Topological properties of nodal superconductors

Monolayer and few-layer transition metal dichalcogenides (TMDs) have been

suggested as a platform to study intrinsic and induced unconventional superconductivity.

This is due to the presence of a strong Ising spin-orbit coupling which locks the spins

perpendicular to the surface resulting in remarkable stability to an in-plane magnetic

field even beyond the Pauli limit. It has been suggested that when the in-plane field

is increased beyond the Pauli limit, a quantum phase transition occurs into a topological

nodal-superconducting phase characterized by Majorana flat bands. We use the

Bogoliubov-de Gennes Hamiltonian formalism and show that the unique topological

properties of this non-trivial phase are reflected in the current across junctions of nodal

superconductors separated by an insulating barrier. By studying the dependence of the

Josephson current on the phase difference between two sides of the junction, one can

infer these topological properties.