Dynamical Properties of Quantum Hall Edge States

TL;DR

This paper investigates the dynamical behavior of quantum Hall edge states, focusing on orthogonality catastrophe, tunneling phenomena, and optical responses, revealing how these properties depend on the filling fraction and phase shifts.

Contribution

It provides a detailed analysis of the dynamical responses of quantum Hall edge states, including orthogonality catastrophe and tunneling characteristics, with new insights into their dependence on filling fraction and phase shifts.

Findings

Orthogonality catastrophe occurs with a specific power-law dependence on system size.

Tunneling from Fermi liquids to QH edges is suppressed at low temperatures.

Nonlinear I-V characteristics follow a power law with exponent related to the filling fraction.

Abstract

We consider the dynamical properties of simple edge states in integer ($\nu = 1$) and fractional ($ \nu = 1/2m+1$) quantum Hall (QH) liquids. The influence of a time-dependent local perturbation on the ground state is investigated. It is shown that the orthogonality catastrophe occurs for the initial and final state overlap $|<i|f>| \sim L^{-{1\over{2\nu}}({\delta\over{\pi}})^2}$ with the phase shift $\delta$. The transition probability for the x-ray problem is also found with the index, dependent on $\nu$. Optical experiments that measure the x-ray response of the QH edge are discussed. We also consider electrons tunneling from one dimensional Fermi liquid into a QH fluid. It is argued that for any filling fraction the tunneling from a Fermi liquid to the QH edge is suppressed at low temperatures and we find the nonlinear $I-V$ characteristics $I\sim V^{1/\nu}$.