) in TBG [12,16,[22][23][24][25]. Such a geometric theory can be naturally generalized to the case of a RBG system, which cannot be modeled by previous theoretical formulations.…”