Hysteretic Melting Transition of a Soliton Lattice in a Commensurate Charge Modulation

We report on the observation of the hysteretic transition of a commensurate charge modulation in ${\mathrm{IrTe}}_2$ from transport and scanning tunneling microscopy (STM) studies. Below the transition ($T_C\approx 275\mathrm{K}$ on cooling), a $q=1/5$ charge modulation was observed, which is consistent with previous studies. Additional modulations [$q_n=(3n+2{)}^{-1}$] appear below a second transition at $T_S\approx 180\mathrm{K}$ on cooling. The coexistence of various modulations persists up to $T_C$ on warming. The atomic structures of charge modulations and the temperature-dependent STM studies suggest that $1/5$ modulation is a periodic soliton lattice that partially melts below $T_S$ on cooling. Our results provide compelling evidence that the ground state of ${\mathrm{IrTe}}_2$ is a commensurate $1/6$ charge modulation, which originates from the periodic dimerization of Te atoms visualized by atomically resolved STM images.

Figure 1

(a) $\rho (T)$ data of a ${\mathrm{IrTe}}_2$ single crystal. The CDW transition ($T_C\approx 275\mathrm{K}$) is indicated by the first resistivity increase. The second resistivity increase at $\sim 180\mathrm{K}$ indicates the partial melting transition ($T_S$) on cooling. (b) STM topographic images with atomic resolution taken at 295, 220, 50 K (cooling) and 215 K (warming). The various new modulations ($1/8$, $1/11$, etc.) are present below $T_S$. (c) STM image ($65\mathrm{nm}\times 3\mathrm{nm}$) at 215 K (warming) showing an example of the coexistence of several modulations: $1/8$, $1/11$, and $1/17$.

Figure 2

Column-averaged line profiles of STM images in Fig. 1 and the cartoon models of multiple modulations $q_n=1/5$, $1/8$ and $1/11$ and RT undistorted state. Here, the double columns (red spheres) are the solitonlike (antiphase) boundaries of fundamental modulation of three rows (blue spheres).

Figure 3

STM topographic images (left) and their FFT maps (right) across the $T_S$ values on cooling (250, 185, 180, and 170 K) and on warming (240 K). The density of solitons (bright stripes) decreases across $T_S$ with the appearance of short-range modulations of $q_n=(3n+2{)}^{-1}$. The sharp $1/5$ superlattice spots turn into diffusive streaks because of the random packing of these short-range modulations (Supplemental Material [22]). On warming (240 K) the $1/8$ superlattice spot becomes sharper.

Figure 4

$T$ dependence of the normalized soliton density $n/n_0$ across $T_S$ (a) and areal fractions of various $q_n$’s on cooling (b) and warming (c). The statistical data are obtained from counting the bright $2a^{*}$ columns in STM images with dimension $>200\mathrm{nm}$ along the ${\mathrm{q⃗}}_n$ direction.

Figure 5

(a) An atomically resolved STM image ($-300\mathrm{mV}$, 0.1 nA) measured at 50 K of a region without any soliton and (b) its column-averaged line profile. The two bright atomic rows are $\sim 0.4\AA$ closer to each other than the undistorted intercolumn spacing (3.4 Å), suggesting a formation of Te double-row stripes separated by unpaired Te atomic rows. There is a subtle difference between alternating unpaired Te atomic rows as noted by two arrows in (b), resulting in a $6a^{*}$ periodicity. (c) Unit cell average of the STM image in (a). The center box highlights the $1\times 6$ supercell. Green circles label the undistorted hexagonal lattice. The atomic displacement of individual atoms is labeled by red arrows. See the main text for numerical values. Yellow dumbbells highlight the Te dimers.