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

Motohiko Ezawa

doi:10.1103/PhysRevB.97.241113

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

Motohiko Ezawa

DOI 10.1103/PhysRevB.97.241113 · Physical Review B

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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 corresponding spin-triplet f-wave superconducting pairings becomes a full-gap topological superconductor possessing 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 spontaneously breaks the time-reversal symmetry. 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.