Andreev bound states in superconductor-barrier-superconductor junctions of Rarita-Schwinger-Weyl semimetals

We consider a superconductor -barrier -superconductor configuration built with Rarita-Schwinger-Weyl semimetal, which features four bands crossing at a single nodal point. Assuming a homogeneous s -wave pairing in each superconducting region, and the barrier region created by applying a voltage of magnitude ������0 across a piece of normal state semimetal, we apply the BdG formalism to compute the discrete energy spectrum ������ of the subgap Andreev bound states in the short -barrier regime. In contrast with the two -band semimetals studied earlier, we find upto four pairs of localized states (rather than one pair for two -band semimetals) in the thin -barrier limit, and each value of ������ has a complicated dependence on the phase difference ������12 via cosine and sine functions, which cannot be determined analytically. These are artifacts of multi -band nodes hosting quasiparticles of pseudospin values greater than 1/2. Using the bound state energies, we compute the Josephson current across the junction configuration.