Evidence for coupling between charge density waves and phonons in two-dimensional rare-earth tritellurides

We report on a Raman-scattering investigation of the charge density wave (CDW), quasi-two-dimensional rare-earth tritellurides $R{\text{Te}}_3$ ($R=\text{La}$, Ce, Pr, Nd, Sm, Gd, and Dy) at ambient pressure, and of ${\text{LaTe}}_3$ and ${\text{CeTe}}_3$ under externally applied pressure. The observed phonon peaks can be ascribed to the Raman-active modes for both the undistorted and the distorted lattices in the CDW state by means of a first-principles calculation. The latter also predicts the Kohn anomaly in the phonon dispersion, driving the CDW transition. The integrated intensity of the two most prominent modes scales as a characteristic power of the CDW-gap amplitude upon compressing the lattice, which provides clear evidence for the tight coupling between the CDW condensate and the vibrational modes.

Figure 1

(Color online) Raman-scattering spectra at 300 K (a) for the $R{\text{Te}}_3$ series at ambient pressure, and (b) for ${\text{LaTe}}_3$ and (c) ${\text{CeTe}}_3$ for increasing (continuous lines) and decreasing (dashed lines) pressures. All spectra have been shifted for clarity.

Figure 2

(Color online) (a) Raman-active phonon frequencies of $R{\text{Te}}_3$, obtained experimentally (solid symbols) and calculated for the undistorted structure (open symbols). The calculated extra peaks arising in the distorted structure (see text) are also shown with star symbols for ${\text{LaTe}}_3$. The lattice-constant values are from Ref. 22. (b) Atomic displacements for the Raman-active $A_{1g}$ vibrational modes in ${\text{LaTe}}_3$. The figure shows the $ab$ plane, whereas large (small) spheres represent atoms having a positive (negative) $c$ coordinate. The dotted lines represent the Te planes. The primitive unit cell and crystal axes are also shown. Arrow lengths are proportional to the calculated displacements.

Figure 3

(Color online) (a) Raman spectra of ${\text{LaTe}}_3$ as a function of the polarization angle of the incident light. (b) Calculated phonon dispersion along the $c$ axis. (c) Enlargement of the $P2$ peak in ${\text{CeTe}}_3$ detailing its double-feature nature (logarithmic $y$ axis).

Figure 4

(Color online) Comparison between the amplitude of the CDW gap (open circles) (Refs. 12, 13) and the integrated intensities $\left(I\right)$ of the $P2$ (full triangles) and $P4$ (full squares) peaks, raised to 1/4 and 1/2, respectively (see text), as a function of the lattice constant (a) for the $R{\text{Te}}_3$ series and (b) for ${\text{CeTe}}_3$ under pressure. The pressure dependence of the lattice constant in ${\text{CeTe}}_3$ was achieved following the procedure of Ref. 13. All quantities are normalized to their starting values.