SciPost Phys. 12, 197 (2022) ·
published 23 June 2022
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Transition metal dichalcogenides (TMDs) offer a unique platform to study
unconventional superconductivity, owing to the presence of strong spin-orbit
coupling and a remarkable stability to an in-plane magnetic field. A recent
study found that when an in-plane field applied to a superconducting monolayer
TMD is increased beyond the Pauli critical limit, a quantum phase transition
occurs into a topological nodal superconducting phase which hosts Majorana flat
bands. We study the current-phase relation of this nodal superconductor in a
Josephson junction geometry. We find that the nodal superconductivity is
associated with an energy-phase relation that depends on the momentum
transverse to the current direction, with a $4\pi$ periodicity in between pairs
of nodal points. We interpret this response as a result of a series of quantum
phase transitions, driven by the transverse momentum, which separate a
topological trivial phase and two distinct topologically non-trivial phases
characterized by different winding invariants. This analysis sheds light on the
stability of the Majorana flat bands to symmetry-breaking perturbations.
