Unusual Superconducting transition in Topological Insulators

Abstract

Superconducting transition generally belongs to the U (1) class of phase transitions. However it was pointed out long time ago that if the normal state dispersion relation is "ultrarelativistic" the transition is unusual: even the mean field critical exponents are different from the standard ones leading to a number of observable effects. Attempts to experimentally discover such a system included chiral condensate in graphene. Recently it was found that some 3D topological insulators (that possess the ultrarelativistic metal on its surface) exhibit surface superconductivity. Starting from microscopic TI Hamiltonian with local four fermions interaction, we calculated the total set of the Gor\'kov equations allowing to build the Ginzburg - Landau (GL) theory including the magnetic field effects. It was shown that the GL equations reflect the novel chiral universality class, very different from original GL equations. For example the temperature dependence of the coherence length diverges at the critical temperature with critical exponent v = 1 in rather than customary v = -1/2, magnetization near the upper critical magnetic field is quadratic as a function of deviation from the upper critical field while the Superfluid density is psi(2) = (T-c - T)(beta), beta = 2, not beta = 1