Fulde–Ferrell State in Spin–Orbit-Coupled Superconductor: Application to Dresselhaus SOC

We show that in the presence of magnetic field, two superconducting phases with the center-of-mass momentum of Cooper pair parallel to the magnetic field are induced in Dresselhaus spin–orbit-coupled superconductor. Specifically, at small magnetic field, the center-of-mass momentum is induced due to the energy-spectrum distortion and no unpairing region with vanishing singlet correlation appears. We refer to this superconducting state as the drift-BCS state. By further increasing the magnetic field, the superconducting state falls into the Fulde–Ferrell state with the emergence of the unpairing regions. The observed abrupt enhancement of the center-of-mass momenta and suppression on the order parameters during the transition indicate the occurrence of a first-order phase transition. Enhanced Pauli limit and hence enlarged magnetic-field regime of the Fulde–Ferrell state, due to the spin-flip terms of the spin–orbit coupling, are revealed. We also address the triplet correlations induced by the spin–orbit coupling, and show that the Cooper-pair spin polarizations, generated by the magnetic field and center-of-mass momentum with the triplet correlations exhibit totally different magnetic-field dependences between the drift-BCS and Fulde–Ferrell states.