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\pi4π
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 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.