Index Theoretic Characterization of d-Wave Superconductors in the Vortex State

Oskar Vafek; Ashot Melikyan

doi:10.1103/PhysRevLett.96.167005

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Index Theoretic Characterization of d-Wave Superconductors in the Vortex State

Oskar Vafek, Ashot Melikyan

DOI 10.1103/PhysRevLett.96.167005 · Physical Review Letters

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Abstract

We study analytically the low energy spectrum of a lattice d-wave superconductor in the vortex lattice state. For an inversion symmetric hc/2e vortex lattice and in the presence of particle-hole symmetry we prove an index theorem that imposes a lower bound on the number of zero-energy modes. Generic cases are constructed in which this bound exceeds the number of zero modes of an equivalent lattice of hc/e vortices, despite the identical point group symmetries. The quasiparticle spectrum around the zero modes is doubly degenerate and exhibits a Dirac-like dispersion, with velocities that become universal functions of Δ0/t in the limit of low magnetic field. For weak particle-hole symmetry breaking, the gapped state can be characterized by a topological quantum number, related to spin-Hall conductivity, which generally differs in the cases of the hc/2e and hc/e vortex lattices.