Dynamical properties of a two-dimensional electron gas in a magnetic field within the composite fermion model

TL;DR

This paper studies the dynamic response of a two-dimensional electron gas in the fractional quantum Hall regime using the composite fermion model, revealing effects like orthogonality catastrophe and proposing an experiment to measure composite fermion mass.

Contribution

It introduces a detailed analysis of the spectral function and response of composite fermions, highlighting differences at various filling factors and suggesting a tunneling experiment to measure effective mass.

Findings

Orthogonality catastrophe occurs at even-denominator filling factors due to compressibility.

No catastrophe at odd-denominator filling factors because of excitation gaps.

Oscillations in spectral function at integer filling relate to composite fermion cyclotron energy.

Abstract

We investigate the response of a two-dimensional electron gas, in the fractional quantum Hall regime, to the sudden appearance of a localised charged probe using the Chern-Simons theory of composite fermions. The dynamic structure factor of the electron gas is found to have a major influence on the spectral function of the probe. In particular, there is an orthogonality catastrophe when the filling factor is an even-denominator filling fraction due to the compressibility of the state, but there is no catastrophe at odd-denominator filling factors because these states have a gap to excitations. The catastrophe is found to be more severe for composite fermions in zero effective magnetic field than it is for electrons in zero real magnetic field. Oscillations in the spectral function, arising when the composite fermions are at integer filling, have a period equal to the composite fermion cyclotron energy. We propose a tunneling experiment which directly measures the spectral function from which one could determine the composite fermion effective mass.