Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number

TL;DR

This paper presents a topological framework for understanding the stability of line nodes in superconductors with time-reversal symmetry, highlighting their topological invariance and examining specific material cases.

Contribution

It introduces a topological classification of line nodes in time-reversal invariant superconductors, demonstrating their stability via topological numbers derived from a real structure.

Findings

Line nodes are topologically stable in single-band superconductors.

Topological numbers protect the stability of line nodes.

Application to high-Tc materials and p-wave states confirms the theory.

Abstract

A topological argument is presented for nodal structures of superconducting states with time-reversal invariance. A generic Hamiltonian which describes a quasiparticle in superconducting states with time-reversal invariance is derived, and it is shown that only line nodes are topologically stable in single-band descriptions of superconductivity. Using the time-reversal symmetry, we introduce a real structure and define topological numbers of line nodes. Stability of line nodes is ensured by conservation of the topological numbers. Line nodes in high-Tc materials, the polar state in p-wave paring and mixed singlet-triplet superconducting states are examined in detail.