Trimer bonding states on the surface of the transition-metal dichalcogenide $\mathrm{TaT}{\mathrm{e}}_2$

We report a comprehensive study on the surface structural and electronic properties of $\mathrm{TaT}{\mathrm{e}}_2$ at room temperature. The surface structure was investigated using both low energy electron diffraction intensity versus voltage and density functional theory calculations. The relaxed structures obtained from the two methods are in good agreement, which is very similar to the bulk, maintaining double zigzag trimer chains. The calculated density of states indicates that such structure originates from the trimer bonding states of the Ta $d_{xz}$ and $d_{xy}$ orbitals. This work will further provide new insights towards the understanding of the charge density wave phase transition in $\mathrm{TaT}{\mathrm{e}}_2$ at low temperature.

Figure 1

(a) Bulk crystal structure of $\mathrm{TaT}{\mathrm{e}}_2$. Ta atoms are labeled yellow and blue, and Te atoms are labeled red. Samples are cleaved between the two Te layers. (b) Top view of the undistorted ideal $1T$ structure. (c) Top view of the double zigzag trimer chain structure. Ta1 and Ta2 atoms are labeled yellow and blue, respectively. The double zigzag trimer structure is formed with both Ta2 atoms moving towards Ta1 atoms. The Ta1-Ta2 bondings are indicated by red sticks. The 2D lattice vectors $a$ and $b$ are labeled by the green and red arrows, forming a $3\times 1$ superstructure. (d) Top view of the single zigzag dimer chain structure. The Ta2-Ta2 bondings are indicated by red sticks. The unit cell has the same lattice vectors, which are also labeled by the green and red arrows. (e) LEED pattern of freshly cleaved $\mathrm{TaT}{\mathrm{e}}_2$ surface at 300 K and 80 eV. The reciprocal lattice vectors of domain 1, $a^{*}$ and $b^{*}$, are labeled by the green and red arrows. (f) Schematic LEED pattern from a $3\times 1$ superstructure with two domains. The red spots are integer diffraction spots from an ideal $1T$ structure, and the yellow and blue spots are fractional diffraction spots from domain 1 and domain 2, respectively.

Figure 2

(a) Comparison between experimental and simulated LEED I-V curves for the best-fit structure. Results for 8 of the total 47 inequivalent beams are represented here. The labeling of each beam is based on the reciprocal lattice vectors $a^{*}$ and $b^{*}$ in Fig. 1. The overall Pendry reliability factor is $R_P=0.29\pm 0.02$. (b) Top view of the $\mathrm{TaT}{\mathrm{e}}_2$ surface. The Cartesian coordinates used in LEED I-V calculation are labeled by the green and red arrows, and dot in a circle. (c) Dependence of $R_P$ values on the Ta-Ta bonding distances as the structure changes from trimer to dimer.

Figure 3

(a) Schematic illustration of $d_{xz}$ and $d_{xy}$ orbitals in an octahedral environment. The red squares indicate the planes formed by corresponding coordinates. (b) $d_{xz}$ and $d_{xy}$ orbitals at Ta sites, participating in strong σ-overlaps along the $xz$ and $xy$ directions, respectively. The red rectangles are consistent with the red squares in (a). (c) Schematic illustration of bonding, nonbonding, and antibonding states. (d) Schematic illustration of dual trimerization of $d_{xz}$ and $d_{xy}$ chains, depicted as thick dark yellow and blue lines, respectively, resulting in the formation of the diamond-shaped chains along the $yz$ direction as shown in the figure. (e) Projected densities of states (PDOS) for the hypothetical ${\mathrm{C}}_3$-symmetric structure (upper panel) and for the room temperature structure (middle and lower panels). Note that, due to the trimerization, $d_{xz}$ (or $d_{xy})$ orbitals split into bonding, nonbonding, and antibonding states.

Figure 4

Complete comparison between experimental and simulated LEED I-V curves for the total 47 inequivalent beams.

Figure 5

(a) Side view of $\mathrm{TaT}{\mathrm{e}}_2$ crystal structure. Different types of atoms are as labeled. The cleaving planes are indicated by the dashed lines. (b) Top view of the $\mathrm{TaT}{\mathrm{e}}_2$ crystal structure. The black parallelogram indicates the in-plane unit cell. (c)–(e) Top view of each composite layer. The top Te layer, Ta layer, and the bottom Te layer are shown by (c), (d), and (e), respectively. The black parallelogram in each subfigure indicates the in-plane unit cell. The Cartesian coordinates used in the calculation are labeled by the green and red arrows, and dot in a circle $(x,y$, and $z)$ in (b).