Coulomb Blockade of Proximity Effect at Large Conductance

TL;DR

This paper investigates how Coulomb interactions affect the proximity-induced minigap in a normal dot coupled to a superconductor, providing exact formulas and revealing a transition from proximity to Coulomb gap regimes.

Contribution

It derives exact expressions for thermodynamic and tunneling minigaps as functions of capacitance, highlighting the crossover between proximity effect and Coulomb blockade regimes.

Findings

Tunneling minigap varies from proximity-induced to Coulomb gap with interaction strength.

Predicted a non-universal two-step structure in the density of states.

Analyzed charge quantization effects in the quantum dot.

Abstract

We consider the proximity effect in a normal dot coupled to a bulk superconducting reservoir by the tunnel contact with large normal conductance. Coulomb interaction in the dot suppresses the proximity minigap induced in the normal part of the system. We find exact expressions for the thermodynamic and tunneling minigaps as functions of the junction's capacitance. The tunneling minigap interpolates between its proximity-induced value in the regime of weak Coulomb interaction to the Coulomb gap in the regime of strong interaction. In the intermediate case a non-universal two-step structure of the tunneling density of states is predicted. The charge quantization in the dot is also studied.