Abstract
We investigate the topological properties of Floquet-engineered twisted bilayer graphene above the magic angle driven by circularly polarized laser pulses. Employing a full Moir\'e-unit-cell tight-binding Hamiltonian based on first-principles electronic structure we show that the band topology in the bilayer, at twisting angles above 1.05$^\circ$, essentially corresponds to the one of single-layer graphene. However, the ability to open topologically trivial gaps in this system by a bias voltage between the layers enables the full topological phase diagram to be explored, which is not possible in single-layer graphene. Circularly polarized light induces a transition to a topologically nontrivial Floquet band structure with the Berry curvature of a Chern insulator. Importantly, the twisting allows for tuning electronic energy scales, which implies that the electronic bandwidth can be tailored to match realistic driving frequencies in the ultraviolet or mid-infrared photon-energy regimes. This implies that Moir\'e superlattices are an ideal playground for combining twistronics, Floquet engineering, and strongly interacting regimes out of thermal equilibrium.
Highlights
Light-matter coupled systems are emerging as an important research frontier bridging condensed matter physics [1], quantum optics [2,3,4,5,6], and cold atoms in optical lattices [7,8,9]
In optical lattices, periodically driven quantum systems are investigated within the realm of Floquet engineering, in which the driving is used as a tool to generate effective Hamiltonians with tunable interactions [24,25,26,27,28], which has been demonstrated in purely photonic systems [29]
We find that the topology of twisted bilayer graphene (TBG) above the magic angles corresponds to two copies of single-layer graphene
Summary
Light-matter coupled systems are emerging as an important research frontier bridging condensed matter physics [1], quantum optics [2,3,4,5,6], and cold atoms in optical lattices [7,8,9]. We find a topologically nontrivial band structure (corresponding to a Chern number C = 4), while in equilibrium, the system exhibits trivial topology with cancellations of valley Berry curvature when inversion symmetry is broken by a back-gate bias voltage between the layers This offers the unique opportunity, in contrast to single-layer graphene, to study the transition between the topologically trivial and nontrivial phases, as originally envisioned by Haldane in his seminal work on the quantum anomalous Hall effect [55]. This is unlike the case of time-reversal symmetry breaking by a magnetic field, where the large magnetic unit cell and corresponding small Brillouin zone cause dramatically different effects such as the emergence of a Hofstadter butterfly [56].
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