Theory of nematic superconductivity in doped topological insulators (brief review)

Theoretical studies of the theory of nematic superconductivity in doped insulators of the Bi$_2$Se$_3$ family have been reviewed. It is experimentally shown that their transition to the superconducting state is accompanied by spontaneous rotational symmetry breaking. This superconductivity is called nematic superconductivity and is described well by a triplet vector order parameter. The main concepts of the microscopic theory and the Ginzburg–Landau theory for nematic superconductivity have been presented. The competition between possible superconducting order parameters in topological insulators has been discussed. It has been shown that hexagonal distortions of the Fermi surface are necessary for implementing the nematic phase. This phase is very sensitive to disorder because charged impurities reduce the critical temperature. The doping-induced transition from the closed to open Fermi surface affects the competition of superconducting phases. Surface Andreev states in nematic superconductors have been discussed. The phenomenological Ginzburg–Landau theory for the two-component order parameter is derived from the microscopic theory. Using the Ginzburg–Landau theory, it has been shown that the ground state is either the real nematic order parameter with the spontaneous deformation of the lattice or a complex chiral order parameter with spontaneous magnetization. The vector structure of the order parameter is responsible for an unconventional relation between superconductivity and the lattice deformation and magnetization. This leads to strong anisotropy of the second critical field, to the appearance of spin vortices (which can be carried by Kramers pairs of Majorana fermions), and to unconventional Pauli paramagnetism for triplet Cooper pairs.