Two elementary band representation model, Fermi surface nesting, and surface topological superconductivity in AV3Sb5 ( A = K, Rb, Cs)

The recently discovered vanadium-based Kagome metals $A{\mathrm{V}}₃{\mathrm{Sb}}₅$ ($A=\text{K,}\phantom{\rule{4.pt}{0ex}}\text{Rb,}\phantom{\rule{4.pt}{0ex}}\text{Cs}$) are of great interest with the interplay of charge density wave (CDW) order, band topology and superconductivity. In this paper, by identifying elementary band representations (EBRs), we construct a two-EBR graphene-Kagome model to capture the two low-energy van-Hove-singularity dispersions and, more importantly, the nontrivial band topology in these Kagome metals. This model consists of ${A}_g@3g$ ($\text{V}\text{\ensuremath{-}}{d}_{{x}²\ensuremath{-}{y}²/{z}²}$, Kagome sites) and ${A}₂^{\ensuremath{''}}@2d$ EBRs (Sb1-${p}_z$, honeycomb sites). We have investigated the Fermi surface instability by calculating the electronic susceptibility $\ensuremath{\chi}(\mathbit{q})$. Prominent Fermi-surface nesting peaks are obtained at three L points, where the $z$ component of the nesting vector shows an intimate relationship with the anticrossing point along M-L. The nesting peaks at L are consistent with the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CDW reconstruction in these compounds. In addition, the sublattice-resolved bare susceptibility is calculated and similar sharp peaks are observed at the L points, indicating a strong antiferromagnetic fluctuation. Assuming a bulk $s$-wave superconducting pairing, the helical surface states and nontrivial superconducting gap are obtained on the (001) surface. Analogous to the ${\mathrm{FeTe}}_{1\ensuremath{-}x}{\mathrm{Se}}_x$ superconductor, our results establish another material realization of a stoichiometric superconductor with nontrivial band topology, providing a promising platform for studying exotic Majorana physics in condensed matter.