Geometric response of quantum Hall states to electric fields
arXiv:1812.04000 · doi:10.1103/PhysRevB.103.155303
Abstract
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the characteristic geometry of electronic motion in the presence of magnetic and electric fields. The geometric picture we provide motivates the following conjecture: non-uniform electric fields mimic the presence of spatial curvature. Consequently, the gravitational coupling constant also appears in the charge response to non-uniform electric fields.
References in corpus (18)
- The quantum spin Hall effect and topological insulators
- Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
- Viscosity of Quantum Hall Fluids
- Geometrical Description of the Fractional Quantum Hall Effect
- Hall Viscosity and Electromagnetic Response
- Disordered Topological Insulators via -Algebras
- Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
- Topological Insulators and C^*-Algebras: Theory and Numerical Practice
- Finite-Wavevector Electromagnetic Response of Fractional Quantized Hall States
- Geometry of Quantum Hall States: Gravitational Anomaly and Kinetic Coefficients
- Geometric adiabatic transport in quantum Hall states
- Quantum Hall effect and Quillen metric
- Landau Level Mixing and Levitation of Extended States in Two Dimensions
- Random normal matrices, Bergman kernel and projective embeddings
- Fractional charge and inter-Landau level states at points of singular curvature
- Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime
- Semiclassical theory of viscosity in quantum Hall states
- Gauge-Invariant Variables Reveal the Quantum Geometry of Fractional Quantum Hall States