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Pauli paramagnetism of triplet Cooper pairs in a nematic superconductor

We investigate the response of a doped topological insulator Bi$_2$Se$_3$ with spin-triplet nematic superconductivity to external magnetization. We calculate the Zeeman part of magnetic susceptibility for nematic and chiral superconducting phases near T$_c$ in Ginzburg-Landau formalism. Superconducting order parameter from $E_u$ representation has non-trivial coupling with the transversal Zeeman field that results in a paramagnetic response to a magnetization. The topology of a Fermi surface has a strong influence on magnetic susceptibility. Lifshitz transition from closed to open Fermi surface eventually leads to 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 found that in a real system, electron-electron interaction can drive nematic to chiral phase only in the vicinity of the phase transition. We compare our results with the existing experimental data.