Green's Function Approach to the Edge Spectral Density

TL;DR

This paper demonstrates that conventional many-body Green's function techniques can be adapted to analyze the spectral density of the edge states in quantum Hall systems, providing a new approach to understanding their tunneling properties.

Contribution

It introduces a method to apply standard Green's function techniques to the quantum Hall edge, assuming stable density modes, and derives the spectral density at finite temperature.

Findings

Spectral density at finite temperature derived

Tunneling characteristics of sharp edges analyzed

Method applicable to wide, compressible edges

Abstract

It is shown that the conventional many-body techniques to calculate the Green's functions can be applied to the wide, compressible edge of a quantum Hall bar. The only ansatz we need is the existence of stable density modes that yields a simple equation of motion of the density operators. We derive the spectral density at a finite temperature and show how the tunneling characteristics of a sharp edge can be deduced as a limiting case.