Topological Floquet engineering of twisted bilayer graphene

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 Moiré-unit-cell tightbinding Hamiltonian based on first-principles electronic structure we show that the band topology in the bilayer, at twisting angles above 1.05 • , 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 singlelayer 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 Moiré superlattices are an ideal playground for combining twistronics, Floquet engineering, and strongly interacting regimes out of thermal equilibrium.

High-order nonlinear optical response of a twisted bilayer graphene

“…One theoretical challenge is that numerous electronic bands are involved in the TBG due to the large unit cell of the moiré structure. Recently, the Floquet band engineering has been proposed based on the tight-binding model [66] and the low-energy effective Hamiltonian involving a few bands [67][68][69]. Another approach is the perturbation theory for the optical field.…”

Toward Programmable Moiré Computation

“…[16] This result implies the possibility for bilayer structures to have a wide range of dielectric constant, which can be used to make a diffractive layer in optical computation. Different Moiré pattern conversion can be triggered with proper techniques like applying laser pulses, [17] adding strain, [18] which can be observed by the change of optical transition energy, second-harmonic generation, and Raman mode frequencies. [19] The femtosecond laser has been widely used in the synthesis of nanoparticles.…”

Optically induced flat bands in twisted bilayer graphene

“…Floquet engineering with optical fields is a valuable technique that could induce topological band structures and electronic correlations in various materials [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Floquet engineering of TBG has been considered as a technique to tune the value of the magic angle using longitudinal waves [36], and to control the topology of the bands near the CNP at large twist angles [37]. However, the idea of significantly reducing the bandwidth of certain bands in the band structure generating flat bands has never been realized in Van der Waals heterostructures with optical fields.…”