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

TL;DR

This paper proposes using acoustic waves as a gravitational-like probe to study the dynamical geometrical response of fractional quantum Hall liquids, revealing collective modes via spectroscopic methods.

Contribution

It generalizes Haldane's geometrical description to time-dependent metrics, enabling experimental access to quantum Hall collective modes through acoustic or gravitational wave analogs.

Findings

Identification of coupling between acoustic waves and collective modes

Proposal of spectroscopic detection of graviton-like excitations

Extension of geometrical framework to dynamical metrics

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.