High-order van Hove singularities and nematic instability in the kagome superconductor CsTi${}_3$Bi${}_5$

ATi${}_3$Bi${}_5$ (A = Cs or Rb) are emerging topological kagome metals that exhibit superconductivity and nematicity without intertwining translational symmetry-breaking charge orders. In this work, we explore the fermiology of their titanium kagome electrons and identify a set of sublattice-pure, high-order van Hove singularities (VHSs) that can suppress charge ordering and enhance electronic correlations and superconductivity. Our calculations of charge susceptibility for kagome bands with both normal and high-order VHSs emphasize the role of these VHSs in driving electronic nematicity in CsTi${}_3$Bi${}_5$. Additionally, we compute the phonon spectrum and electron-phonon interactions for CsTi${}_3$Bi${}_5$ under pristine, doped, and kagome-exposed surface conditions, revealing its robustness against structural instabilities while enhancing the superconducting transition temperature. Our work positions ATi${}_3$Bi${}_5$ as a key platform for investigating superconductivity and electronic nematicity without translational symmetry-breaking states in kagome metals.