New application of decomposition of U(1) gauge potential:Aharonov-Bohm effect and Anderson-Higgs mechanism

TL;DR

This paper explores the decomposition of U(1) gauge potential in superconductors to analyze the Aharonov-Bohm effect and Anderson-Higgs mechanism, revealing gauge-invariant expressions and new physical effects in ring geometries.

Contribution

It introduces a novel gauge potential decomposition approach to study fundamental superconducting phenomena, providing exact expressions and insights into flux quantization and gauge invariance.

Findings

Derived gauge-invariant expression for transverse gauge potential in A-B experiment

Identified the role of phase gradients in the Anderson-Higgs mechanism

Discovered new effects like flux quantization in superconducting rings

Abstract

In this paper we study the Aharonov-Bohm (A-B) effect and Anderson-Higgs mechanism in Ginzburg-Landau model of superconductors from the perspective of the decomposition of U(1) gauge potential. By the Helmholtz theorem, we derive exactly the expression of the transverse gauge potential $\vec{A}_\perp$ in A-B experiment, which is gauge-invariant and physical. For the case of a bulk superconductor, we find that the gradient of the total phase field $\theta$ provides the longitudinal component ${\vec A}_{\parallel}$, which reflects the Anderson-Higgs mechanism. For the case of a superconductor ring, the gradient of the longitudinal phase field $\theta_1$ provides the longitudinal component ${\vec A}_{\parallel}$, while the transverse phase field $\theta_2$ produces new physical effects such as the flux quantization inside a superconducting ring.