Topological effects on magnitude of persistent current in a ring

TL;DR

This paper investigates how defects in one-dimensional rings affect persistent currents and conductance, revealing that defects significantly reduce conductance but have a lesser impact on persistent currents, due to dimensional effects on electron localization.

Contribution

It demonstrates the differential impact of defects on conductance and persistent currents in 1D rings, highlighting the role of boundary conditions and dimensionality.

Findings

Defects greatly reduce conductance in 1D rings.

Persistent currents are less affected by defects than conductance.

Dimensionality influences electron localization and transport properties.

Abstract

We show that defects in 1D rings decrease the conductance (when the ring is opened up) many more times than it decreases the persistent currents. This means that the states in such a 1D ring are very sensitive to twisting of boundary condition but conductance of the system is small. In 1D the electron effectively sees a periodic potential and escapes localization. This does not happen in higher dimensions. This helps us to understand the simulations of G. Kirczenow[13] and also suggests that a rough boundary in a 3D ring that provide effectively a strong 1D potential to the electron will have this type of different effects on conductance and persistent currents.