Symmetry and topology of two-dimensional noncentrosymmetric superconductors

Abstract

We present a detailed study of the gap symmetry and the quasiparticle wave function topology in two-dimensional superconductors without inversion center. The strong spin-orbit coupling of electrons with the crystal lattice makes it necessary to describe superconductivity in terms of one or more nondegenerate bands characterized by helicity. We develop a topological classification of the superconducting states using the integer-valued Maurer-Cartan invariants and the Bogoliubov Wilson loops, and also calculate the spectrum of fermionic boundary modes.

21 pages, 1 figure, 4 tables

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• Crystalline Nodal Topological Superconductivity and Bogolyubov Fermi Surfaces in Monolayer NbSe${}_2$
• Classification of multipole superconductivity in multi-orbital systems and its implications
• Majorana flat bands, chiral Majorana edge states, and unidirectional Majorana edge states in noncentrosymmetric superconductors
• Mechanism, time-reversal symmetry and topology of superconductivity in noncentrosymmetric systems
• Enhanced spin-triplet pairing in magnetic junctions with s-wave superconductors
• Ultrathin Films of Superconducting Metals as a Platform for Topological Superconductivity
• Superconductivity in the Bi/Ni bilayer
• Competing superconducting phases in interacting two-dimensional electron gas with strong Rashba spin-orbit coupling
• Interplay between singlet and triplet pairings in multi-band two-dimensional oxide superconductors
• Topological d-wave superconductivity in two dimensions
• Fermionic boundary modes in two-dimensional noncentrosymmetric superconductors
• Manifestations of spin-orbit coupling in a cuprate superconductor
• Proximity-Induced Superconductivity at Non-Helical Topological Insulator Interfaces
• Noncentrosymmetric superconductors in one dimension
• Andreev spectroscopy of nonhelical spin textures in topological insulators
• Signatures of enhanced spin-triplet superconductivity induced by interfacial properties
• Theory of surface spectroscopy for noncentrosymmetric superconductors
• Stability of the boundary zero modes in one-dimensional topological superconductors
• Non-Lifshitz invariants corrections to Dzyaloshinskii-Moriya interaction energy