The quantum geometric origin of capacitance in insulators
arXiv:2306.08035 · doi:10.1038/s41467-024-48808-x
Abstract
In band insulators, where the Fermi surface is absent, adiabatic transport is allowed only due to the geometry of the Hilbert space. By driving the system at a small but finite frequency , transport is still expected to depend sensitively on the quantum geometry. Here we show that this expectation is correct and can be made precise by expressing the Kubo formula for conductivity as the variation of the \emph{time-dependent polarization} with respect to the applied field. In particular, a little appreciated effect is that at linear order in frequency, the longitudinal conductivity results from an intrinsic capacitance, determined by the ratio of the quantum metric and the spectral gap. We demonstrate that this intrinsic capacitance has a measurable effect in a wide range of insulators with non-negligible metric, including the electron gas in a quantizing magnetic field, the gapped bands of hBN-aligned twisted bilayer graphene, and obstructed atomic insulators such as diamond whose large refractive index has a topological origin. We also discuss the influence of quantum geometry on the dielectric constant.
6+14 pages
References in corpus (7)
- Band geometry, Berry curvature and superfluid weight
- Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
- Moiré Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride
- Fundamental bound on topological gap
- Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide
- Steady-state Hall response and quantum geometry of driven-dissipative lattices
- Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
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- Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
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