Three-dimensional metallic and two-dimensional insulating behavior in octahedral tantalum dichalcogenides

Using density functional theory with added on-site interactions, we study the electronic structure of bulk, monolayer, and bilayer of the layered transition-metal dichalcogenide $1T\text{−}\mathrm{TaS}{}_2$. We show that a two-dimensional spin-$\frac{1}{2}$ Mott phase exists for the monolayer in the charge density wave (CDW) state and that such a phase is systematically destroyed by packing of the distorted layers leading to a one-dimensional metal for bulk, CDW-distorted $\mathrm{TaS}{}_2$. The latter finding is in contrast with previous dynamical mean-field theory predictions—we explain the disagreement by the weak effective interaction felt by the electrons in the CDW state. Experimental observations of insulating behavior may arise from disorder due to stacking faults.

Figure 1

Spin-resolved band structures (top) and density of states (bottom) for the distorted (a) monolayer, (b) bilayer, and (c) bulk of $\mathrm{TaS}{}_2$ computed with GGA + $U(U=2.27\mathrm{eV})$ for vertically stacked centers of distortion. The red dotted line indicates the Fermi energy.

Figure 2

Phase diagram of distorted $1T\text{−}\mathrm{TaS}{}_2$ in plane of atomic on-site electron-electron interaction $U$ and interlayer distance $c$, for vertical (left) and trigonal (right) stackings of the centers of distortion. The contours in the left and right panels indicate the 0.4 (dotted green line), 0.8 (dashed red line), and 1.5 (solid black line) contours of the parametrized $\frac{U_{\mathrm{eff}}}{W}$ ratio [$U_{\mathrm{eff}}$ is the effective interaction as defined in Eq. (1); $W$ is the out-of-plane bandwidth calculated in DFT for $U=0$]. Gaps in the insulating state are indicated by colors. In each panel, the vertical orange line indicates the calculated value $U=2.27$ eV for undistorted bulk $1T\text{−}\mathrm{TaS}{}_2$. The hashed and plain areas, respectively, indicate out-of-plane antiferromagnetic and ferromagnetic ground states.

Figure 3

(a) Side and top views of the spin density for monolayer $\mathrm{TaS}{}_2$. Spin-up (-down) isosurfaces are indicated in blue (orange). (b) Atom-projected integrated charge density in the range $\left[E_F-0.1;E_F\right]$ for different values of the on-site electron-electron interaction $U$ ($U\in \left[0\mathrm{eV};4\mathrm{eV}\right]$), for the monolayer of $\mathrm{TaS}{}_2$. (c) Corresponding effective electron-electron interaction $U_{\mathrm{eff}}$ compared with the gap of the monolayer computed in DFT.