Light-matter coupling and quantum geometry in moiré materials

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Physical Review B, Volume 104, issue 6
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.
Funding Information: We acknowledge discussions with J. W. McIver. G.T. and P.T. acknowledge support by the Academy of Finland under Project No. 303351, 307419, and 327293. M.A.S. acknowledges financial support through the DFG Emmy Noether program (SE 2558/2). D.M.K. acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through RTG 1995, within the Priority Program SPP 2244 “2DMP” and under Germany's Excellence Strategy-Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC2004/1-390534769. We acknowledge support from the Max Planck-New York City Center for Non-Equilibrium Quantum Phenomena. Publisher Copyright: © 2021 American Physical Society.
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Topp, G E, Eckhardt, C J, Kennes, D M, Sentef, M A & Törmä, P 2021, ' Light-matter coupling and quantum geometry in moiré materials ', Physical Review B, vol. 104, no. 6, 064306 .