Interplay of charge ordering and superconductivity in two-dimensional 2H group V transition-metal dichalcogenides

Abstract

Layered $2H\text{\ensuremath{-}}T{X}_{2}$ with $T=\mathrm{Nb}$, Ta and $X=\mathrm{S}$, Se exhibit rich dimensionality effects on charge density wave (CDW) order and superconductivity, but comprehensive understanding of these correlated quantum phases in the two-dimensional limit of $2H\text{\ensuremath{-}}T{X}_{2}$ is still lacking, hindering their practical applications. Here, I calculate from first principles the phonon linewidth and bare susceptibility to study the origin of CDW formation in ${\mathrm{NbSe}}_{2}$, ${\mathrm{TaS}}_{2}$, ${\mathrm{TaSe}}_{2}$, and ${\mathrm{NbS}}_{2}$ monolayers, analyze their relative CDW strength, and evaluate electron-phonon superconductivity within the fully anisotropic Migdal-Eliashberg theory. A peaked linewidth of the longitudinal acoustic branch and no Fermi-surface nesting around ${\mathbf{q}}_{\mathrm{CDW}}$ indicate CDW instability driven by the wave-vector-dependent electron-phonon coupling. The $3\ifmmode\times\else\texttimes\fi{}3$ CDW ground state favors a distinct hollow-centered clustering of transition-metal atoms, with larger distortion amplitude in ${\mathrm{NbSe}}_{2}$ and ${\mathrm{TaSe}}_{2}$ than in ${\mathrm{TaS}}_{2}$ and ${\mathrm{NbS}}_{2}$. Superconducting results of the monolayer CDW phase prove that strong spin-orbit coupling effects are dominant in determining the critical temperature ${T}_{\mathrm{c}}$ of each system via modifying both the strength and anisotropic extent of electron-phonon interactions. I also recapitulate measured opposite thickness dependencies of ${T}_{\mathrm{c}}$ in $\mathrm{Nb}{X}_{2}$ and $\mathrm{Ta}{X}_{2}$, and show that whether superconductivity is weakened or enhanced in monolayer limit relies on specific evolution of CDW-modulated Fermi-level density of states and electron-phonon matrix elements under reduced dimensionality. This work lays the foundation for applications of $2H$ group V transition-metal dichalcogenides in versatile nanoscale quantum devices.