We study, for the first time, the effects of strong short-range electron-electron interactions in generic Rarita-Schwinger-Weyl semimetals hosting spin-$3/2$ electrons with linear dispersion at a fourfold band crossing point. The emergence of this novel quasiparticle, which is absent in high-energy physics, has recently been confirmed experimentally in the solid state. We combine symmetry considerations and a perturbative renormalization group analysis to discern three interacting phases that are prone to emerge in the strongly correlated regime: The chiral topological semimetal breaks a ${\mathbb{Z}}_2$ symmetry and features four Weyl nodes of monopole charge $+1$ located at vertices of a tetrahedron in momentum space. The $s$-wave superconducting state opens a Majorana mass gap for the fermions and is the leading superconducting instability. The Weyl semimetal phase removes the fourfold degeneracy and creates two Weyl nodes with either equal or opposite chirality depending on the anisotropy of the band structure. We find that symmetry breaking occurs at weaker coupling if the total monopole charge remains constant across the transition.

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Rarita-Schwinger-Weyl半金属中拓扑与电子-电子相互作用的相互作用

我们首次研究了强自发性短程电子-电子相互作用在具有自旋能级的通用Rarita-Schwinger-Weyl半金属中的作用。$3/2$电子在四重能带交叉点具有线性色散。高能物理中不存在的这种新型准粒子的出现，最近在固态实验中得到证实。我们将对称性考虑因素和微扰化重整化组分析相结合，以辨别在强相关机制中容易出现的三个相互作用阶段：手性拓扑半金属断裂${\mathbb{ž}}_2$ 对称且具有四个单极电荷Weyl节点 $+\mathrm{1个}$位于动量空间中四面体的顶点。的$s$波超导状态为费米子打开了马约拉纳质量差，并且是主要的超导不稳定性。Weyl半金属相消除了四重简并性，并根据带结构的各向异性创建了两个具有相同或相反手性的Weyl节点。我们发现，如果总的单极电荷在整个跃迁中保持恒定，则对称耦合将在较弱的耦合处发生。