How general is Legett's conjecture for a mesoscopic ring?

TL;DR

This paper investigates how multiple topological defects in mesoscopic rings can disrupt Legett's conjecture by causing discontinuous phase changes in electron wavefunctions, especially when defect ratios vary.

Contribution

It demonstrates that many small topological defects can significantly violate Legett's conjecture, extending previous single-defect studies and explaining the physical mechanisms involved.

Findings

Multiple defects can destroy the parity effect.

Discontinuous phase changes occur at specific defect ratios.

Legett's conjecture may not hold in complex defect scenarios.

Abstract

It has been shown[19] that in a loop of length u to which a single stub of length v is attached (fig. 1 in ref. 19), the parity effect is completely destroyed when v/u$>2$. It was also shown that such minute topological defects (v/u$<<1$) act as singular perturbations. However ref. 19 studies the effect of a single topological defect and says that for v/u$<<1$ parity effect is not violated in the ring. In this paper we show that topological defects of the type v/u$<<1$ can also violate the parity effect depending on the exact value of v/u and the parity effect is significantly destroyed if we have many such geometric scatterers. This paper brings out the physical reasons for the destruction of parity effect. We show that the generic feature of topological defects as this is that they can produce discontinuous phase change (due to change in energy) of the electron wavefunction in the ring for special value of v/u and then Legett's cojecture breaks down. This may have implications on the experimental observations.