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 insulators. 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 singlets or pure triplets pairs of electrons in and out of the condensate, a corollary to the non-conservation 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 exist 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 unity, in contrast to the half-flux in the case of two-dimensional $p_x\pm i{p}_y$ superconductors that break time-reversal symmetry.

Published version. References added. 24 pages

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• Superconductivity of doped Weyl semimetals: finite-momentum pairing and electronic analogues of the 3He-A phase
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• Time reversal non-invariant non-Abelian topological order in non-centrosymmetric superconductors
• Majorana zero modes on a necklace
• Odd-frequency superconducting pairing in one-dimensional systems
• Surface spectral function in the superconducting state of a topological insulator
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• Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions
• Superconductivity of disordered Dirac fermions
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• Excitons and Optical Absorption on the Surface of a Strong Topological Insulator with a Magnetic Energy Gap
• Suppression of surface p-wave superconductivity in disordered topological insulators
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• Transport signatures of superconducting hybrids with mixed singlet and chiral triplet states
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall
• Tunneling between Two Helical Superconductors via Majorana Edge Channels
• Spin Currents and Spontaneous Magnetization at Twin Boundaries of Noncentrosymmetric Superconductors
• Model Hamiltonian for topological Kondo insulator SmB6
• Magic angle conditions for twisted 3D topological insulators
• Topological qubits in graphenelike systems
• Majorana zero modes bound to a vortex line in a topological superconductor
• Pairing symmetry and vortex zero-mode for superconducting Dirac fermions
• Catalogue of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires
• Z${}_2$ index theorem for Majorana zero modes in a class D topological superconductor
• Proximity induced time-reversal topological superconductivity in Bi2Se3 films without phase tuning
• Stability of Unconventional Superconductivity on Surfaces of Topological Insulators
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Phase segregation of superconductivity and ferromagnetism at LaAlO${}_3$/SrTiO${}_3$ interface
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Functional renormalization and mean-field approach to multiband systems with spin-orbit coupling: Application to the Rashba model with attractive interaction
• Transport and noise properties of a normal metal-superconductor-normal metal junction with mixed singlet and chiral triplet pairings
• Helical states and solitons in noncentrosymmetric superconductors
• Edge superconducting state in attractive U Kane-Mele-Hubbard model
• Supercurrent vortices and Majorana zero modes induced by an inplane Zeeman field on the surface of a three-dimensional topological insulator
• Ginzburg-Landau description of twin boundaries in noncentrosymmetric superconductors
• Impurity Effects on Superconductivity on Surfaces of Topological Insulators
• Green's Function Method for Line Defects and Gapless Modes in Topological Insulators : Beyond Semiclassical Approach
• Nematic order on the surface of a three-dimensional topological insulator
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
• Fermi surface instabilities of symmetry-breaking and topological types on the surface of a three-dimensional topological insulator
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points
• Realizing attractive interacting topological surface fermions: A resonating TI- thin film hybrid platform