Absence of local fluctuating dimers in superconducting ${\mathrm{Ir}}_{1-x}{(\mathrm{Pt},\mathrm{Rh})}_x{\mathrm{Te}}_2$

The compound ${\mathrm{IrTe}}_2$ is known to exhibit a transition to a modulated state featuring Ir-Ir dimers, with large associated atomic displacements. Partial substitution of Pt or Rh for Ir destabilizes the modulated structure and induces superconductivity. It has been proposed that quantum critical dimer fluctuations might be associated with the superconductivity. Here we test for such local dimer correlations and demonstrate their absence. X-ray pair distribution function approach reveals that the local structure of ${\mathrm{Ir}}_{0:95}{\mathrm{Pt}}_{0:05}{\mathrm{Te}}_2$ and ${\mathrm{Ir}}_{0:8}{\mathrm{Rh}}_{0:2}{\mathrm{Te}}_2$ dichalcogenide superconductors with compositions just past the dimer/superconductor boundary is explained well by a dimer-free model down to 10 K, ruling out the possibility of there being nanoscale dimer fluctuations in this regime. This is inconsistent with the proposed quantum-critical-point-like interplay of the dimer state and superconductivity, and precludes scenarios for dimer fluctuations mediated superconducting pairing.

Figure 1

Sketch of the local atomic environments in ${\mathrm{IrTe}}_2$ for the (a) undistorted high-temperature structure (trigonal $P\overline{3}m1$) and (b) distorted low-temperature structure (triclinic $P\overline{1}$) featuring Ir-Ir and Te-Te dimers. Dimerization results in dramatic distortions of associated interatomic distances relative to the high-temperature structure, as indicated by block arrows and described in the text. Comparison of PDFs (c) calculated from trigonal (red line) and triclinic (blue line) models and (d) measured at 275 K (red line) and at 220 K (blue line). Numbered vertical arrows in (c) and (d) mark features associated with these distortions. $\mathrm{\Delta }G\left(r\right)$ is the difference, offset for clarity.

Figure 2

Electrical resistivity of ${\mathrm{IrTe}}_2, {\mathrm{Ir}}_{0.95}{\mathrm{Pt}}_{0.05}{\mathrm{Te}}_2$, and ${\mathrm{Ir}}_{0.8}{\mathrm{Rh}}_{0.2}{\mathrm{Te}}_2$ samples, normalized to their 300 K values. Insets: low-temperature resistivity (top left) and low-temperature susceptibility (bottom right) collected in the zero-field-cooling mode.

Figure 3

Azimuthally integrated 2D diffraction patterns of ${\mathrm{Ir}}_{1-x}{(\mathrm{Pt},\mathrm{Rh})}_x{\mathrm{Te}}_2$ for 300 K (red line) and 10 K (blue line) over a narrow range of momentum transfer $Q$ for (a) $x=0$, (b) $x=0.05$ Pt, and (c) $x=0.2$ Rh. All patterns are normalized by the intensity of the (001) reflection ($P\overline{3}m1$ indexing). Vertical arrows in (a) indicate superlattice reflections observed in 10 K data. Corresponding PDFs are compared in (d), (e), and (f), respectively, with differences shown underneath and offset for clarity.

Figure 4

A comparison of the 10 K (blue) and 300 K (red) PDF data for (a) ${\mathrm{IrTe}}_2$, (b) ${\mathrm{Ir}}_{0.95}{\mathrm{Pt}}_{0.05}{\mathrm{Te}}_2$, and (c) ${\mathrm{Ir}}_{0.8}{\mathrm{Rh}}_{0.2}{\mathrm{Te}}_2$, where the 10 K data were adjusted in the simple optimization procedure described in the text. Differences are plotted underneath and offset for clarity.

Figure 5

Temperature dependence of the isotropic ADPs of Ir (olive symbols) and Te (gray symbols) in ${\mathrm{Ir}}_{1-x}{(\mathrm{Pt},\mathrm{Rh})}_x{\mathrm{Te}}_2$ obtained from $P\overline{3}m1$ model fits to (a) $x=0$, (b) $x=0.05$ Pt, and (c) $x=0.2$ Rh sample data over the 10–300 K temperature range. Inset: detection of the onset of dimer fluctuations from temperature-dependent Ir-ADP in 20% Cr-doped ${\mathrm{CuIr}}_2{\mathrm{S}}_4$, where Ir-Ir dimerization sets in below 200 K on only a nanometer length scale, while the long-range dimer order is absent at all temperatures [38]. Such behavior is not observed in (b) and (c) for superconducting ${\mathrm{Ir}}_{1-x}{(\mathrm{Pt},\mathrm{Rh})}_x{\mathrm{Te}}_2$.

Figure 6

Quantification of PDF sensitivity to the presence of dimers. (a) Simulated PDFs of ${\mathrm{IrTe}}_2$ comprising mixtures of dimer ($P\overline{1}$) and nondimer ($P\overline{3}m1$) phases, with a mixing ratio increment of 0.1. The different solid profiles correspond to dimer fractions ranging from 6% of dimerized Ir-Ir nearest neighbors (as observed in the $P\overline{1}$ phase, blue) to no dimers (which is the case for $P\overline{3}m1$, red). PDFs for the intermediates are shown in gray. (b) Isotropic ADP of Ir obtained by fitting the dimer-free $P\overline{3}m1$ model to the simulated PDFs in (a) as a function of absolute fraction of dimerized Ir-Ir bonds. The gray shaded region represents typical uncertainty on the $2\sigma$ level in determining this parameter from the experimental PDFs using the same $P\overline{3}m1$ model.

Figure 7

Fits of the trigonal structure model (solid red lines) to experimental PDF data (open blue symbols) of the ${\mathrm{IrTe}}_2$ sample at (a) 300 K and (b) 10 K and (c) 5% Pt-substituted sample at 10 K and (d) 20% Rh-substituted sample at 10 K. The difference between the data and the model $\mathrm{\Delta }G\left(r\right)$, plotted below, is offset for clarity. See text for details.

Figure 8

Normalized dimer density as a function of Pt and Rh content in ${\mathrm{IrTe}}_2$ estimated from published magnetic susceptibility measurements [19, 21].