On the impact of surface defects on a condensate of electron pairs in a quantum wire

TL;DR

This paper models how surface defects affect electron pair condensation in quantum wires, showing that defects can destroy or recover the condensate depending on pair density and defect quantity.

Contribution

It introduces a mathematical model to analyze surface defect effects on electron pair condensates, including conditions for destruction and recovery of the condensate.

Findings

Surface defects can destroy the condensate in non-interacting systems.

Repulsive interactions can restore the condensate above a critical density.

The model quantifies the impact of defect quantity on condensate stability.

Abstract

In this paper we are interested in understanding the impact of surface defects on a condensate of electron pairs in a quantum wire. Based on previous results we establish a simple mathematical model in order to account for such surface effects. For a system of non-interacting pairs, we will prove the destruction of the condensate in the bulk. Finally, taking repulsive interactions between the pairs into account, we will show that the condensate is recovered for pair densities larger than a critical one given the number of the surface defects is not too large.