Quantum anomalous Hall phase in synthetic bilayers via twistronics without a twist
Tymoteusz Salamon, Ravindra W. Chhajlany, Alexandre Dauphin, Maciej Lewenstein, Debraj Rakshit
Abstract
We recently proposed quantum simulators of ``twistroniclike'' physics based on ultracold atoms and synthetic dimensions, T. Salamon et al. [Phys. Rev. Lett. 125, 030504 (2020).]. In this scheme, Moir\'e-like patterns can be directly imprinted on the lattice by spatially modulating the interlayer coupling via laser induced Raman transitions, without the need of a physical twist of the layers. As a result, certain ``magic'' configurations host Dirac cones and quasiflat bands with tunable bandwidths. In this paper we extend these ideas and demonstrate that our system exhibits topological band structures under appropriate conditions. To achieve nontrivial band topology we consider imaginary next-to-nearest neighbor tunnelings that drive the system into a quantum anomalous Hall phase. In particular, we focus on three groups of bands, whose Chern numbers triplet can be associated to a trivial insulator (0,0,0), a standard nontrivial $(\ensuremath{-}1,0,1)$, and a nonstandard nontrivial $(\ensuremath{-}1,1,0)$. We identify regimes of parameters where these three situations occur. We show the presence of an anomalous Hall phase and the appearance of topological edge states. Our work opens the path for experiments on topological effects in twistronics without a twist.