Topological gapless points in superconductors: From the viewpoint of symmetry

TL;DR

This paper reviews a modern topological classification theory for superconducting gap nodes, emphasizing the role of symmetry and revealing complex gap structures due to nonsymmorphic symmetry and angular momentum.

Contribution

It introduces a new classification framework for nodal superconductors based on symmetry, capturing phenomena beyond conventional theories.

Findings

Classification of gap nodes using symmetry principles

Identification of nontrivial gap structures from nonsymmorphic symmetry

Extension of topological methods to gapless superconductors

Abstract

Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the topology of a gapped Hamiltonian is investigated from the viewpoint of its onsite/crystal symmetry. On the other hand, topological physics also appears in semimetals, whose gapless points can be characterized by topological invariants. Stimulated by this background, we shed light on the topology of nodal superconductors. In this paper, we review our modern topological classification theory of superconducting gap nodes in terms of symmetry. The classification method elucidates nontrivial gap structures arising from nonsymmorphic symmetry or angular momentum, which cannot be predicted by a conventional theory.