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

Dingping Li, Rosenstein Baruch*, B. Ya Shapiro, I. Shapiro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Pairing in the Weyl semimetal appearing on the surface of a topological insulator is considered. It is shown that due to an " ultrarelativistic" 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, and its magnetic properties and critical exponents close to the quantum critical point. The Ginzburg-Landau (GL) effective theory is derived for small chemical potential, allowing us to consider effects of spatial dependence of order parameters in a 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 for some three-dimensional topological insulators, and we estimate feasibility of the phonon pairing.

Original languageEnglish
Article number054517
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number5
StatePublished - 25 Aug 2014

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