2D Weyl Fermi gas model of Superconductivity in the Surface state of a Topological Insulator at High Magnetic fields

Abstract

The Nambu-Gorkov Green's function approach is applied to strongly type-II superconductivity in a 2D spin-momentum locked (Weyl) Fermi gas model at high perpendicular magnetic fields. When the chemical potential is sufficiently close to the branching (Dirac) point, such that the cyclotron effective mass, $m^{\ast }$, is a very small fraction of the free electron mass, $m_{e}$, relatively large portion of the $H-T$ phase diagram is exposed to magneto-quantum oscillation effects. This model system is realized in the 2D superconducting state, observed recently on the surface of the topological insulator Sb$_{2}$Te$_{3} $, for which high field measurements were reported at low carrier densities with $m^{\ast}=0.065m_{e}$. Calculations of the pairing condensation energy in such a system, as a function of $H$ and $T$, using both the Weyl model and a reference standard model, that exploits a simple quadratic dispersion law, are found to yield indistinguishable results in comparison with the experimental data. Significant deviations from the predictions of the standard model are found only for very small carrier densities, when the cyclotron energy becomes very large, the Landau level filling factors are smaller than unity, and the Fermi energy shrinks below the cutoff energy.