Origin of First-Order-Type Electronic and Structural Transitions in ${\mathrm{IrTe}}_2$

We have explored the origin of unusual first-order-type electronic and structural transitions in ${\mathrm{IrTe}}_2$, based on the first-principles total energy density functional theory analysis. We have clarified that the structural transition occurs through the interplay among the charge density wavelike lattice modulation with $q_{1/5}=(1/5,0,1/5)$, in-plane dimer ordering, and the uniform lattice deformation. The Ir-Ir dimer formation via a molecular-orbital version of the Jahn-Teller distortion in the Ir-Ir zigzag stripe is found to play the most important role in producing the charge disproportionation state. Angle-resolved photoemission spectroscopy reveals the characteristic features of structural transition, which are in good agreement with the density functional theory bands obtained by the band-unfolding technique.

Figure 1

(a) High-$T$ HEX unit cell (blue), and $$low-$T$ 5X unit cell (black) of ${\mathrm{IrTe}}_2$. The violet (grey) spheres are Ir (Te) atoms, yellow octahedra represent ${\mathrm{IrTe}}_6$ octahedra, and red rods indicate ${\mathrm{Ir}}_3\text{−}{\mathrm{Ir}}_3$ dimers. (b) The near-$E_F$ Ir wave function of $d_{z(x-y)}$ character forms antibonding with Te wave functions located along diagonal directions. The bright (dark) red triangle describes the Te lattice above (below) the Ir layer. $x$, $y$, and $z$ are local coordinates of Ir, approximately pointing toward Te sites. $x-y$ lies in the Ir plane. (c) The orbital-projected Fermi surface (FS) of the high-$T$ phase of ${\mathrm{IrTe}}_2$. The color of the FS indicates the weight contribution from Ir $d_{z(x-y)}$, which shows the clear 1D nature (to plot orbital-projected FS, we used the moliso package [12]).

Figure 2

(a) Energy contour of ${\mathrm{IrTe}}_2$ in the structural phase space. $A$ and $B$ stand for the structural parameters of HEX5 and 5X, respectively. The horizontal and vertical axes represent the in-plane dimerization coupled to the $1/5$ lattice modulation and the uniform lattice deformation, respectively, which are linearly interpolated between structural parameters of $A$ and $B$ on $13\times 13$ mesh points [18, 26]. Energy zero corresponds to the energy of the HEX5 structure. $C$ represents a saddle point where the energy barrier is the lowest. (b) Energy profile along the path connecting $A$ and $B$ directly. The 5X structure is seen to be lower in energy than the HEX5 by 6.25 meV per formula unit. (c) A schematic mechanical model describing the interplay between the ${\mathrm{Ir}}_3\text{−}{\mathrm{Ir}}_3$ dimerization ($x$) and the uniform lattice deformation ($y$), which are coupled through ${\mathrm{Te}}_1$ distortion ($z$) [18].

Figure 3

(a)–(c) Partial densities of states (DOSs) for HEX5, no-DO, and 5X structures, where no-DO corresponds to an artificial structure without dimer ordering, as depicted in (e). (d)–(f) In-plane structures and corresponding schematic DOSs for HEX5, no-DO, and 5X. The yellow shade represents the compressed region due to the $1/5$ lattice modulation. Large (small) circles denote Ir (Te) atoms. The red and white small circles are Te atoms located above and below the Ir layer. Te atoms in the yellow shade are ${\mathrm{Te}}_1$. Two DOS peaks in blue and green correspond to bonding and antibonding states of $d_{xy}$ and $d_{yz}$. Note that $d_{xy}$ and $d_{yz}$ orbitals participate in two different dimer orderings: one specific dimer ordering (red thick lines) is shown in (f), which is associated with the $d_{xy}$ orbital.

Figure 4

(a) The DFT band structure of 5X ${\mathrm{IrTe}}_2$ unfolded into the HEX Brillouin zone (BZ). The intensity of band dispersion represents the weight of Ir-projected character. (b) The relation between the large HEX and the small 5X BZ. (c) The $\mathrm{\Gamma }$ ($k_z=0$) plane of the HEX BZ. (d) The DFT FSs of 5X ${\mathrm{IrTe}}_2$ unfolded into the HEX BZ for different $k_z$. (e) The DFT bands calculated for the HEX structure (left) are compared with ARPES data (right) at $T=290\mathrm{K}$ above $T_S$. (f) The unfolded DFT bands for the 5X structure (left) are compared with ARPES data (right) at $T=260\mathrm{K}$ below $T_S$. The vertical lines in the DFT bands represent the experimental scan range (0.9 Å). Photon energy used in this ARPES is 75.0 eV.