Dimerization-Induced Cross-Layer Quasi-Two-Dimensionality in Metallic ${\mathrm{IrTe}}_2$

The crystal structure of layered metal ${\mathrm{IrTe}}_2$ is determined using single-crystal x-ray diffraction. At $T=220\mathrm{K}$, it exhibits Ir and Te dimers forming a valence-bond crystal. Electronic structure calculations reveal an intriguing quasi-two-dimensional electronic state, with planes of reduced density of states cutting diagonally through the Ir and Te layers. These planes are formed by the dimers exhibiting a signature of covalent bonding character development. Evidence for significant charge disproportionation among the dimerized and nondimerized Ir (charge order) is presented. We argue that the structural transition is driven by the Ir dimerization and bonding, while electronic correlations (dynamical mean field theory corrections to density functional theory) and spin orbit coupling play a secondary role.

Figure 1

The structure of ${\mathrm{IrTe}}_2$ at (a) room temperature (RT) and (b) $T=220\mathrm{K}$. The elementary crystallographic unit cells (boxes), axes (arrows), and reciprocal axes $c_0*$ and $c*$ (thick arrows) are shown. Calculated Fermi surface at RT (c), and 220 K (d). At RT, the triclinic unit cell vectors $a$, $b$, $c$ corresponding to those shown in (b) can also be introduced: $a=b_0$, $b=-a_0-b_0+c_0$, $c=4a_0+2b_0+c_0$. However, the triclinic cell is nonelementary at RT.

Figure 2

(a) Triangular Ir layer at $T=220\mathrm{K}$. Dashed line shows the projection of the triclinic unit cell. (b) Triangular Te layer at $T=220\mathrm{K}$. The Ir layer directly above is also shown. In both panels, the bond lengths are color coded as shown in the legend, and Ir(3)-Ir(3) dimers are marked with dashed ovals.

Figure 3

(a) The density of states at $E_F$ for the planes of Ir and Te atoms running normal to the $c*$ axis shown in panel (b) directly below. Each plane is identified with an arrow. The ratio of the low- (220 K-) and high- (300 K-)temperature DOS for each of these planes is also shown. (b) Projection of the $T=220\mathrm{K}$ structure along the triclinic $a$ axis. The atoms form perfect columns; i.e., Ir(1) is directly below Ir(1), etc. Black box shows the projection of the unit cell. Ovals identify the Ir dimers. Shortened Te-Te bonds are shown in blue and cyan. The shaded region identifies a plane of suppressed DOS at $E_F$ formed by Ir and Te dimers. This plane is normal to the $c*$ axis. In contrast, the structural Ir and Te layers run normal to the $c_0$ direction.

Figure 4

(a) Total density of states (TDOS), and Ir DOS at $T=300\mathrm{K}$ (HT) and 220 K (LT). (b) Combined DOS of the $5d$ (all $t_{2g}$) orbitals for Ir(1) and Ir(3) at LT, as well as for any Ir at HT. The DOS for the Ir(3) $d_{xy}$ orbital at LT is also shown. The arrows point to the DOS peaks associated with the bonding and antibonding molecular orbitals in the Ir dimers. The corresponding antibonding orbital is sketched at right. The $x$, $y$, and $z$ axes for the $d$ orbitals are the local axes of the ${\mathrm{IrTe}}_6$ octahedra. (c) LT DOS of the Te(1), Te(2), and Te(5) $4p_x$ orbitals for the Te(1)-Te(3), Te(2)-Te(2), and Te(5)-Te(1) bonds, respectively. The bonds are shown in Fig. 3 using the same color code. The $x$ axis of each $p_x$ orbital coincides with the corresponding Te-Te bond direction. The averaged HT Te $p$ DOS is also shown.