Acoustic Wave Absorption as a Probe of Dynamical Geometrical Response of Fractional Quantum Hall Liquids

Abstract

We show that acoustic crystalline wave gives rise to an effect similar to that of a gravitational wave to an electron gas. Applying this idea to a two-dimensional electron gas in the fractional quantum Hall regime, this allows for experimental study of its dynamical gravitational response. To study such response we generalize Haldane's geometrical description of fractional quantum Hall states to situations where the external metric is time-dependent. We show that such time-dependent metric (generated by acoustic or effective gravitational wave) couples to collective modes of the system, including a quadrapolar mode similar to graviton at long wave length, and magneto-roton at finite wave length. Energies of these modes can be revealed in spectroscopic measurements. We argue that such gravitational probe provides a potentially highly useful alternative probe of quantum Hall liquids, in addition to the usual electromagnetic response.

5 pages with two figures. Published version

References in corpus (13)

• Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
• Thermal Hall Effect and Geometry with Torsion
• Density-curvature response and gravitational anomaly
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Geometry of Fractional Quantum Hall Fluids
• Geometry of Quantum Hall States: Gravitational Anomaly and Kinetic Coefficients
• Transference of Transport Anisotropy to Composite Fermions
• Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions
• Splitting of Long-Wavelength Modes of the Fractional Quantum Hall Liquid at $\nu =1/3$
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect

Cited by in corpus (20)

• Quantum Nanophotonics in Two-Dimensional Materials
• Bimetric Theory of Fractional Quantum Hall States
• Chiral Gravitons in Fractional Quantum Hall Liquids
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Evidence of a fractional quantum Hall nematic phase in a microscopic model
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• Quantum chaos associated with emergent ergosurface in transition layer between type-I and type-II Weyl semimetals
• Hyperbolic Fractional Chern insulators
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Geometry of flux attachment in anisotropic fractional quantum Hall states
• Interaction-dependent anisotropy of fractional quantum Hall states
• A numerical study of bounds in the correlations of fractional quantum Hall states
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Chiral Gravitons on the Lattice
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators