Shift-current response as a probe of quantum geometry and electron-electron interactions in twisted bilayer graphene

Abstract

Moiré materials, and in particular twisted bilayer graphene (TBG), exhibit a range of fascinating phenomena, that emerge from the interplay of band topology and interactions. We show that the non-linear second-order photoresponse is an appealing probe of this rich interplay. A dominant part of the photoresponse is the shift-current, which is determined by the geometry of the electronic wave-functions and carrier properties, and thus becomes strongly modified by electron-electron interactions. We analyze its dependence on the twist angle and doping, and investigate the role of interactions. In the absence of interactions, the response of the system is dictated by two energy scales: the mean energy of direct transitions between the hole and electron flat bands, and the gap between flat and dispersive bands. Including electron-electron interactions, both enhance the response at the non-interacting characteristic frequencies as well as produce new resonances. We attribute these changes to the filling-dependent band renormalization in TBG. Our results highlight the connection between non-trivial geometric properties of TBG and its optical response, as well as demonstrate how optical probes can access the role of interactions in moiŕe materials.

Superfluidity and Quantum Geometry in Twisted Multilayer Systems

“…The quantum metric is a fundamental quantity describing distances between the eigenstates of a system, and hence appears in many observables of interacting systems. For instance, light-matter interactions in TBG reflect the underlying quantum geometry as well [148,149]. Recently, quantum geometry was predicted to stabilize Bose-Einstein condensates in flat bands [150], relevant for bosonic condensates in ultracold gas and polariton systems, or even for 2D moiré materials at the bosonic end of the BCS-BEC crossover [98].…”

Momentum-space Gravity from the Quantum Geometry and Entropy of Bloch Electrons

“…Although, Berry curvature and the quantum metric have the same physical dimension and are often combined into a complexvalued quantity called the quantum geometric tensor with Berry curvature (quantum metric) as its imaginary (real) part, the role of the latter in determining the elec- * ajit.srivastava@emory.edu tronic properties of crystals is far less studied. Recently, its importance has been identified in a wide variety of phenomena including localization of Wannier functions [18][19][20], superconductivity and other phenomena in flat bands systems [21][22][23][24][25][26], nonlinear response [23,[27][28][29][30][31][32][33][34][35], fractional Chern insulators [36,37], current noise [38], magnetic susceptibility [39], quantum phase transitions [40][41][42][43], excitonic fine structure [13,14], and has been experimentally measured in photonic and atomic systems [44,45].…”

“…Our predictions for the geodesic term are particularly relevant for charge carriers in quasi-flat bands where the group velocity term, of lowest order in applied electric field, becomes negligible. Such flat bands exist in moiré heterostructures of van der Waals materials such as graphene and transition metal dichalcogenides, making them an ideal platform to detect momentum-space geodesic dynamics [25,51,52].…”

Quantum plasmonic non-reciprocity in parity-violating magnets

“…TBG is a particularly attractive venue for quantum metric plasmons due to its strong Coulomb interactions with typical values that can exceed the bandwidth of the narrow bands [34]. Additionally, when combined with hBN, TBG heterostructures break inversion symmetry to display large values of quantum geometric quantities [35][36][37][38] in its narrow bands (Fig. 3a).…”