Linking structures of doubly charged nodal surfaces in centrosymmetric superconductors

TL;DR

This paper explores the linking structures of doubly charged nodal surfaces in centrosymmetric superconductors, revealing their topological properties and the importance of global band structure in gapless topological phases.

Contribution

It provides a complete classification of linking structures of doubly charged nodes in centrosymmetric systems using AZ$+ ext{I}$ symmetry.

Findings

Doubly charged nodal surfaces always link with nodal points or lines below $E_F$.

Linking structures explain the relationship between charges at $E_F$ and below.

Global band structure influences the topological characterization of gapless phases.

Abstract

In topological semimetals and nodal superconductors, band crossings between occupied and unoccupied bands form stable nodal points/lines/surfaces carrying quantized topological charges. In particular, in centrosymmetric systems, some nodal structures at the Fermi energy $E_F$ carry two distinct topological charges, and thus they are called doubly charged nodes. Here we show that doubly charged nodal surfaces of centrosymmetric superconductors in three-dimensions always develop peculiar linking structures with nodal points or lines formed between occupied bands below $E_F$. Such linking structures can naturally explain the inherent relationship between the charge of the node below $E_F$ and the two charges of the nodal surfaces at $E_F$. Based on the Altland-Zirnbauer (AZ)-type ten-fold classification of nodes with additional inversion $\mathcal{I}$ symmetry, which is called the AZ$+\mathcal{I}$ classification, we provide the complete list of linking structures of doubly charged nodes in centrosymmetric systems. The linking structures of doubly charged nodes clearly demonstrate that not only the local band structure around the node but also the global band structure play a critical role in characterizing gapless topological phases.