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 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 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.

中文翻译：

---

Rarita-Schwinger-Weyl 半金属超导-势垒-超导结中的 Andreev 束缚态

我们考虑用 Rarita-Schwinger-Weyl 半金属构建的超导体-势垒-超导体配置，其特征是四个能带在单个节点交叉。假设每个超导区域中都有均匀的 s 波配对，并且势垒区域是通过在一块正常状态半金属上施加一定幅度的电压而创建的，我们应用 BdG 形式来计算亚能隙 Andreev 束缚态的离散能谱短壁垒制度。与之前研究的双能半金属相比，我们在薄势垒极限中发现了多达四对局域态（而不是两能半金属的一对），并且每个值都对相位差具有复杂的依赖关系余弦和正弦函数，无法通过分析确定。这些是多带节点的伪影，其赝自旋值大于 1/2。使用束缚态能量，我们计算跨结配置的约瑟夫森电流。