Tunneling in the Electron Box in the Nonperturbative Regime

TL;DR

This paper investigates the effects of tunneling and charge screening in the single electron box, revealing how virtual tunneling and strong coupling influence charge states and tunneling strength, with implications for superconducting junctions.

Contribution

It introduces a unified scaling approach for tunneling effects in the nonperturbative regime, including strong coupling and superconducting cases, supported by Monte Carlo simulations.

Findings

Charge screening is strong near degeneracy even with weak tunneling.

Virtual tunneling reduces level splitting and tunneling strength.

Strong-coupling scaling renormalizes effective capacitance.

Abstract

We study charging effects and tunneling in the single electron box. Tunneling mixes different charge states and in the nonperturbative regime the charge in the island may be strongly screened. When charge states are nearly degenerate the screening of the charge is strong even in the weak tunneling regime. Virtual tunneling processes reduce both the level splitting and the tunneling strength. The charge on the island and the decay rates are calculated. In the strong tunneling regime also nondegenerate states are affected by tunneling. Strong-coupling scaling renormalizes the effective capacitance, a result which we confirm by Monte Carlo simulations. The tunneling strength scales to smaller values into the regime where the weak-coupling scaling applies. We propose a two stage scaling procedure providing the unified picture for the problem. The scaling analysis is also extended to superconducting tunnel junctions with finite subgap conductance. (9 figures upon request)