Finite momentum superconductivity in superconducting hybrids: Orbital mechanism

Normally, in superconductors, as in conductors, in a state with zero current $I$ the momentum of superconducting electrons $\ensuremath{\hbar}q=0$. Here we demonstrate theoretically and present experimental evidence that in a superconducting/normal metal (SN) hybrid strip placed in an in-plane magnetic field ${B}_{\mathrm{in}}$ a finite momentum state ($\ensuremath{\hbar}q\ensuremath{\ne}0$) is realized when $I=0$. This state is characterized by current-momentum dependence $I(q)\ensuremath{\ne}\ensuremath{-}I(\ensuremath{-}q)$, nonreciprocal kinetic inductance ${L}_k(I)\ensuremath{\ne}{L}_k(\ensuremath{-}I)$, and different values of depairing currents ${I}_{\mathrm{dep}}^{\ifmmode\pm\else\textpm\fi{}}$ flowing along the SN strip in opposite directions. The properties found have orbital nature and originate from the density gradient of superconducting electrons $\ensuremath{\nabla}n$ across the thickness of the SN strip and field-induced Meissner currents. We argue that this type of finite momentum state should be a rather general phenomenon in superconducting structures with artificial or intrinsic inhomogeneities.