Abstract
We recently proposed quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions [Phys. Rev. Lett. 125, 030504 (2020)]. Conceptually, the scheme is based on the idea that aphysical monolayer optical lattice of desired geometry is upgraded to a synthetic bilayer system by identifyingthe internal states of the trapped atoms with synthetic spatial dimensions. The couplings between the internalstates, i.e. between sites on the two layers, can be exquisitely controlled by laser induced Raman transitions.By spatially modulating the interlayer coupling, Moir\'e-like patterns can be directly imprinted on the latticewithout the need of a physical twist of the layers. This scheme leads practically to a uniform pattern across thelattice with the added advantage of widely tunable interlayer coupling strengths. The latter feature facilitates theengineering of flat bands at larger "magic" angles, or more directly, for smaller unit cells than in conventionaltwisted materials. In this paper we extend these ideas and demonstrate that our system exhibits topologicalband structures under appropriate conditions. To achieve non-trivial band topology we consider imanaginarynext-to-nearest neighbor tunnelings that drive the system into a quantum anomalous Hall phase. In particular,we focus on three groups of bands, whose their Chern numbers triplet can be associated to a trivial insulator(0,0,0), a standard non-trivial (-1,0,1) and a non-standard non-trivial (-1,1,0). We identify regimes of parameterswhere these three situations occur. We show the presence of an anomalous Hall phase and the appearance oftopological edge states. Our works open the path for experiments on topological effects in twistronics without atwist
Highlights
Twistronics is a term commonly used nowadays to describe the physics resulting from the twist between layers of two-dimensional materials
In the present paper we developed further the idea of “twistronics without a twist” and demonstrated that it can be used to engineer interesting topological band structures under various conditions
Focussing on a square lattice system with synthetic dimensions, we showed the appearance of an anomalous Hall phase in presence of artificial complex next-to-nearest neighbor interlayer tunneling
Summary
Twistronics (from twist and electronics) is a term commonly used nowadays to describe the physics resulting from the twist between layers of two-dimensional materials. The intimate relation between topology and condensed matter goes back to the discovery of the integer quantum Hall effect (IQHE) [30]: A 2D electron gas at low temperature and under a strong magnetic field presents a quantized transverse conductivity very robust against local perturbations It was soon realized [31] that this robustness was coming from a new paradigm: a global topological order which cannot be described by the usual Ginzburg Landau theory of phase transitions. The rapid development of twistronics in condensed matter physics of 2D material stimulated an extensive quest for quantum simulators of twistronics with ultracold atoms [93] and of Moiré patterns in photonic systems [94] We combined these two worlds in a recent work, quantum simulators and synthetic dimensions, and proposed twistronics without a twist [95].
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