Tunneling into low-dimensional and strongly correlated conductors

TL;DR

This paper develops a nonperturbative theoretical framework to analyze the low-energy electron propagator and tunneling density of states in strongly correlated low-dimensional systems, capturing phenomena like the pseudogap in quantum Hall fluids.

Contribution

It introduces a versatile method using Hubbard-Stratonovich transformation and saddle-point approximation to compute the electron density of states in various strongly correlated systems.

Findings

Exact density of states for the Tomonaga-Luttinger model

Reproduction of the pseudogap in fractional quantum Hall fluids

Demonstration of the method's applicability to models of any dimensionality

Abstract

A general nonperturbative theory of the low-energy electron propagator is developed and used to calculate the single-particle density of states in a variety of systems. This method involves the decoupling of the electron-electron interaction through a Hubbard-Stratonovich transformation, followed by a saddle-point approximation of the remaining functional integral. The final expression is found to be the tunneling analog of the infrared catastrophe that occurs in the x-ray edge problem; here, the host system responds to the potential produced by the abrupt addition of an electron during a tunneling event. This response can lead to a suppression in the tunneling density of states near the Fermi energy. This method is adaptable to lattice or continuum models of any dimensionality, with or without translational invariance. When applied, the exact density of states is obtained for the Tomonaga-Luttinger model, and the pseudogap of a fractional quantum Hall fluid is recovered.