Supergap anomalies in cotunneling between N-S and between S-S leads via a small quantum dot

TL;DR

This paper investigates nonanalytic anomalies in cotunneling currents through a quantum dot connected to normal and superconducting leads, revealing threshold behaviors and the influence of density of states on inelastic transport.

Contribution

It provides a detailed analysis of threshold anomalies in cotunneling involving superconducting leads, highlighting the effects of density of states and inelastic processes.

Findings

Threshold bias voltages for inelastic cotunneling are V_c=3Δ for N-S and 4Δ for S-S cases.

Current exhibits nonanalytic behavior near thresholds, proportional to (V-V_c)^{3/2} and (V-tilde{V}_c).

Enhanced density of states at the gap edges amplifies anomalies, especially in S-S lead configurations.

Abstract

Cotunneling current through a resonant level coupled to either normal and superconducting or to two superconducting leads is studied for the domain of bias voltages, V, exceeding the superconducting gap, 2\Delta. Due to the on-site repulsion in the resonant level, cotunneling of an electron is accompanied by creation of a quasiparticle in a superconducting lead. Energy conservation imposes a threshold for this inelastic transport channel: V_c=3\Delta for N-S case and \tilde{V}_c=4\Delta for the S-S case. We demonstrate that the behavior of current near the respective thresholds is nonanalytic, namely, \delta I^{in}(V)\propto (V-V_c)^{3/2}\Theta(V-V_c) and \delta I^{in}(V) \propto (V-\tilde{V}_c)\Theta(V-\tilde{V}_c). Stronger anomaly for the S-S leads is the consequence of the enhanced density of states at the edges of the gap. In addition, the enhanced density of states makes the threshold anomalies for two-electron cotunneling processes in the Coulomb-blockaded regions more pronounced than for the N-N leads.