The nontrivial ground state topology in the coexistence phase of chiral d-wave superconductivity and 120 degrees magnetic order on a triangular lattice

TL;DR

This paper investigates the topological properties of a chiral d-wave superconductor on a triangular lattice with 120-degree magnetic order, revealing conditions for nontrivial phases and Majorana zero modes.

Contribution

It introduces a method to determine topological phases in a magnetic superconductor, accounting for weak pairing interactions and linking topological invariants with Green function formulations.

Findings

Nontrivial topological phases are achievable with weak first-neighbor pairing.

Zero energy Majorana modes are found in topologically nontrivial phases.

A connection between Z2 invariants and Green function topological invariants is established.

Abstract

The Z2 topological invariant is defined in the chiral d-wave superconductor having a triangular lattice in the presence of the 120 degrees magnetic ordering. By analyzing the Z2 invariant, we determine the conditions of implementing nontrivial phases in the model with regard to superconducting pairings between nearest and next nearest neighbors. It is often supposed in such system that the pairing parameter between nearest neighbors should be equal to zero due to influence of the intersite Coulomb interaction. We show that taking into account even weak pairings in the first coordination sphere leads to the disappearance of the gapless excitations of the bulk spectrum in the wide region of the parameter space. Thus topological invariants can be defined in such region. Solving the problem of open edges it is shown that the zero energy modes are realized basically in the topologically nontrivial phases. Such zero modes are topologically protected Majorana modes. A connection between the Z2 invariant calculated at the symmetric points of the Brillouin zone with respect to the electron-hole symmetry and the integer topological invariant of the ground state of the 2D lattice expressed in terms of the Green functions is established in the presence of noncollinear magnetic ordering.