Emergent charge density wave featuring quasi-one-dimensional chains in Ta-intercalated bilayer 2$H$-TaS$_{2}$ with coexisting superconductivity

Recently, intercalation emerges as an effective way to manipulate ground-state properties and enrich quantum phase diagrams of layered transition metal dichalcogenides (TMDCs). In this work, we focus on fully Ta-intercalated bilayer 2$H$-TaS$_{2}$ with a stoichiometry of Ta$_{3}$S$_{4}$, which has recently been experimentally synthesized. Based on first-principles calculations, we computationally show the suppression of an intrinsic $3\times3$ charge-density wave (CDW) in the TaS$_{2}$ layer, and the emergence of a $2\times1$ CDW in intercalated Ta layer. The formation of the CDW in Ta$_{3}$S$_{4}$ is triggered by strong electron-phonon coupling (EPC) between the $d$-like orbitals of intercalated Ta atoms via the imaginary phonon modes at M point. A 2$\times$1 CDW structure is identified, featuring quasi-one-dimensional Ta chains, attributable to the competition between the CDW displacements associated with potential CDW vectors ($\boldsymbol{q}_{\text{CDW}}$s). Superconductivity is found to coexist with the 2$\times$1 CDW in Ta$_{3}$S$_{4}$, with an estimated superconducting transition temperature ($T_{\mathrm{c}}$) of 3.0 K, slightly higher than that of bilayer TaS$_{2}$. The Ta$_{3}$S$_{4}$ structures of non-CDW, 2$\times$1 CDW, and $2\times$2 CDW can be switched by strain. Our work enriches the phase diagram of TaS$_{2}$, offers a candidate material for studying the interplay between CDW and superconductivity, and highlights intercalation as an effective way to tune the physical properties of layered materials.