Unified theory of PT and CP invariant topological metals and nodal superconductors

TL;DR

This paper develops a unified topological framework for PT and CP invariant metals and nodal superconductors using KO theory, revealing how bulk topological charges influence boundary modes and establishing a bulk-boundary correspondence.

Contribution

It introduces a comprehensive topological theory for PT and CP invariant systems, constructing models in 1D, 2D, and 3D, and elucidates the physical implications of bulk-boundary relationships.

Findings

Topological charges determine boundary subgap mode distribution.

Models constructed for all nontrivial cases in 1D, 2D, 3D.

Bulk-boundary correspondence links Fermi points to boundary gapless modes.

Abstract

As PT and CP symmetries are fundamental in physics, we establish a unified topological theory of PT and CP invariant metals and nodal superconductors, based on the mathematically rigorous $KO$ theory. Representative models are constructed for all nontrivial topological cases in dimensions $d=1,2$, and $3$, with their exotic physical meanings being elucidated in detail. Intriguingly, it is found that the topological charges of Fermi surfaces in the bulk determine an exotic direction-dependent distribution of topological subgap modes on the boundaries. Furthermore, by constructing an exact bulk-boundary correspondence, we show that the topological Fermi points of the PT and CP invariant classes can appear as gapless modes on the boundary of topological insulators with a certain type of anisotropic crystalline symmetry.