Nonlinear diode effect and Berezinskii-Kosterlitz-Thouless transition in purely two-dimensional noncentrosymmetric superconductors

Phase diagrams and electronic transport properties of the helical states in purely two-dimensional (2D) Rashba superconductors coupled with in-plane Zeeman fields are studied. The continuum XY action is derived microscopically by integrating out the Gaussian amplitude fluctuation from the effective action. We show that the superfluid stiffness obtained from this procedure is exactly equivalent to the second-order derivative of the mean-field free-energy density with respect to Cooper pair momentum, indicating an essential role of the amplitude fluctuation. The vortex core energy is also included in this work, and its effects on the Berezinskii-Kosterlitz-Thouless (BKT) transition line are discussed. The theory of nonlinear $V\text{\ensuremath{-}}I$ characteristics in purely 2D superconductors is also revised to incorporate recent developments in the theory of the superconducting diode effect. The main results are as follows. We find that the nonlinear $V\text{\ensuremath{-}}I$ characteristics of the system become nonreciprocal in finite in-plane Zeeman fields. This is reminiscent of the superconducting diode effect in 2D systems, although the critical current is zero in purely 2D superconductors. Furthermore, we find that the bare effective superfluid stiffness along the BKT transition line has a local minimum at a certain temperature, and the nonreciprocity of the $V\text{\ensuremath{-}}I$ characteristics is strongly enhanced around this temperature.