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 intraband quantum metric allows diamagnetic coupling inside a flat band; the interband 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 twist-angle 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.

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

“…For instance, Berry curvature governs the anomalous transport of an electron wave packet [3], while its integral over the Brillouin zone (BZ) gives the Chern number, which, among other topological invariants, is central in explaining the quantum Hall effect and topological insulators [4][5][6][7][8][9]. The importance of the quantum metric for phenomena such as superconductivity [10][11][12][13], orbital magnetic susceptibility [14,15], and light-matter coupling [16] has been understood only recently, and the interest in the quantum metric is rapidly growing [17][18][19][20]. Quantum geometric concepts have also been proposed for bosonic systems composed of light, bosonic atoms, or collective excitations [21][22][23][24][25][26][27][28][29][30].…”

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].…”

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 lightmatter 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].…”