Majorana bands, Berry curvature, and thermal Hall conductivity in the vortex state of a chiral p-wave superconductor

Abstract

Majorana quasiparticles localized in vortex cores of a chiral p-wave superconductor hybridize with one another to form bands in a vortex lattice. We begin by solving a fully microscopic theory describing all quasiparticle bands in a chiral p-wave superconductor in magnetic field, then use this solution to build localized Wannier wavefunctions corresponding to Majorana quasiparticles. A low-energy tight-binding theory describing the intervortex hopping of these is then derived, and its topological properties---which depend crucially on the signs of the imaginary intervortex hopping parameters---are studied. We show that the energy gap between the Majorana bands may be either topologically trivial or nontrivial, depending on whether the Chern number contributions from the Majorana bands and those from the background superconducting condensate add constructively or destructively. This topology directly affects the temperature-dependent thermal Hall conductivity, which we also calculate.

8 pages, 6 figures. Added references and added discussion regarding edge states

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• Vortex Lattice Structure and Topological Superconductivity in the Quantum Hall Regime
• Tricritical Ising phase transition in two-ladder Majorana fermion lattice
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
• Transport properties of spin-triplet superconducting monolayer $Mo{S}_2$
• Phase diagram of superconductivity in the integer quantum Hall regime
• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
• Spin-triplet $f$-wave symmetry in superconducting monolayer $Mo{S}_2$
• Non-centrosymmetric superconductors on honeycomb lattice
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• Chiral Majorana edge states in the vortex core of a $p+ip$ Fermi superfluid
• Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids
• Josephson junction arrays as a platform for topological phases of matter
• Drastic enhancement of the thermal Hall angle in a $d$-wave superconductor
• How vortex bound states affect the Hall conductivity of a chiral $p\pm ip$ superconductor
• Generic Weyl phase in the vortex state of quasi-two-dimensional chiral superconductors
• Semiclassical theory for the orbital magnetic moment of superconducting quasiparticles
• Classification of Majorana Fermions in Two-Dimensional Topological Superconductors