Superconductivity by Berry Connection from Many-body Wave Functions: Revisit to Andreev−Saint-James Reflection and Josephson Effect

Abstract

Although the standard theory of superconductivity based on the BCS theory is a successful one, several experimental results indicate the necessity for a fundamental revision. We argue that the revision is on the origin of the phase variable for superconductivity; this phase appears as a consequence of the electron-pairing in the standard theory, but its origin is a Berry connection arising from many-body wave functions. When this Berry connection is non-trivial, it gives rise to a collective mode that generates supercurrent; this collective mode creates number-changing operators for particles participating in this mode, and these number-changing operators stabilize the superconducting state by exploiting the Cooper instability. In the new theory, the role of the electron-pairing is to stabilize the nontrivial Berry connection; it is not the cause of superconductivity. In BCS superconductors, however, the simultaneous appearance of the nontrivial Berry connection and the electron-pairing occurs. Therefore, the electron-pairing amplitude can be used as an order parameter for the superconducting state. We revisit the Andreev−Saint-James reflection and the Josephson effect. They are explained as consequences of the presence of the Berry connection. Bogoliubov quasiparticles are replaced by the particle-number conserving Bogoliubov excitations that describe the transfer of electrons between the collective and single-particle modes. There are two distinct cases for the Josephson effect; one of them contains the common Bogoliubov excitations for the two superconductors in the junction, and the other does different Bogoliubov excitations for different superconductors. The latter case is the one considered in the standard theory; in this case, the Cooper pairs tunnel through without Bogoliubov excitations, creating an impression that the supercurrent is a flow of Cooper pairs; however, it does not explain the observed ac Josephson effect under the experimental boundary condition. On the other hand, the former case explains the ac Josephson effect under the experimental boundary condition. In this case, it is clearly shown that the supercurrent is a flow of electrons brought about by the non-trivial Berry connection which provides an additional U(1) gauge field besides the electromagnetic one.