Optical signatures of phase transitions and structural modulation in elemental tellurium under pressure

A room-temperature infrared spectroscopy study of elemental tellurium at pressures up to 8.44 GPa in the energy range $0.015–2$ eV is reported. Optical signatures of the high-pressure polymorphs are investigated and compared to the results of density-functional band-structure calculations. A Drude peak is first seen in the optical conductivity around 3.5 GPa indicating a semiconductor-to-metal transition within trigonal Te-I. A sharp increase in the Drude spectral weight and dc conductivity around 4.3 GPa signals the transformation toward the triclinic Te-II polymorph. An absorption peak around 0.15 eV appears above 5 GPa concomitant with the gradual transformation of Te-II into the structurally similar but incommensurately modulated Te-III. Microscopically, this peak can only be reproduced within a sufficiently large commensurate approximant, suggesting the low-energy optical response as a fingerprint of the structural modulation.

Figure 1

(a) Successive phase transitions of tellurium. Pressures are given as observed in the optical experiment also consistent with the presented XRD studies [14, 15] (b) Te-I phase consist of the helical chains with only two covalent bonds formed by each tellurium atom. (c) Te-II phase organized as sheets with fourfold coordinated tellurium atoms with $2\text{−}1\text{−}2\text{−}1$ zigzag pattern. (d) Te-III phase built by the sheets with fourfold coordinated tellurium atoms with a complex pattern sequence with incommensurate periodicity.

Figure 2

(a) Pressure-dependent reflectivity measured across the structural phase transitions. The shaded region is the diamond absorption range with the linear extrapolation of the reflectivity. (b) Pressure-dependent optical conductivity. (c) Spectral weight (SW) as a function of energy and pressure. While the Te-I phase can be identified with a slight redshift of the high-energy bands in the optical conductivity and a small increase in the SW below 0.1 eV, the appearance of high-pressure polymorphs significantly modifies the optical conductivity, with a drastic increase of the spectral weight in a broader energy range.

Figure 3

(a) Relativistic band structures of Te-I in the semiconducting (0 GPa) and metallic (3.85 GPa) states. Standard notation of $k$ points for trigonal symmetry is used. (b) Relativistic band structures of Te-II and Te-III ($q=\frac{1}{3}$) with $k$ points given by $\mathrm{\Gamma }(0,0,0)$, $X(0.5,0,0)$, $M(0.5,0.5,0)$, $Y(0,0.5,0)$, $Z(0,0,0.5)$, $T(0.5,0,0.5)$, $R(0.5,0.5,0.5)$, $A(0,0.5,0.5)$ in the reciprocal coordinates corresponding to the 5.06 GPa lattice parameters of Te-III from Table 1 ($b$ is multiplied by 3 to account for $q=\frac{1}{3}$). The 4.5 GPa Te-II structure is transformed to the same setting using $\mathbf{a}={\mathbf{a}}_t$, $\mathbf{b}=({\mathbf{a}}_t+{\mathbf{b}}_t+{\mathbf{c}}_t)/2$, and $\mathbf{c}={\mathbf{c}}_t$, where ${\mathbf{a}}_t$, ${\mathbf{b}}_t$, and ${\mathbf{c}}_t$ are lattice vectors of the $I\overline{1}$ cell given in Ref. [14].

Figure 4

(a) Decomposition of the $p=8.44$ GPa optical conductivity into the Drude component for the free-carrier contribution and two Lorentz components for the MIR absorption (Lorentz 1) and high-energy absorption (Lorentz 2), respectively. (b) Optical conductivity in the $\omega \to 0$ limit as a comparison to the dc resistivity measurements (black and red triangles at the low and high pressure range, respectively) [35], demonstrating the accuracy of the fit parameters. (c) Spectral weight of the Drude component. Drude SW is calculated from the individual Drude components obtained by fitting the optical conductivity, with the frequency limit of Eq. (1) taken as ${\omega }_c=0.7$ eV that covers the entire Drude contribution. The orange arrows in (b) and (c) demonstrate the Te-I $\to$ Te-II transitions. The blue arrow shows the disappearance of the Te-II phase. The lines are guide to the eye.

Figure 5

(a) Calculated optical conductivity for Te-I, Te-II, and Te-III ($q=\frac{2}{7}$). (b) Experimental optical conductivity with the intraband contributions subtracted for a comparison to the calculations. (c) Calculated optical conductivity for Te-II and Te-III. In the Te-III case, two different modulation vectors ($q=\frac{1}{3}$ and $q=\frac{2}{7}$) have been used to demonstrate that the low-energy absorption band appears only with the increased periodicity of the structure.