Strain engineering of superconductivity in the kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$: Combined first-principles and Eliashberg theory study

The kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ provides a unique platform for studying intertwined quantum orders. Combing first-principles calculations and the Eliashberg theory of electron-phonon coupling (EPC), this work reveals axial-strain effects on superconducting properties of the kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ via EPC modulation. We demonstrate that compressive strains along distinct crystallographic directions induce contrasting phonon-mode responses: The $c$-axis compression softens M-point phonons while hardening L-point modes, whereas $ab$-plane strain directly enhances V-V orbital hybridization. These strain-induced electronic and lattice dynamics changes lead to nonmonotonic EPC evolution and monotonic suppression of superconducting transition temperature (${T}_{c}$). Carrier doping further modulates superconductivity through dual mechanisms: Hole doping enhances EPC (\ensuremath{\lambda} up to 1.65) through phonon softening and Van Hove singu