Theory of Supercurrent in Superconductors

Abstract

In the standard theory of superconductivity, the origin of superconductivity is the electron-pairing. The induced current by a magnetic field is calculated by the linear response to the vector potential, and the supercurrent is identified as the dissipationless flow of the paired-electrons, while single electrons flow with dissipation. This supercurrent description suffers from the following serious problems: 1) it contradicts the reversible superconducting-normal phase transition in a magnetic field observed in type I superconductors; 2) the gauge invariance of the supercurrent induced by a magnetic field requires the breakdown of the global $U(1)$ gauge invariance, or the non-conservation of the particle number; 3) the explanation of the ac Josephson effect is based on the boundary condition that is different from the real experimental one. We will show that above problems are resolved if the supercurrent is attributed to the collective mode arising from the Berry connection for many-body wave functions. The problem 1) is resolved by attributing the appearance and disappearance of the supercurrent to the abrupt appearance and disappearance of topologically-protected loop currents produced by the Berry connection; the problem 2) is resolved by assigning the non-conserved number to that for the particle number participating in the collective mode produced by the Berry connection; and the problem 3) is resolved by identifying the relevant phase in the Josephson effect is that arising from the Berry connection, and using the modified Bogoliubov transformation that conserves the particle number.

References in corpus (4)

• Momentum of superconducting electrons and the explanation of the Meissner effect
• Spin polarization in the Hubbard model with Rashba spin-orbit coupling on a ladder
• Inconsistency of the conventional theory of superconductivity
• Entropy generation and momentum transfer in the superconductor-normal and normal-superconductor phase transformations and the consistency of the conventional theory of superconductivity

Cited by in corpus (6)

• Interplay between band structure and Hund's correlation to increase T${}_c$ in FeSe
• London moment, London's superpotential, Nambu-Goldstone mode, and Berry connection from many-body wave functions
• Schroedinger representation of quantum mechanics, Berry connection, and superconductivity
• Constrained Hamiltonian dynamics for electrons in magnetic field and additional forces besides the Lorentz force acting on electrons
• Two-fluid Physical Modeling of Superconducting Resonators in the ARTEMIS Framework
• Berry connection from many-body wave functions and superconductivity: Calculations by the particle number conserving Bogoliubov-de Gennes equations