Hierarchical stripe phases in $\mathrm{IrT}{\mathrm{e}}_2$ driven by competition between Ir dimerization and Te bonding

Layered $5d$ transition metal dichalcogenide (TMD) $\mathrm{IrT}{\mathrm{e}}_2$ is distinguished from the traditional TMDs (such as $\mathrm{NbS}{\mathrm{e}}_2)$ by the existence of multiple charge-density wave (CDW)-like stripe phases and superconductivity at low temperatures. Despite intensive studies, there is still no consensus on the physical origin of the stripe phases or even the ground state modulation for this $5d$ material. Here we present atomic-scale evidence from scanning tunneling microscopy and spectroscopy (STM/STS) that the ground state of $\mathrm{IrT}{\mathrm{e}}_2$ is a $q=1/6$ stripe phase, identical to that of the Se-doped compound. Furthermore, our data suggest that the multiple transitions and stripe phases are driven by the intralayer Ir-Ir dimerization that competes against the interlayer Te-Te bonding. The competition results in a unified phase diagram with a series of hierarchical modulated stripe phases, strikingly similar to the renowned “devil's staircase” phenomena.

Figure 1

Visualizing the Te-Te dimer stripes on the surface of $\mathrm{IrT}{\mathrm{e}}_2$ and $\mathrm{IrT}{\mathrm{e}}_{2-x}\mathrm{S}{\mathrm{e}}_x$. (a) and (b) Topographic images of the $q=1/6$ states in $\mathrm{IrT}{\mathrm{e}}_2$ and $\mathrm{IrT}{\mathrm{e}}_{2-x}\mathrm{S}{\mathrm{e}}_x$ at 4.5 K without the 1/3 charge density modulation. The inset of (a) shows the crystal structure of $\mathrm{IrT}{\mathrm{e}}_2$. The atoms in the STM images correspond to the top Te layer (Te1). (c) and (e) The unit-cell-averaged images of (a) and (b), respectively. Here the alternating Te-Te dimers are clearly visible (indicated by the red dashed curves). (d) Schematic diagram of the unit cell for the 1 × 6 structure, illustrating individual atomic shifts and the Te-Te dimers. The gray/cyan spheres represent the undistorted/distorted positions of top Te atoms. (f) The Fourier transform of the topographic image (including the 1/3 modulation) of $\mathrm{IrT}{\mathrm{e}}_2$ in the area shown in (a). A 1/6 peak near (010) is clearly seen. (g) The line profiles along the red and blue arrows show the peaks (1/6 and 1/3) associated with the $q=1/6$ modulation. The tunneling setup conditions for (a) and (b) are $V_{\mathrm{bias}}=5\mathrm{mV}$ and $I_{\mathrm{set}}=5/15\mathrm{nA}$.

Figure 2

LDOS of $\mathrm{IrT}{\mathrm{e}}_{2-x}\mathrm{S}{\mathrm{e}}_x$ and $\mathrm{IrT}{\mathrm{e}}_2$ at 4.5 K. (a) and (b) Typical topographic image (4.5 K) of $\mathrm{IrT}{\mathrm{e}}_{2-x}\mathrm{S}{\mathrm{e}}_x$ and $\mathrm{IrT}{\mathrm{e}}_2$, respectively. These suggest that the ground state of $\mathrm{IrT}{\mathrm{e}}_{2-x}\mathrm{S}{\mathrm{e}}_x$ is a long range ordered $q=1/6$ phase, even in the presence of Te/Se disorder. (c) and (d) Averaged $dI/dV$ spectroscopy data (LDOS) with large energy range of $\mathrm{IrT}{\mathrm{e}}_{2-x}\mathrm{S}{\mathrm{e}}_x$ and $\mathrm{IrT}{\mathrm{e}}_2$, respectively, indicating qualitatively identical LDOS. (e) STS of individual atomic columns [defined in (f)] within half period of the 1/6 phase. (f) Unit-cell-averaged STM image with labels of atomic columns (1, 2, 3) and a cartoon of $\mathrm{IrT}{\mathrm{e}}_2$ lattice (side view). The crystal orientation is determined by tracing the shift of the stripes across a step edge on the same surface (see Fig. S4 [24]). (g) Calculated LDOS of Te $p_z$ orbitals on the top Te layer [defined in (f)], while the $p_z$ orbital is pointing out of plane. Here the spectroscopic data were measured over a very wide high energy range (±2 V).

Figure 3

LDOS of soliton crest in $\mathrm{IrT}{\mathrm{e}}_2$ and Pt-doped $\mathrm{IrT}{\mathrm{e}}_2$ at 4.5 K. (a) Diluted solitons occasionally observed in $\mathrm{IrT}{\mathrm{e}}_2$ at 4.5 K. (b) Areal averaged STS of soliton crest (blue) in comparison with that of 1/6 phase (red). (c) Typical topographic image of slightly Pt doped $\mathrm{IrT}{\mathrm{e}}_2$, where the 1/5 phase is stabilized at 4.5 K. (d) Column-averaged STS data of crest (purple) and valley (green) in the 1/5 phase. The LDOS of soliton (crest) at Fermi energy $E_{\mathrm{F}}$ is higher than that of valley (dimerized stripes). (e) Typical topographic image of ∼10% Pt doped $\mathrm{IrT}{\mathrm{e}}_2$. The stripe modulated phases is completely suppressed with significant Pt doping, resulting in the high temperature phase (1 × 1). (f) Averaged STS data of $\mathrm{I}{\mathrm{r}}_{0.9}\mathrm{P}{\mathrm{t}}_{0.1}\mathrm{T}{\mathrm{e}}_2$ (orange) in comparison with that of soliton crest in (a) (blue). The qualitative similarity between these data suggests that the soliton (crest) is undimerized atomic rows.

Figure 4

A unified-phase diagram of doped $\mathrm{IrT}{\mathrm{e}}_2$. The first order phase transition $T_{\mathrm{C}}$ is enhanced when Te is partially replaced by Se, suggesting that Se doping strengthens the Ir-Ir dimerization. The large hysteretic transition $T_{\mathrm{S}}$ is suppressed by the enhancement of dimerization. In contrast, Pt doping weakens dimerization tendency so that $T_{\mathrm{C}}$ is suppressed and superconductivity emerges at low temperature (∼3 K).