Light-matter coupling and quantum geometry in moiré materials

Abstract

Quantum geometry has been identified as an important ingredient for the physics of quantum materials and especially of flat-band systems, such as moiré materials. On the other hand, the coupling between light and matter is of key importance across disciplines and especially for Floquet and cavity engineering of solids. Here we present fundamental relations between light-matter coupling and quantum geometry of Bloch wave functions, with a particular focus on flat-band and moiré materials, in which the quenching of the electronic kinetic energy could allow one to reach the limit of strong light-matter coupling more easily than in highly dispersive systems. We show that, despite the fact that flat bands have vanishing band velocities and curvatures, light couples to them via geometric contributions. Specifically, the intra-band quantum metric allows diamagnetic coupling inside a flat band; the inter-band Berry connection governs dipole matrix elements between flat and dispersive bands. We illustrate these effects in two representative model systems: (i) a sawtooth quantum chain with a single flat band, and (ii) a tight-binding model for twisted bilayer graphene. For (i) we highlight the importance of quantum geometry by demonstrating a nonvanishing diamagnetic light-matter coupling inside the flat band. For (ii) we explore the twistangle dependence of various light-matter coupling matrix elements. Furthermore, at the magic angle corresponding to almost flat bands, we show a Floquet-topological gap opening under irradiation with circularly polarized light despite the nearly vanishing Fermi velocity. We discuss how these findings provide fundamental design principles and tools for light-matter-coupling-based control of emergent electronic properties in flat-band and moiré materials.

Effective theory of lattice electrons strongly coupled to quantum electromagnetic fields

“…The cavity confinement leads to similar effects, such as induced hopping as in the ultrastrong coupling regime, while the strength of effects is relatively small. The effects can be enhanced for, e.g., subwavelength cavities and metamaterials or heterostructures 83,84 . Coldatom systems represent another family of possible implementations 17,18 , which can also be studied using the same formulation discussed in Sec.…”

An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration

“…8. Another motivation is that although Floquet engineering of TBG has been systematically studied [18,19,69,70], most of them have focued on light frequency driven regime or sliding TBG as a 2d Thouless pump [20,71]. The non-adiabatic structurally rotating driving TBG is still in need of investigation [72].…”

Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers

“…Recent advances have revealed the central role played by the Fubini-Study metric [1] in various fields of quantum sciences [2], with a direct impact on quantum technologies [3,4] and many-body quantum physics [2,5]. In condensed matter, the quantum metric generally defines a notion of distance over momentum space, and it was shown to provide essential geometric contributions to various phenomena, including exotic superconductivity [6][7][8] and superfluidity [9], orbital magnetism [10,11], the stability of fractional quantum Hall states [12][13][14][15][16][17], semiclassical wavepacket dynamics [18,19], topological phase transitions [20], and light-matter coupling in flat-band systems [21]. Besides, the quantum metric plays a central role in the construction of maximally-localized Wannier functions in crystals [22,23], and it provides practical signatures for exotic momentum-space monopoles [24,25] and entanglement in topological superconductors [26,27].…”