Dirac Monopole and Spin Hall Conductance for Anisotropic Superconductivities

TL;DR

This paper explores the topological properties of anisotropic superconductivities, focusing on Dirac monopoles and spin Hall conductance, revealing how topological invariants characterize different superconducting states.

Contribution

It introduces a topological framework using Dirac monopoles and Chern numbers to analyze anisotropic superconductivities, including non-trivial orders on triangular lattices.

Findings

Chern number relates to Dirac monopole covering degree.

Topological order distinguishes superconductivities with identical symmetry.

Topological objects demonstrate non-trivial orders on triangular lattices.

Abstract

Concept of the topological order is useful to characterize anisotropic superconductivities. The spin Hall conductance distinguishes superconductivities with the same symmetry. The Chern number for the spin Hall conductance is given by the covering degree of a closed surface around the Dirac monopole. It gives a clear illustration for the on-critical condition for the $d_{x^2-y^2}$ supreconductivitiy with non zero chemical potential. Non trivial topological orders on the triangular lattice are also presented and demonstrated by the topological objects.