Spontaneous breaking of time-reversal symmetry in topological superconductors

Igor N Karnaukhov

doi:10.1038/s41598-017-07673-z

Abstract

We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the superconducting order parameter. The solutions for the phases corresponding to the energy minimuma, lead to a topological superconducting state with the nontrivial Chern numbers. We focus our quantitative analysis on the properties of topological states of superconductors with different crystalline symmetry and show that the phase transition in the topological superconducting state is result of spontaneous breaking of time-reversal symmetry in the superconducting state. The peculiarities in the chiral gapless edge modes behavior are studied, the Chern numbers are calculated.

Highlights

Within a mean-field treatment of the problem, the superconducting state is characterized by the pairing of a macroscopic number of electrons with opposite spins
We demonstrate that due to stable solutions for phases of the superconducting order parameter, spontaneous breaking of time-reversal symmetry leads to topological state of superconductors
We have shown that due to nontrivial stable solutions for the phases of the superconducting order parameter, the time-reversal symmetry is spontaneously broken

Summary

TSC on a square lattice

We consider a superconducting state with a spontaneously broken time reversal symmetry and show that the state of TSC is realized in the case of symmetry breaking. In TSC state the nontrivial Chern number C = sign (μ) is realized if the excitation spectrum is gapped at a half-filling:. In our case topological state, with static configurations φx(j), φy(j) for nonhomogeneous phases of the superconducting order parameter, is realized at φx(j) = φx, φy(j) = φy.

TSC on a centered square lattice

TSC on a hexagonal lattice

Conclusions

Methods

Additional Information