Topological phase in a $d_{x^2-y^2}+(p+ip)$ superconductor in presence of spin-density-wave

TL;DR

This paper investigates a mean-field model of a superconductor with mixed pairing and spin-density-wave order, revealing a topological phase characterized by non-trivial Chern numbers and edge states.

Contribution

It introduces a model combining $d_{x^2-y^2}$ and $p+ip$ superconductivity with SDW order, demonstrating the emergence of a topological phase and constructing its phase diagram.

Findings

The energy spectrum is gapped in the combined order state.

A topological phase with non-zero Chern number is identified.

Edge states and vortex zero modes are analyzed.

Abstract

We consider a mean-field Hamiltonian for a $d_{x^2-y^2}+(p+ip)$ superconductor(SC) in presence of spin-density-wave(SDW) order. This is due to the fact that the non-commutativity of any two orders produces the third one. The energy spectrum of such a Hamiltonian is shown to be gapped and it yields a topological phase in addition to the conventional one. A phase diagram characterizing different topological phases is construted. The Chern numbers and hence the nature of the topological phases are determined. The edge state spectrum and the possibility of whether the vortex state harbouring the zero modes are discussed.