We analyze theoretically two different setups for $s$-wave superconductivity proximitized $j=\frac{3}{2}$ particles in Luttinger materials that are able to host Majorana bound states (MBSs). First, we consider a one-dimensional superconductor (SC) wire with intrinsic bulk inversion asymmetry (BIA). In contrast to wires, modeled by a quadratic dispersion with Rashba spin-orbit coupling, there are two topological phase transitions in our systems at finite magnetic fields. Second, we analyze a two-dimensional Josephson junction on the Luttinger model finding a topological region even in the absence of BIA and Rashba spin-orbit couplings. This originates from the hybridization of the light and heavy hole bands of the $j=\frac{3}{2}$ states in combination with the SC pairing. As a consequence, both systems can be driven into a topological phase hosting MBSs. Hence, we predict that MBSs form in any SC proximitized Josephson junction on two-dimensional Luttinger materials by the application of magnetic field alone. This opens an avenue for the search of topological SC.

中文翻译：

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Luttingerj=32systems 中马约拉纳模式的内在出现

我们从理论上分析了两种不同的设置$s$波超导近似$j=\frac{3}{2}$Luttinger 材料中能够承载马约拉纳束缚态 (MBS) 的粒子。首先，我们考虑具有本征体反转不对称性 (BIA) 的一维超导体 (SC) 线。与由具有 Rashba 自旋轨道耦合的二次色散建模的导线相比，我们的系统在有限磁场中存在两个拓扑相变。其次，我们分析了 Luttinger 模型上的二维约瑟夫森结，即使在没有 BIA 和 Rashba 自旋轨道耦合的情况下也能找到拓扑区域。这源于轻和重空穴带的杂交$j=\frac{3}{2}$状态与 SC 配对相结合。因此，两个系统都可以进入托管 MBS 的拓扑阶段。因此，我们预测 MBS 在任何 SC 接近约瑟夫森结中通过单独施加磁场在二维 Luttinger 材料上形成。这为搜索拓扑 SC 开辟了一条途径。