Kramers Fulde-Ferrell state and superconducting spin diode effect

We study a novel equal-spin pairing state with opposite center-of-mass momentum for each spin polarization. This state, dubbed a Kramers Fulde-Ferrell (KFF) state, respects time-reversal symmetry and can be realized in a one-dimensional system with spin-orbit coupling and nearest-neighbor attraction. We find that the KFF state supports nonreciprocal spin transport for both bulk superconductor and Josephson junctions. In addition to the spin Josephson diode effect, the charge transport is controlled by intriguing dynamics of bound states whose transitions can be manipulated by the length of the KFF superconductor. The KFF state is relevant for embedded quantum structures in monolayer Fe-based superconductors and dissipationless superconducting spintronics.