Materials realization of chiral topological superconductivity is a crucial condition for observing and manipulating Majorana fermions in condensed matter physics. Here we develop a tight-binding description of ${\mathrm{Pb}}_3\mathrm{Bi}/\mathrm{Ge}\left(111\right)$, identified recently as an appealing candidate system for realizing chiral $p$-wave topological superconductivity [Nat. Phys. 15, 796 (2019)]. We first show that our phenomenological model can capture the two main features of the electronic band structures obtained from first-principles calculations, namely, the giant Rashba splitting and type-II van Hove singularity. Next, when the $s$-wave superconducting property of the parent Pb system is explicitly considered, we find the alloyed system can be tuned into a chiral topological superconductor with Chern number $\mathcal{C}=-2$, resulting from the synergistic effect of a sufficiently strong Zeeman field and the inherently large Rashba spin-orbit coupling. The nontrivial topology with $\mathcal{C}=-2$ is further shown to be detectable as two chiral Majorana edge modes propagating along the same direction of the system with proper boundaries. We finally discuss the physically realistic conditions to establish the predicted topological superconductivity and observe the corresponding Majorana edge modes, including the influence of the superconducting gap, Landé $g$ factor, and critical magnetic field. The present study provides useful guides in searching for effective $p$-wave superconductivity and Majorana fermions in two-dimensional or related interfacial systems.

中文翻译：

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陈数C=−2inPb3Bi/Ge(111)的手性拓扑超导态

手性拓扑超导的材料实现是凝聚态物理中观察和操纵马约拉纳费米子的关键条件。在这里，我们开发了一个紧绑定的描述${铅}_3双/葛\left(111\right)$，最近被确定为实现手性的有吸引力的候选系统 $磷$-波拓扑超导[ Nat. 物理。 15 , 796 (2019)]。我们首先表明，我们的现象学模型可以捕获从第一性原理计算获得的电子能带结构的两个主要特征，即巨型 Rashba 分裂和 II 型范霍夫奇点。接下来，当$秒$明确考虑母铅系统的波超导特性，我们发现合金系统可以调谐成具有陈数的手性拓扑超导体 $\mathcal{C}=-2$，由足够强的塞曼场和固有的大 Rashba 自旋轨道耦合的协同效应产生。非平凡拓扑$\mathcal{C}=-2$进一步表明可检测为两个手性 Majorana 边缘模式，沿着系统的相同方向传播，具有适当的边界。我们最后讨论了物理现实条件，以建立预测的拓扑超导并观察相应的马约拉纳边缘模式，包括超导间隙的影响，Landé$G$因子和临界磁场。本研究为寻找有效的$磷$二维或相关界面系统中的波超导性和马约拉纳费米子。