Impact of electrostatic fields in layered crystalline BCS superconductors

TL;DR

This study investigates how strong electrostatic fields affect the superconducting gap in layered crystalline BCS superconductors, revealing increased sensitivity under reduced pairing strength and surface effects.

Contribution

It provides a self-consistent numerical analysis of electrostatic field effects on the superconducting gap, highlighting the role of pairing strength and surface modifications.

Findings

Increased gap sensitivity with reduced pairing strength.

Observation of sudden rises and falls in the gap.

Effect diminishes with stronger pairing or disorder.

Abstract

Motivated by recent experiments reporting the suppression of the critical current in superconducting Dayem bridges by the application of strong electrostatic fields, in this work we study the impact on the superconducting gap of charge redistribution in response to an applied electric field in thin crystalline metals. By numerically solving the BCS gap equation and the Poisson equation in a fully self-consistent way, we find that by reducing the pairing strength we observe an increased sensitivity of the gap on the applied field, showing sudden rises and falls that are compatible with surface modifications of the local density of states. The effect is washed out by increasing the pairing strength towards the weak-to-moderate coupling limit or by introduction of a weak smearing in the density of states, showing the evolution from a clean crystal to a weakly disordered metal.