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The recently discovered vanadium-based Kagome metals $A$V$_{3}$Sb$_{5}$ ($A =\text{K, Rb, Cs}$) are of great interest with the interplay of charge densitywave (CDW) order, band topology and superconductivity. In this paper, byidentifying elementary band representations (EBRs), we construct a two-EBRgraphene-Kagome model to capture the two low-energy van-Hove-singularitydispersions and, more importantly, the nontrivial band topology in these Kagomemetals. This model consists of $A_g@3g$ (V-$d_{x^2-y^2/z^2}$, Kagome sites) and$A_2''@2d$ EBRs (Sb1-$p_z$, honeycomb sites). We have investigated the Fermisurface instability by calculating the electronic susceptibility$\chi(\mathbf{q})$. Prominent Fermi-surface nesting peaks are obtained at threeL points, where the $z$ component of the nesting vector shows intimaterelationship with the anticrossing point along M--L. The nesting peaks at L areconsistent with the $2\times 2\times 2$ CDW reconstruction in these compounds.In addition, the sublattice-resolved bare susceptibility is calculated andsimilar sharp peaks are observed at the L points, indicating a strongantiferromagnetic fluctuation. Assuming a bulk $s$-wave superconductingpairing, helical surface states and nontrivial superconducting gap are obtainedon the (001) surface. In analogous to FeTe$_{1-x}$Se$_{x}$ superconductor, ourresults establish another material realization of a stoichiometricsuperconductor with nontrivial band topology, providing a promising platformfor studying exotic Majorana physics in condensed matter

physical review. b./physical review. b

Two elementary band representation model, Fermi surface nesting, and  surface topological superconductivity in $A$V$_{3}$Sb$_ {5}$ ($A = \text{K,  Rb, Cs}$)