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

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.

4 pages, 1 figure and supplemental material, to be published in PRL

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• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
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• Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice
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