The influence of recently discovered topological transition between type I and type II Weyl semimetals on superconductivity is considered. A set of Gorkov equations for weak superconductivity in Weyl semi-metal under topological phase transition is derived and solved. The critical temperature and superconducting gap both have spike in the point the transition point as function of the tilt parameter of the Dirac cone determined in turn by the material parameters like pressure. The spectrum of superconducting excitations is different in two phases: the sharp cone pinnacle is characteristic for a type I, while two parallel almost flat bands, are formed in type II. Spectral density is calculated on both sides of transition demonstrate different weight of the bands. The superconductivity thus can be used as a clear indicator for the topological transformation. Results are discussed in the light of recent experiments.
F >> Ω, and the nonadiabatic, F << Ω, regimes. The high temperature superconductivity in 1UCF eSe/STO is possible due to a combination of three factors: high LO phonon frequency, large electron-phonon coupling λ ∼ 0.5 and huge dielectric constant of the substrate suppression the Coulomb repulsion. It is shown that very low density electron gas in the interfaces is still capable of generating superconductivity of the order of 0.1K in LAO/STO.
Pairing in the Weyl semi -metal appearing on the surface of topological insulator is considered. It is shown that due to an "ultra-relativistic" dispersion relation there is a quantum critical point governing the zero temperature transition to a superconducting state. Starting from the microscopic Hamiltonian with local attraction, we calculated using the Gor'kov equations, the phase diagram of the superconducting transition at arbitrary chemical potential, its magnetic properties and critical exponents close to the quantum critical point. The Ginzburg -Landau effective theory is derived for small chemical potential allowing to consider effects of spatial dependence of order parameters in magnetic field. The GL equations are very different from the conventional ones reflecting the chiral universality class of the quantum phase transition. The order parameter distribution of a single vortex is found to be different as well. The magnetization near the upper critical field is found to be quadratic, not linear as usual. We discuss the application of these results to recent experiments in which surface superconductivity was found that some 3D topological insulators and estimate feasibility of the phonon pairing.
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