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 (43)
- Topological Insulators
- Topological insulators and superconductors
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Berry Phase Effects on Electronic Properties
- Maximally-localized generalized Wannier functions for composite energy bands
- Maximally localized Wannier functions: Theory and applications
- Moire bands in twisted double-layer graphene
- Topological quantum chemistry
- Topological Crystalline Insulators in the SnTe Material Class
- Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides
- Superfluidity in topologically nontrivial flat bands
- Fractional Chern insulators in magic-angle twisted bilayer graphene
- Polarization and localization in insulators: generating function approach
- Geometry and non-adiabatic response in quantum and classical systems
- The Insulating State of Matter: A Geometrical Theory
- Band geometry of fractional topological insulators
- Band geometry, Berry curvature and superfluid weight
- Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
- Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
- Geometric and conventional contribution to superfluid weight in twisted bilayer graphene
- Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
- Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
- Relations between topology and the quantum metric for Chern insulators
- Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
- Dynamics of Berry-phase polarization in time-dependent electric fields
- Extracting the quantum metric tensor through periodic driving
- Superfluid weight bounds from symmetry and quantum geometry in flat bands
- Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
- Band gaps of crystalline solids from Wannier-localization based optimal tuning of a screened range-separated hybrid functional
- Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
- Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole
- Moiré Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride
- Fundamental bound on topological gap
- Band structure of twisted bilayer graphene on hexagonal boron nitride
- Bound on resistivity in flat-band materials due to the quantum metric
- Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide
- Unconventional Correlation between Quantum Hall Transport Quantization and Bulk State Filling in Gated Graphene Devices
- Steady-state Hall response and quantum geometry of driven-dissipative lattices
- Longitudinal and anomalous Hall conductivity of a general two-band model
- Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
- General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
- Giant boost of the quantum metric in disordered one dimensional flat band systems
- Optical -insulators: topological obstructions in the atomistic susceptibility tensor
Cited by in corpus (42)
- Roadmap for Photonics with 2D Materials
- Universal relation between energy gap and dielectric constant
- Quantum weight: A fundamental property of quantum many-body systems
- Theory of Generalized Landau Levels and Implication for non-Abelian States
- Topological bound on structure factor
- Quantum Geometric Kohn-Luttinger Superconductivity
- Instantaneous response and quantum geometry of insulators
- The multi-state geometry of shift current and polarization
- Quantum entanglement and quantum geometry measured with inelastic X-ray scattering
- Quantum Metric in Step Response
- Altermagnetic Instabilities from Quantum Geometry
- Quantum Geometry Probed by Chiral Excitonic Optical Response of Chern Insulators
- Dielectric and optical markers originating from quantum geometry
- Optical bounds on many-electron localization
- Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
- Drude weight of an interacting flat-band metal
- Quantum Geometry and the Hidden Scales in Materials
- Scaling of the Integrated Quantum Metric in Disordered Topological Phases
- Detecting the spread of valence band Wannier functions by optical sum rules
- Quantum geometric bounds for observables: Linear responses, Drude weight, and orbital magnetization
- Disorder-Induced Delocalization in Magic-Angle Twisted Bilayer Graphene
- Quantum response theory and momentum-space gravity
- Quantum geometric origin of the Meissner effect and superfluid weight marker
- Thermal and thermoelectric transport in flat bands with non-trivial quantum geometry
- Time-dependent quantum geometric tensor and some applications
- Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
- Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
- Nonadiabatic quantum geometry and optical conductivity
- Superfluid stiffness of superconductors with delicate topology
- Phonon spectra, quantum geometry, and the Goldstone theorem
- Reinforcement Fine-Tuning for Materials Design
- Real space quantum metric of solids
- Theory of thermopolarization effect
- Electronic bounds in magnetic crystals
- Quantum metric driven transition between superfluid and incoherent fluid
- Normal state quantum geometry, non-locality and superconductivity
- Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
- Superconductivity and geometric superfluid weight of a tunable flat band system
- Superconducting Berry Curvature Dipole
- Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
- From Divergent Series to Geometry: Resurgence of the Quantum Metric
- Average density of Bloch electrons in a homogeneous magnetic field: A second-order response