Spin-triplet pair density wave superconductors

Recent experiments have shown that the nonzero center of mass momentum pair density wave (PDW) is a widespread phenomenon observed over different superconducting materials. However, concrete theoretical model realizations of the PDW order have remained elusive. Here, we study a one-dimensional model with nearest-neighbor pairing attraction, i.e. a spinful Kitaev chain, under generic spin-orbit couplings such that the spin-rotation symmetry is fully broken. The most general superconducting order parameter is described by a spatial dependent di-vector. We show that a spin-triplet pair density wave (t-PDW) emerges in the ground state and occupies a large part of the phase diagram. The di-vector of the t-PDW rotates with a pitch Qpdw along the chain and spans an ellipsoid. The pure t-PDW is fully gapped and realizes a class-DIII topological superconductor, characterized by two Majorana zero modes localized at each end of the chain and protected by time-reversal symmetry. Our findings reveal unprecedented insights into the exotic pure PDW superconductor and provide a possible explanation for the one-dimensional PDW detected along domain walls in monolayer iron-based superconductor Fe(Te,Se) and potentially realizable using other quantum structures in unconventional superconductors. Recent experiments suggest that pair-density wave (PDW) states can occur in various superconductors, yet concrete theoretical models remain rare. Here, the authors introduce a simple 1D model where spin-orbit coupling and interactions stabilize a topological, spin-triplet PDW order.