Persistent Current in Metallic Rings and Cylinders

TL;DR

This paper investigates how persistent currents and magnetic responses in mesoscopic metallic rings and cylinders depend on electron number, disorder, and system configuration, revealing exact sign predictions only in specific one-channel cases.

Contribution

It provides a detailed analysis of persistent current behavior in mesoscopic systems, highlighting the dependence on system parameters and the limitations of predicting current sign in multi-channel cylinders.

Findings

Persistent current properties depend on electron number, chemical potential, and disorder.

Exact sign prediction is possible only for one-channel rings with fixed electron number.

Multi-channel cylinders show complex behavior with sign depending on multiple factors.

Abstract

We explore the behavior of persistent current and low-field magnetic response in mesoscopic one-channel rings and multi-channel cylinders within the tight-binding framework. We show that the characteristic properties of persistent current strongly depend on total number of electrons $N_e$, chemical potential $\mu$, randomness and total number of channels. The study of low-field magnetic response reveals that only for one-channel rings with fixed $N_e$, sign of the low-field currents can be predicted exactly, even in the presence of disorder. On the other hand, for multi-channel cylinders, sign of the low-field currents cannot be mentioned exactly, even in the perfect systems with fixed $N_e$ as it significantly depends on the choices of $N_e$, $\mu$, number of channels, disordered configurations, etc.