Andreev bound states in Josephson junctions of semi-Dirac semimetals

Abstract

We consider a Josephson junction built with the two-dimensional semi-Dirac semimetal, which features a hybrid of linear and quadratic dispersion around a nodal point. We model the weak link between the two superconducting regions by a Dirac delta potential because it mimics the thin-barrier-limit of a superconductor-barrier-superconductor configuration. Assuming a homogeneous pairing in each region, we set up the BdG formalism for electronlike and holelike quasiparticles propagating along the quadratic-in-momentum dispersion direction. This allows us to compute the discrete bound-state energy spectrum $\epsilon$ of the subgap Andreev states localized at the junction. In contrast with the Josephson effect investigated for propagation along linearly dispersing directions, we find a pair of doubly degenerate Andreev bound states. Using the dependence of $\epsilon$ on the superconducting phase difference $\varphi$, we compute the variation of Josephson current as a function of $\varphi$.

arXiv commentjournal version; companion paper of arXiv:2312.16164

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