Charge Density Wave Behaviour of the Integer Quantum Hall Effect Edge States

TL;DR

This paper investigates how Coulomb interactions influence edge excitations in the integer quantum Hall effect, revealing a charge density wave behavior with unique spectral properties and zero conductance in long systems.

Contribution

It demonstrates that long-range Coulomb interactions induce a charge density wave state in quantum Hall edge excitations, a novel insight into edge state behavior.

Findings

Edge excitations exhibit quasi-long range order similar to a charge density wave.

Spectral density vanishes at zero frequency and increases faster than any power law with frequency.

Conductance of an infinitely long system is zero.

Abstract

We analyze the effect that the Coulomb interaction has on the edge excitations of an electron gas confined in a bar of thickness $W$, and in presence of a magnetic field corresponding to filling factor 1 Quantum Hall effect. We find that the long-range interaction between the edges leads the system to a ground state with a quasi-long range order, similar to a Charge Density Wave. The spectral density of states vanishes at zero frequency, and increases with frequency faster than any power law, being the conductance of a infinite long system zero.