2D massless Dirac 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 * , is a very small fraction of the free electron mass, me, 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 Sb2Te3, for which high field measurements were reported at low carrier densities with m * = 0.065me. 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. PACS numbers: 74.78.-w, 74.25.Ha, 74.20.-z Expanding the above normal state Green's functions in terms of the complete set of solutions, ϕ n (y − k x ) =

Interplay between orbital-quantization effects and the Fulde-Ferrell-Larkin-Ovchinnikov instability in multiple-band layered superconductors

“…83 that the orbital quantization in superconducting materials with such Diraclike spectrum can also lead to the reentrant superconductivity in high magnetic fields. Furthermore, the similar reentrant behavior has also been found in the theoretical study on the Dirac-like surface states of a topological insulator 84 . In contrast to the conventional quadratic electronic dispersion, the linearly-dispersive band yields nonuniform Landau-level spacing and it has been argued that this intriguing feature makes the quantum limit much easier to attain.…”

“…In contrast to the conventional quadratic electronic dispersion, the linearly-dispersive band yields nonuniform Landau-level spacing and it has been argued that this intriguing feature makes the quantum limit much easier to attain. 83 In addition to this feature, due to the small cyclotron effective mass near the Dirac point, the Landau quantization is more robust against disorders 84,85 . So far, the above studies only considered the Landau-quantization effects in the uniform states.…”

Upper critical magnetic field in superconducting Dirac semimetal

“…[20], [3] and [21], respectively). Going beyond the semiclassical approximation is typically more complicated and has been contemplated in parabolic band materials [31] and recently in Weyl semimetals [18,33].…”