Superconductivity of VSe 2 under pressure and charge doping: Suppressed charge density wave

By employing the first-principles calculations, the influence mechanism of external pressure and charge doping on the electron-phonon coupling (EPC) and superconductivity (SC) of bulk ${\mathrm{VSe}}_{2}$ is investigated. Our calculations reveal that with increasing pressure the charge density wave (CDW) of $1\mathrm{T}\text{\ensuremath{-}}{\mathrm{VSe}}_{2}$ is gradually suppressed, and a SC state subsequently emerges which is accompanied by a structural phase transition from the trigonal phase to a monoclinic phase at $15.5\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$. Increasing pressure from 15.5 to $35\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$, the SC transition temperature ${T}_{c}$ of ${\mathrm{VSe}}_{2}$ slightly increases from 4.2 to $5.2\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and no SC dome is found, which are in good agreement with the previous experimental results [S. Sahoo et al., Phys. Rev. B 101, 014514 (2020)]. Through electron- or hole-doping (denoted by ${n}_{e}$ and ${n}_{h}$), the CDW order of the trigonal phase can be suppressed and SC states with ${T}_{c}$ greater than 10.5 and $9.0\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, respectively, emerge. The highest ${T}_{c}$ under charge doping can be up to about $12\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, and a weak double-dome like dependence of ${T}_{c}$ on ${n}_{e}$ and ${n}_{h}$ is found. Combining systematical analysis of effects of pressure and charge doping, we demonstrate that the Kohn anomalies of phonons at certain $Q$ points associated with the in-plane vibrations of V atoms play key roles in strengthening the EPC, which brings about the intriguing SC in ${\mathrm{VSe}}_{2}$. However, due to the weak pressure-induced modifications of phonon spectrum as well as Fermi surface (FS), the changes of EPC and ${T}_{c}$ caused by pressure are not significant. Interestingly, charge doping will produce a local flat band along $\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ direction near the FS, which is mainly contributed by V $3d$-orbitals, and result in large values of electronic density of states at Fermi level. Therefore, the effects caused by charge doping to the electronic structures, phonon anomalies, EPC, and ${T}_{c}$ are evident. Our findings may provide a promising understanding to the pressure and doping-dependent SC of ${\mathrm{VSe}}_{2}$, and may be valuable for designing new materials with enhanced SC through the strategic manipulation of electronic and phononic properties.