Mesoscopic Charge Density Wave in a Magnetic Flux

TL;DR

This paper investigates how a charge density wave in a one-dimensional ring responds to magnetic flux, revealing size and parity-dependent stability and flux effects on the CDW gap and persistent current.

Contribution

It introduces a mean-field analysis of CDW stability in mesoscopic rings, highlighting the influence of electron number parity and size on the gap and current behavior.

Findings

CDW stability depends on electron number parity.

CDW gap varies with flux differently for even and odd N.

Harmonics expansion of persistent current derived with finite gap.

Abstract

The stability of a Charge Density Wave (CDW) in a one-dimensional ring pierced by a Aharonov-Bohm flux is studied in a mean-field picture. It is found that the stability depends on the parity of the number $N$ of electrons. When the size of the ring becomes as small as the coherence length $\xi$, the CDW gap increases for even $N$ and decreases for odd $N$. Then when $N$ is even, the CDW gap decreases with flux but it increases when $N$ is odd. The variation of the BCS ratio with size and flux is also calculated. We derive the harmonics expansion of the persistent current in a presence of a finite gap.