Pauli paramagnetism of triplet Cooper pairs in a nematic superconductor

Abstract

We investigate the response of a doped topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ with spin-triplet nematic superconductivity to external magnetization. We calculate the Zeeman part of the magnetic susceptibility for nematic and chiral superconducting phases near ${T}_{c}$ in the Ginzburg-Landau formalism. The superconducting order parameter from the ${E}_{u}$ representation has nontrivial coupling with the transversal Zeeman field that results in a paramagnetic response to magnetization. The topology of a Fermi surface has a strong influence on magnetic susceptibility. The Lifshitz transition from a closed to open Fermi surface eventually leads to a phase transition from the nematic to chiral phase. At the transition point, magnetic susceptibility diverges. Also, we study the effects of the electron-electron interaction on the competition between nematic and chiral phases. We find that in a real system, electron-electron interaction can drive the nematic to chiral phase only in the vicinity of the phase transition. We compare our results with the existing experimental data.