Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials

Abstract

We study the superconducting instabilities of a single species of two-dimensional Rashba-Dirac fermions, as it pertains to the surface of a three-dimensional time-reversal symmetric topological band insulator. We also discuss the similarities as well as the differences between this problem and that of superconductivity in two-dimensional time-reversal symmetric noncentrosymmetric materials with spin-orbit interactions. The superconducting order parameter has both s-wave and p-wave components, even when the superconducting pair potential only transfers either pure singlet or pure triplet pairs of electrons in and out of the condensate, a corollary to the nonconservation of spin due to the spin-orbit coupling. We identify one single superconducting regime in the case of superconductivity in the topological surface states (Rashba-Dirac limit), irrespective of the relative strength between singlet and triplet pair potentials. In contrast, in the Fermi limit relevant to the noncentrosymmetric materials we find two regimes depending on the value of the chemical potential and the relative strength between singlet and triplet potentials. We construct explicitly the Majorana bound states in these regimes. In the single regime for the case of the Rashba-Dirac limit, there exists one and only one Majorana fermion bound to the core of an isolated vortex. In the Fermi limit, there are always an even number (0 or 2 depending on the regime) of Majorana fermions bound to the core of an isolated vortex. In all cases, the vorticity required to bind Majorana fermions is quantized in units of the flux quantum, in contrast to the half flux in the case of two-dimensional p x ± ip y superconductors that break time-reversal symmetry.

Surface spectral function in the superconducting state of a topological insulator

“…There have already been many papers focusing on this possibility, which usually start from the effective model. [43,44,45] The Andreev bound states that appear in many different superconducting pairings as shown above confirm the idea that superconducting states realized in a topological insulator are very probable to have nontrivial topological characters. The Andreev bound states, if exist, should be easily detectable in a tunneling type experiments as a well defined zero energy peak.…”

“…[23] This kind of pairing could be favored by interorbital ferromagnetic Heisenberg interactions. [43] The two independent choices for the pairing matrix are…”

Spin-orbital ground states of superconducting doped topological insulators: A Majorana platform

“…Following the axiomatic principle that "more is different" in many-body systems, this novel surface environment has been the subject of numerous predictions for emergent many-body states and device physics that cannot be readily realized by other material systems [14][15][16][17][18][19][20][21][22][23][24][25] . Shortly following the first experimental identification of a three dimensional topological insulator material, it was theoretically predicted that the introduction of superconductivity at a topological insulator (TI) surface can under the right conditions give rise to braidable (non-Abelian) quasiparticles which might be applied in quantum information science.…”

Superconductivity of disordered Dirac fermions

“…While the phase structure at the Dirac point (chemical potential µ = 0) as a function of attraction strength g has previously been understood, 15,16,[25][26][27][28] the full phase diagram in the g − µ plane has not been presented as far as we are aware. Indeed, the µ → ∞ limit remains controversial, with the existing literature [25][26][27] in apparent disagreement. We resolve this disagreement by means of a careful analysis that takes into account the finite ultraviolet cutoff for the interaction, which justifies use of a projected Hamiltonian.…”