Helical phases and Bogoliubov Fermi surfaces probed by superconducting diode effects

Abstract: Noncentrosymmetric superconductors (NCSs) with Rashba spin-orbit coupling (SOC) and in-plane magnetic fields have emerged as natural platforms for realizing both the bulk superconducting diode effect (SDE) and the Josephson diode effect (JDE) - phenomena characterized by unequal critical currents in opposite directions due to the simultaneous breaking of time-reversal and inversion symmetries. Using the quasiclassical Eilenberger formalism, we systematically investigate both the bulk SDE and the JDE in a clean NCS with Rashba SOC and in-plane magnetic fields. For the bulk system, we find that the diode efficiency can nominally approach its maximal value at the critical endpoint of the first-order Lifshitz transition between weak and strong helical phases featuring finite-momentum Cooper pairs, the latter marked by the emergence of Bogolyubov Fermi surfaces (BFSs). In a Josephson junction, we show that finite-momentum pairing in the superconducting leads is the dominant mechanism behind the JDE in short junctions, whereas in long junctions it is primarily governed by the Zeeman field in the normal region. In the long-junction regime, the diode efficiency additionally oscillates between positive and negative values as a function of magnetic field at low fields, providing a route toward a highly tunable Josephson diode. At higher fields, the onset of BFSs in the strong helical phase leads to a sharp suppression of both the JDE and the Josephson current when the current direction is aligned with momenta along the BFS, resulting in strong anisotropy. We propose that this anisotropy in the Josephson current offers an alternative method for detecting BFSs, applicable to systems with or without a JDE.