Origin of the Insulating Phase and First-Order Metal-Insulator Transition in $1T\text{−}{\mathrm{TaS}}_2$

Using density functional theory calculations, we investigate the origin of the insulating phase and metal-insulator transition (MIT) in octahedral tantalum disulfide ($1T\text{−}{\mathrm{TaS}}_2$), a layered van der Waals material with a prominent two-dimensional (2D) charge density wave (CDW) order. We show that the MIT is driven not by the 2D order itself, but by the vertical ordering of the 2D CDWs or the 3D CDW order. We identify two exceptionally stable 3D CDW configurations; one is insulating and the other is metallic. The competition and mixing of the two CDW configurations account for many mysterious features of the MIT in $1T\text{−}{\mathrm{TaS}}_2$, including the pressure- and doping-induced transitions and the hysteresis behavior. The present results emphasize that interlayer electronic ordering can play an important role in electronic phase transitions in layered materials.

Figure 1

3D CDW ordering. (a) Atomic structure of $1T\text{−}{\mathrm{TaS}}_2$. (b) In-plane star-of-David distortion and labeling convention of the 13 Ta atoms in a star. The Ta atoms at the star center have a half-filled localized state with $d_{z^2}$ character. (c) Arrangement of the localized states of the central Ta atoms for the three representative CDW stacking configurations: $A$, $L$, and $AL$. Side views are shown schematically. (d) Calculated unfolded band structures for the $A$, $L$, and $AL$ stacking configurations along the high symmetry line in the Brillouin zone depicted in (e). Experimental ARPES data [17] are shown for comparison. The Fermi level is set to zero. The peak near $-1.0\mathrm{eV}$ around the $\mathrm{\Gamma }\text{−}A$ line is from S $3p$ orbitals, the binding energies of which are underestimated in our GGA calculations and should be located below $-1.2\mathrm{eV}$ [18] (Fig. S1). We used the BandUP code [28] for band unfolding.

Figure 2

Dependence on pressure and doping. Total energies of the $AL$ and $L$ stacking configurations are shown as a function of the layer spacing ($c$) for undoped and electron-doped cases. Relative values are shown with offsets for doped cases.

Figure 3

Hysteresis behavior. (a) Evolution of the CDW stacking configuration under cooling, obtained from the 1D MC simulations. The CDW stacking interfaces for 200 layers are color coded with blue for $AL$, light green for $L$, and yellow and red for the other stacking interfaces. The cooling rate was 0.1 K per MC sweep. (b) Population ratio of the $AL$ stacking configuration, $P_{\mathrm{pair}}$, as a function of temperature for various cooling and heating rates. The curves were smoothed to remove fluctuation.