Coulomb Zero-Bias Anomaly: A Semiclassical Calculation

TL;DR

This paper develops a semiclassical approach to analyze the Coulomb zero-bias anomaly, especially near zero bias where traditional perturbation methods fail, by relating it to electrodynamics in imaginary time and exact conductivity.

Contribution

It introduces a semiclassical method for Coulomb blockade problems that accurately captures strong coupling effects and relates the anomaly to critical exponents at the metal-insulator transition.

Findings

Derived exact relation between anomaly and conductivity exponent.

Compared semiclassical results with perturbation theory for diffusive systems.

Provided a framework for analyzing Coulomb anomalies at the metal-insulator transition.

Abstract

Effective action is proposed for the problem of Coulomb blocking of tunneling. The approach is well suited to deal with the ``strong coupling'' situation near zero bias, where perturbation theory diverges. By a semiclassical treatment, we reduce the physics to that of electrodynamics in imaginary time, and express the anomaly through exact conductivity of the system $\sigma(\omega, q)$ and exact interaction. For the diffusive anomaly, we compare the result with the perturbation theory of Altshuler, Aronov, and Lee. For the metal-insulator transition we derive exact relation of the anomaly and critical exponent of conductivity.