Current precision in interacting hybrid Normal-Superconducting systems

TL;DR

This paper investigates how Coulomb interactions affect transport and fluctuations in normal-superconducting quantum-dot systems, revealing reduced current precision and thermodynamic bound modifications due to interactions.

Contribution

It introduces a generalized master equation approach to analyze interaction effects on Andreev transport, fluctuation properties, and thermodynamic bounds in hybrid systems.

Findings

Coulomb interactions renormalize resonant conditions and suppress superconducting coherence.

Interactions lead to a significant reduction in current precision, especially at high temperatures.

The hybrid thermodynamic bound remains satisfied despite interactions, unlike the quantum bound.

Abstract

We study Andreev-mediated transport and current fluctuations in interacting normal-superconducting quantum-dot systems. Using a generalized master equation based on real-time diagrammatics and full counting statistics, we compute the steady-state current, zero-frequency noise, and rate of entropy production in the large superconducting-gap limit. We show how Coulomb interactions modify Andreev-mediated transport by renormalizing resonant conditions and suppressing superconducting coherence, leading to a pronounced reduction of current precision even when average currents are only weakly affected. These effects are particularly evident at high temperatures, where conventional Coulomb-blockade features are thermally smeared while fluctuation properties remain highly sensitive. By analyzing thermodynamic uncertainty relations, we demonstrate that violations of the quantum bound present in the noninteracting regime are progressively reduced and eventually suppressed as interactions increase, whereas the recently proposed hybrid bound remains satisfied. Our results clarify how Coulomb interactions, and nonequilibrium fluctuations jointly determine transport properties in hybrid superconducting devices, and establish current precision as a robust benchmark for interacting Andreev transport beyond the noninteracting limit.