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

Abstract

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 $V_0$ across a piece of normal state semimetal, we apply the BdG formalism to compute the discrete energy spectrum $\epsilon$ 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 $\epsilon$ has a complicated dependence on the phase difference ${\phi }_{12}$ 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.

journal version

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• Andreev bound states in Josephson junctions of semi-Dirac semimetals
• Chiral anomaly and internode scatterings in multifold semimetals
• Nature of Andreev bound states in Josephson junctions of triple-point semimetals
• Delta-function-potential junctions with quasiparticles occupying tilted bands with quadratic-in-momentum dispersion
• Transmission through rectangular potentials in semimetals featuring quadratic dispersion