Collective Modes and Electronic Spectral Function in Smooth Edges of Quantum Hall Systems

TL;DR

This paper develops a microscopic theory for collective modes at smooth quantum Hall edges, analyzing their bosonic nature and calculating the electronic spectral function, revealing distinct tunneling behavior from sharp edges.

Contribution

It introduces a microscopic model for smooth edge modes in quantum Hall systems and connects it to bosonization, extending understanding beyond sharp edge approximations.

Findings

Collective modes can be described as independent bosons under certain conditions.

Spectral function calculations show power-law tunneling behavior at low voltage.

Exponents differ significantly from sharp edge models.

Abstract

We present a microscopic theory of the collective modes of a ``smooth'' edge of a quantum Hall system, showing under what conditions these modes can be described as a set of independent bosons. We then calculate the electronic spectral function in an independent-boson model - a procedure that reduces to standard bosonization in the limit of ``sharp'' edge. The I-V tunneling characteristics deduced from this model exhibit, for low voltage, a power law behavior, with exponents that differ significantly from those of the sharp edge model.