The Single-Electron-Box and the Helicity Modulus of an inverse square XY-Model

TL;DR

This paper investigates how the average electron number in a single-electron box varies with gate voltage across different tunneling conductances, linking it to the helicity modulus of a classical inverse square XY-model, and employs multiple methods for a comprehensive analysis.

Contribution

It introduces a combined approach using perturbation theory, renormalization group, and Monte Carlo simulations to describe Coulomb staircase smearing at zero temperature.

Findings

Quantitative description of Coulomb staircase smearing with conductance increase

Connection established between single-electron box behavior and XY-model helicity modulus

Validation of theoretical predictions through Monte Carlo simulations

Abstract

We calculate the average number of electrons on a metallic single-electron-box as a function of the gate voltage for arbitrary values of the tunneling conductance. In the vicinity of the plateaus the problem is equivalent to calculating the helicity modulus of a classical inverse square XY-model in one dimension. By a combination of perturbation theory, a two-loop renormalization group calculation and a Monte-Carlo simulation in the intermediate regime we provide a complete description of the smearing of the Coulomb staircase at zero temperature with increasing conductance.