Josephson junctions of topological nodal superconductors

Transition metal dichalcogenides (TMDs) offer a unique platform to study \nunconventional superconductivity, owing to the presence of strong spin-orbit \ncoupling and a remarkable stability to an in-plane magnetic field. A recent \nstudy found that when an in-plane field applied to a superconducting monolayer \nTMD is increased beyond the Pauli critical limit, a quantum phase transition \noccurs into a topological nodal superconducting phase which hosts Majorana flat \nbands. We study the current-phase relation of this nodal superconductor in a \nJosephson junction geometry. We find that the nodal superconductivity is \nassociated with an energy-phase relation that depends on the momentum \ntransverse to the current direction, with a $4\\pi$ periodicity in between pairs \nof nodal points. We interpret this response as a result of a series of quantum \nphase transitions, driven by the transverse momentum, which separate a \ntopological trivial phase and two distinct topologically non-trivial phases \ncharacterized by different winding invariants. This analysis sheds light on the \nstability of the Majorana flat bands to symmetry-breaking perturbations.