Two-loop approximation in the Coulomb blockade problem

TL;DR

This paper investigates Coulomb blockade oscillations in a metallic grain with high conductance, using instanton analysis and renormalization group methods to refine the understanding of temperature dependence and ground state energy effects.

Contribution

It introduces a two-loop approximation approach to analyze Coulomb blockade oscillations, providing new insights into their temperature dependence and ground state energy behavior.

Findings

Derived the temperature dependence of CB oscillation amplitude.

Estimated the ground state energy oscillation magnitude.

Identified deviations from previous theoretical results.

Abstract

We study Coulomb blockade (CB) oscillations in the thermodynamics of a metallic grain which is connected to a lead by a tunneling contact with a large conductance $g_0$ in a wide temperature range, $E_Cg_0^4 e^{-g_0/2}<T<E_C$, where $E_C$ is the charging energy. Using the instanton analysis and the renormalization group we obtain the temperature dependence of the amplitude of CB oscillations which differs from the previously obtained results. Assuming that at $T < E_Cg_0^4 e^{-g_0/2}$ the oscillation amplitude weakly depends on temperature we estimate the magnitude of CB oscillations in the ground state energy as $E_Cg_0^4 e^{-g_0/2}$.