Supercurrent without a spatially varying phase or a vector potential from time-reversal and inversion symmetries breaking in superconductors

The superconducting state allows materials to lose electrical resistance and have a current flowing without energy dissipation – a supercurrent. Conventional superconductors require a spatially varying phase to generate a supercurrent, and this is achieved by Josephson junctions. In contrast, asymmetric superconductors promise to give a supercurrent in the absence of a vector potential or varying phase. To start off, the supercurrent density and Josephson effects of an asymmetric superconductor were derived by solving the system’s time-dependent Schrodinger equation. In addition, Ginzburg-Landau equations were also derived by minimizing the free enthalpy of an asymmetric superconductor. Finally, the expectation value of the supercurrent operator was obtained by operator algebra using Bogoliubov de Gennes formalism. As a result, we estimated the contribution of the asymmetric supercurrent density from specific non-centrosymmetric superconductors in a finite lattice across a large variety of parameters.