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Materials realization of chiral topological superconductivity is a crucialcondition for observing and manipulating Majorana fermions in condensed matterphysics. Here we develop a tight-binding description of Pb$_3$Bi/Ge(111),identified recently as an appealing candidate system for realizing chiral$p$-wave topological superconductivity [Nat. Phys. 15, 796 (2019)]. We firstshow that our phenomenological model can capture the two main features of theelectronic 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 explicitlyconsidered, we find the alloyed system can be tuned into a chiral topologicalsuperconductor with Chern number $\mathcal{C} = -2$, resulting from thesynergistic effect of a sufficiently strong Zeeman field and the inherentlylarge Rashba spin-orbit coupling. The nontrivial topology with $\mathcal{C} =-2$ is further shown to be detectable as two chiral Majorana edge modespropagating along the same direction of the system with proper boundaries. Wefinally discuss the physically realistic conditions to establish the predictedtopological superconductivity and observe the corresponding Majorana edgemodes, including the influence of the superconducting gap, Land\'{e}$g$-factor, and critical magnetic field. The present study provides usefulguides in searching for effective $p$-wave superconductivity and Majoranafermions in two-dimensional or related interfacial systems.

Chiral topological superconducting state with Chern number $\mathcal{C} =-2$ in Pb$_3$Bi/Ge(111)