Topologically stable gapless phases of time-reversal invariant superconductors

Details Topologically stable gapless phases of time-reversal invariant superconductors Topologically stable gapless phases of time-reversal invariant superconductors

2009-09-30

arxiv.org/abs/0909.5680v3

Phys. Rev. B 81, 134515 (2010)

Physics

Condensed Matter

Superconductivity

7 pages, 1 figure; v3: expanded version

Scientific paper

10.1103/PhysRevB.81.134515

We show that time-reversal invariant superconductors in d=2 (d=3) dimensions can support topologically stable Fermi points (lines), characterized by an integer topological charge. Combining this with the momentum space symmetries present, we prove analogs of the fermion doubling theorem: for d=2 lattice models admitting a spin X electron-hole structure, the number of Fermi points is a multiple of four, while for d=3, Fermi lines come in pairs. We show two implications of our findings for topological superconductors in d=3: first, we relate the bulk topological invariant to a topological number for the surface Fermi points in the form of an index theorem. Second, we show that the existence of topologically stable Fermi lines results in extended gapless regions in a generic topological superconductor phase diagram.

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