Abstract:

The discovery of nematic triplet superconductivity in doped topological insulators CuxBi₂Se₃ triggers interest in the identification of the d-vector of the triplet, which is related to the antinodal direction of the gap function and determines whether the superconductor is topological. We perform self-consistent analysis of the vortex state properties in a nematic spin-triplet p_x-wave superconductor. We first derive a Ginzburg-Landau theory to determine the shape of the vortex and vortex lattice. We find the spatial profile of the isolated vortex is elongated along the antinodal direction, and the vortex lattice is a distorted triangular lattice elongated along x, becoming square in the specific case of a small circular Fermi surface. Finally, we calculate the local density of states self-consistently for an isolated vortex and the vortex lattice using the microscopic Bogoliubov-de Gennes equation. We find that the profile of the local density of states at low in-gap energies is always elongated along the antinodal direction. Our findings are valuable for the experimental detection of the antinodal direction of the gap function in nematic triplet superconductors, and subsequently the identification of the topological character of the superconducting state as in CuxBi₂Se₃.

Key words: p_x-wave superconductivity, Ginzburg-Landau theory, Bogoliubov-de Gennes equation, vortex, vortex lattice