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

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.