Euler-Chern correspondence via topological superconductivity
Fan Yang, Xingyu Li, Chengshu Li
DOI 10.1103/PhysRevResearch.5.033073 · Physical Review Research
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Abstract
The Fermi sea topology is characterized by the Euler characteristic χF. In this paper, we examine how χF of the metallic state is inherited by the topological invariant of the superconducting state. We establish a correspondence between the Euler characteristic and the Chern number C of p-wave topological superconductors without time-reversal symmetry in two dimensions. By rewriting the pairing potential Δk=Δ1−iΔ2 as a vector field u=(Δ1,Δ2), we found that χF=C when u and fermion velocity v can be smoothly deformed to be parallel or antiparallel on each Fermi surface. We also discuss a similar correspondence between the Euler characteristic and three-dimensional winding number of time-reversal-invariant p-wave topological superconductors in three dimensions.
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