Real-Space Observation of Emergent Complexity of Phase Evolution in Micrometer-Sized ${\mathrm{IrTe}}_2$ Crystals

We report complex behaviors in the phase evolution of transition-metal dichalcogenide ${\mathrm{IrTe}}_2$ thin flakes, captured with real-space observations using scanning Raman microscopy. The phase transition progresses via growth of a small number of domains, which is unlikely in statistical models that assume a macroscopic number of nucleation events. Consequently, the degree of phase evolution in the thin flakes is quite variable for the selected specimen and for a repeated measurement sequence, representing the emergence of complexity in the phase evolution. In the $\sim 20\text{−}\mu {\mathrm{m}}^3$-volume specimen, the complex phase evolution results in the emergent coexistence of a superconducting phase that originally requires chemical doping to become thermodynamically stable. These findings indicate that the complexity involved in phase evolution considerably affects the physical properties of a small-sized specimen.

Figure 1

(a) Raman spectra obtained from an ${\mathrm{IrTe}}_2$ thin plate. The two peaks at $\sim 128{\mathrm{cm}}^{-1}$ and $\sim 165{\mathrm{cm}}^{-1}$ in the Ir-undimerized (UD; top panel) phase split into multiple peaks because of symmetry lowering occurring upon transition to the Ir-dimerized (D; middle panel) phase [34, 35]. The Raman spectrum at (or near) a domain wall (DW; bottom panel) can be reproduced by superposition of the Raman spectra of the UD and D phases (broken line). (b), (c) Domain images at 280 (b) and 270 K (c) upon cooling from 300 K. The spatial distribution of the spectral weight of the D state is represented by the color of each pixel, representing a domain structure consisting of the UD (blue) and D (red) phases. (d), (e) Domain images at 270 K in the second (d) and third (e) cooling runs from 300 K. (f) Superposed image of the three initial-domain images shown in (c)–(e). The color of each pixel represents the number of times—0 (gray), 1 (green), 2 (blue), or 3 (red)—that the Raman spectrum of the D phase was observed in the three repeated sequences.

Figure 2

(a) Consecutive domain images of sample #1 for a thermal cycle of $300\to 200\to 300\mathrm{K}$. For those of sample #2, see Fig. S3 [30]. (b) Temperature evolution of the volume fraction of the charge-ordered phase in samples #1 and #2.

Figure 3

(a), (b) Isothermal time evolution of the domain images at 270 K after cooling from 300 K for twice repeated sequences. (c) Isothermal time evolution of the volume fraction of the charge-ordered phase at 270 K after cooling from 300 K. The times corresponding to the domain images shown in (a), (b) are indicated by arrows in (c).

Figure 4

(a) Temperature-resistivity profiles in samples #3 and #4 near the lowest temperature. Inset: temperature-resistivity profiles near the first-order phase transition. The sample perimeter, thickness, and volume are $86\mu \mathrm{m}$, 580 nm, and $180\mu {\mathrm{m}}^3$ for sample #3 and $44\mu \mathrm{m}$, 160 nm, and $18\mu {\mathrm{m}}^3$ for sample #4. (b), (c) Domain images at 2 K of samples #1 (b) and #2 (c). Note that although the sample geometries are close to each other [samples #1 (#2) and #3 (#4)], the sample used for the resistivity measurement (a) is different from those used for scanning Raman microscopy [(b) and (c)]. Cooling from 300 to 2 K was performed several times, and the domain images for repeated cooling are shown in Fig. S5 [30]. When the sample-holder temperature was cooled to 2 K, the excitation laser was switched off, and hence, the sample temperature was equilibrated with the sample-holder temperature during cooling. At the lowest temperature, the specific heat of the sample became small, and thus the local temperature at the focused laser spot may be increased by on the order of tens of degrees K. Nevertheless, we confirmed that the applied laser intensity did not induce a phase change between the UD and D states (Fig. S6 [30]), and therefore, it is safe to say that the domain pattern is unaffected by the laser power used for scanning (5 mW).