Correlation between electronic and structural orders in $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$

The correlation between electronic and crystal structures of $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$ in the charge-density wave (CDW) state is studied by x-ray diffraction in order to clarify basic properties in the CDW state, transport properties, and chirality. Three families of reflections are used to probe atomic displacements and the orbital asymmetry in Se. Two distinct onset temperatures are found: $T_{\mathrm{CDW}}$ and a lower $T^{*}$ indicative for an onset of Se out-of-plane atomic displacements. $T^{*}$ coincides with a DC resistivity maximum and the onset of the proposed gyrotropic (chiral) electronic structure. However, no indication for chirality is found. The relation between the atomic displacements and the transport properties is discussed in terms of Ti $3d$ and Se $4p$ states that only weakly couple to the CDW order.

Figure 1

Crystal structure of $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$ in the CDW state viewed along (a) [001] and (b) [110] (drawn by vesta [43]). Arrows indicate the displacement directions from the normal state. Gray circles in (a) show Se in the lower layer with respect to the adjacent Ti layer. Schematic band structures of $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$ at (c) $T^{*}<T<T_{\mathrm{CDW}}$ and (d) $T<T^{*}$. Panel (d) is similar to a sketch shown in Ref. [35]. $T_{\mathrm{CDW}}$ and $T^{*}$ denote the CDW transition temperature and the onset temperature of reflections of family B (see text), respectively.

Figure 2

Integrated intensities of reflections belonging to families A (0.5 1 1.5), B (0 0.5 8), and C (0 0.5 9.5), and DC resistivity as functions of temperature. XRD data shown in (a) [(b)] were acquired at 12.6 keV [the Se K edge]. The DC resistivity is normalized by the data at 300 K. The green, red, and blue solid lines represent power-law fits $[\propto {(T_c-T)}^{\alpha }]$, where $T_c$ and α are the critical temperature and critical exponent, respectively. The black line represents the quartic term with an onset at $T_{\mathrm{CDW}}$.

Figure 3

(a) Photon-energy and (b) azimuthal-angle dependence of the (0 0.5 9.5). XAS (black line) is also shown in (a). Blue and black curves in (b) show the result of simulation using the FDMNES code [44]. Gray dotted line in (b) indicates the azimuthal angle where the data for Fig. S3 were taken.

Figure 4

Numerically calculated intensities of (0.5 1 1.5) (green) and (0 0.5 8) (blue) reflections as functions of (a) ${\delta }_{\mathrm{Ti}}$ and (b) $\mathrm{\Delta }{z}_{\mathrm{Se}}$. The data are normalized by the intensity calculated for the reported structure in the CDW state [32]. The respective displacements are schematically displayed as insets. The green line in (a) and blue line in (b) represent a quadratic and the blue line in (a) a quartic function.