Magnetic-field-induced helical and stripe phases in Rashba superconductors

Abstract

Due to the lack of both parity and time-reversal symmetries, the Rashba superconductors $\mathrm{Ce}{\mathrm{Pt}}_{3}\mathrm{Si}$, $\mathrm{Ce}\mathrm{Rh}{\mathrm{Si}}_{3}$, and $\mathrm{Ce}\mathrm{Ir}{\mathrm{Si}}_{3}$, in the presence of a magnetic field, are unstable to helical (single plane wave) order. We develop a microscopic theory for such superconductors and examine the stability of this helical phase. We show that the helical phase typically occupies most of the magnetic field--temperature phase diagram. However, we also find that this phase is sometimes unstable to a multiple-$q$ phase (loosely called a stripe phase), in which both the magnitude and the phase of the order parameter are spatially varying. We find the position of this helical to multiple-$q$ phase transition. We further examine the density of states and identify features unique to the helical phase.