Charge transfer and multiple density waves in the rare earth tellurides

We use high-resolution synchrotron x-ray diffraction to uncover a second, low-temperature, charge density wave (CDW) in TbTe${}_3$. Its $T_c$${}_2=41.0\pm 0.4$ K is the lowest discovered so far in the rare earth telluride series. The CDW wave vectors of the high temperature and low temperature states differ significantly and evolve in opposite directions with temperature, indicating that the two nested Fermi surfaces are separated and the CDWs coexist independently. Both the in-plane and out-of-plane correlation lengths are robust, implying that the density waves on different Te layers are well coupled through the TbTe layers. Finally, we rule out any low-temperature CDW in GdTe${}_3$ for temperatures above 8 K, an energy scale sufficiently low to make pressure tuning of incipient CDW order a realistic possibility.

Figure 1

(a) Lattice structure of TbTe${}_3$ with Te bilayers sandwiched between corrugated TbTe planes. (b) A general sketch of the calculated Fermi surface[14, 17] showing the $q_a$ and $q_c$ vectors. Each drawn line of the Fermi surface would eventually split into two by the bilayer structure of the Te layers.[14] (c) HKL scans of CDW order (2 − $q_a$, 0, 0). Smooth curves are a pseudo-Voigt fit in the $H$ scan along the longitudinal direction and guides to the eye in the $K$ and $L$ scans. The double peak structure in the $K$ scan is due to sample mosaicity.

Figure 2

The $a$-axis lattice constant versus temperature demonstrates continuous behavior through the CDW transition at $T_c$${}_2=41.0$ K (vertical dotted line). Fit is a two-dimensional Debye model[29] with ${\Theta }_D=144\pm 7$ K.

Figure 3

(a) The order parameter as a function of temperature. $I_{(2-q,0,2)}$ is the integrated intensity of the (2 − $q_a$, 0, 2) peak, normalized to the integrated intensity of the (2, 0, 0) Bragg peak $I_{\left(200\right)}$. (b) The FWHM of the θ-2θ scans show no broadening effects at $T_c$${}_2$ within error bars on either the (2, 0, 0) Bragg peak or the CDW ($q_a$, 0, 0) and (2 − $q_a$, 0, 2) peaks. The horizontal dot-dashed line at 0.0079° indicates our instrument resolution at the (2, 0, 0) order. The vertical dot-dashed line marks the position of $T_c$${}_2$ at 41.0 K.

Figure 4

The evolution of the CDW $q$ vectors in TbTe${}_3$ as a function of temperature normalized by the transition temperatures $T_c$${}_1=336$ K and $T_c$${}_2=41.0$ K for the $c$ and $a$ axes, respectively. (a) $q_c$, from Ref. 14. (b) $q_a$. The two $q$ vectors have different values and opposing temperature dependencies, consistent with independent coexistence.