Andreev bound states in Josephson junctions of semi-Dirac semimetals
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913306001801216 |
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| author | Mandal, Ipsita |
| author_facet | Mandal, Ipsita |
| contents | 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 $\varepsilon $ 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 $\varepsilon $ on the superconducting phase difference $ϕ$, we compute the variation of Josephson current as a function of $ϕ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00506 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Andreev bound states in Josephson junctions of semi-Dirac semimetals Mandal, Ipsita Superconductivity Mesoscale and Nanoscale Physics High Energy Physics - Theory 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 $\varepsilon $ 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 $\varepsilon $ on the superconducting phase difference $ϕ$, we compute the variation of Josephson current as a function of $ϕ$. |
| title | Andreev bound states in Josephson junctions of semi-Dirac semimetals |
| topic | Superconductivity Mesoscale and Nanoscale Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.00506 |