Quantum critical point in the superconducting transition on the surface of topological insulator

TL;DR

This paper investigates a quantum critical point in the surface superconductivity of topological insulators, deriving a unique Ginzburg-Landau theory and analyzing magnetic properties near the transition.

Contribution

It introduces a novel quantum critical point in surface superconductivity of topological insulators and derives a distinct Ginzburg-Landau theory reflecting chiral universality.

Findings

Quantum critical point governs zero-temperature transition to superconductivity.

Ginzburg-Landau equations differ from conventional forms, reflecting chiral universality.

Magnetization near upper critical field is quadratic, not linear.

Abstract

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.