Topological classification of intrinsic 3D superconductors using anomalous surface construction

TL;DR

This paper develops a comprehensive classification of intrinsic 3D topological superconductors protected by symmetries, using anomalous surface states and homotopy theory to understand their boundary phenomena.

Contribution

It introduces a unified framework for classifying 3D intrinsic topological superconductors based on stacking irreducible surface states and homotopy groups, expanding understanding of their boundary anomalies.

Findings

Complete classification of intrinsic 3D topological superconductors.

Unified description of surface anomalies away from high-symmetry points.

Method for constructing topological phases from building blocks.

Abstract

Intrinsic topological superconductors have protected gapless Majorana modes, bound and/or propagating, at the natural boundaries of the sample, without requiring field, defect, or heterostructure. We establish the complete classification/construction of intrinsic topological superconductors jointly protected by point-group and time-reversal symmetries in three dimensions. This is obtained from enumerating distinct ways for stacking $n$th-order irreducible building blocks, minimal anomalous surface states of $n$th-order topological superconductors. Particularly, our method provides a unified description of possible surface anomalies away from high-symmetry points/lines in terms of the homotopy group of the surface mass field.