First-principles study of Na-intercalated bilayer NbSe2 : Suppressed charge-density wave and strain-enhanced superconductivity

Layered ${\mathrm{NbSe}}_{2}$ is a metallic layered transition metal dichalcogenide (TMD) that has attracted much interest for the coexistence of superconductivity and charge-density wave (CDW) down to the monolayer limit. Here we report first-principles calculations of the lattice dynamics, electronic structure, and electron-phonon coupling of Na-intercalated bilayer ${\mathrm{NbSe}}_{2}$. We show that upon the Na atom intercalation, the CDW instability in the bilayer ${\mathrm{NbSe}}_{2}$ can be effectively suppressed, accompanied by the removal of the soft phonon modes at ${\mathbf{q}}_{\mathrm{CDW}}=\frac{2}{3}\mathrm{\ensuremath{\Gamma}}M$. The underlying mechanism for this phenomenon is that a large electron doping from the intercalated Na contracts the Fermi surface of bilayer ${\mathrm{NbSe}}_{2}$ and reduces the electron-phonon coupling at ${\mathbf{q}}_{\mathrm{CDW}}$. In spite of the disappearance of CDW, the superconductivity still survives in the ${\mathrm{NbSe}}_{2}$ intercalate, with a predicted superconducting transition temperature ${T}_{c}$ of 3 K. Moreover, we find that the biaxial compressive strain can greatly increase density of states near the Fermi surface and soften characteristic phonons contributing to superconductivity, leading to an increase of ${T}_{c}$ by more than 100% at a low strain level of 3%. Our results would have significant implications for tuning CDW and superconductivity in ${\mathrm{NbSe}}_{2}$ and other metallic TMD materials.