Exact solutions in two-dimensional topological superconductors: Hubbard interaction induced spontaneous symmetry breaking

TL;DR

This paper introduces an exactly solvable model of a two-dimensional topological superconductor on a honeycomb lattice, revealing how Hubbard interactions induce spontaneous symmetry breaking and transition the system from a topological to a trivial phase.

Contribution

It presents an exactly solvable model of a spin-triplet f-wave topological superconductor with Hubbard interactions, showing how interactions lead to spontaneous symmetry breaking.

Findings

Hubbard interaction induces spontaneous time-reversal symmetry breaking.

The model exhibits perfect flat bands at zero energy with conserved quantities.

System transitions from topological to trivial superconductor due to interactions.

Abstract

We present an exactly solvable model of a spin-triplet $f$-wave topological superconductor on the honeycomb lattice in the presence of the Hubbard interaction for arbitrary interaction strength. First we show that the Kane-Mele model with the corresponding spin-triplet $f$-wave superconducting pairings becomes a full-gap topological superconductor possessing the time-reversal symmetry. We then introduce the Hubbard interaction. The exactly solvable condition is found to be the emergence of perfect flat bands at zero energy. They generate infinitely many conserved quantities. It is intriguing that the Hubbard interaction breaks the time-reversal symmetry spontaneously. As a result, the system turns into a trivial superconductor. We demonstrate this topological property based on the topological number and by analyzing the edge state in nanoribbon geometry.