Exact Solution to Sodium-Iridate-BCS-Hubbard Model along the Symmetric Line: Non-trivial topology in the ferromagnetic order

TL;DR

This paper provides an exact solution to a sodium-iridates model on the honeycomb lattice, revealing how magnetic order influences topological properties and superconductivity.

Contribution

It introduces an exact solution method for the model with specific pairing gaps, linking magnetic order to topological phases.

Findings

Ground state is antiferromagnetic, breaking time-reversal symmetry and leading to trivial topology.

Ferromagnetic configuration preserves nontrivial topology, characterized by isospin Chern number.

Exact solutions detail band structures on different geometries.

Abstract

We study the sodium-iridates model on the honeycomb lattice with both BCS pairing potential and Hubbard interaction term. It is shown that this model can be exactly solved with appropriate choices of amplitude of pairing gaps, where the interacting terms are transformed to external field terms. The band structures of these exact solutions on both torus and cylinder geometry are discussed in great details. It is found that the ground state assumes an anti-ferromagnetic configuration, which breaks the time reversal symmetry spontaneously and renders the superconductor topologically trivial. On the other hand, the nontrivial topology is preserved with ferromagnetic configuration and can be characterized by the isospin Chern number.