Charge density wave formation in $R_2{\mathrm{Te}}_5$ ($R=\mathrm{Nd}$, Sm, and Gd)

The rare earth $\left(R\right)$ tellurides $R_2{\mathrm{Te}}_5$ have a crystal structure intermediate between that of $R{\mathrm{Te}}_2$ and $R{\mathrm{Te}}_3$, consisting of alternating single and double Te planes sandwiched between $R\mathrm{Te}$ block layers. We have successfully grown single crystals of ${\mathrm{Nd}}_2{\mathrm{Te}}_5$, ${\mathrm{Sm}}_2{\mathrm{Te}}_5$, and ${\mathrm{Gd}}_2{\mathrm{Te}}_5$ from a self-flux and we describe here evidence for charge density wave formation in these materials. The superlattice patterns for all three compounds are relatively complex, consisting at room temperature of at least two independent wave vectors. Consideration of the electronic structure indicates that, to a large extent, these wave vectors are separately associated with sheets of the Fermi surface which are principally derived from the single and double Te layers.

Figure 1

(Color online) (a) Schematic diagram showing the average (unmodulated) crystal structure of $R_2{\mathrm{Te}}_5$. $b$ axis is vertical in the figure. Solid gray lines indicate a unit cell. (b) High resolution TEM of ${\mathrm{Gd}}_2{\mathrm{Te}}_5$ along the [101] direction showing alternating single and double Te layers.

Figure 2

High resolution TEM image of ${\mathrm{Gd}}_2{\mathrm{Te}}_5$ at room temperature as viewed looking down the $\left[\overline{1}01\right]$ direction. The image shows a regular crystal structure over a macroscopic length scale (more than $25\mathrm{nm}$) without intercalation or stacking faults in the layering along the $b$ direction.

Figure 3

(Color online) SADPs along the (010) zone axis at room temperature for (a) ${\mathrm{Nd}}_2{\mathrm{Te}}_5$, (b) ${\mathrm{Sm}}_2{\mathrm{Te}}_5$, and (c) ${\mathrm{Gd}}_2{\mathrm{Te}}_5$. Bragg peaks are labeled by $\left(hl\right)$. Systematic modulation wave vectors are listed in Table .

Figure 4

(Color online) (a) Band structure of $R_2{\mathrm{Te}}_5$ calculated by LMTO for $R=\mathrm{Lu}$. The blue solid lines arise from $\mathrm{Te}5p$ states in the square planar layers. [(b) and (c)] The resulting Fermi surfaces, illustrating the trilayer splitting that arises due to coupling between the three Te planes. Red and yellow sheets in (b) and blue and purple sheets in (c) indicate the weaker bilayer splitting originating from a Te double layer, while orange and green sheets in (b) and (c) are due to a Te single layer and the splitting is significant. The $\Gamma$ point at the center of the zone and other high symmetry points have been labeled.

Figure 5

(Color online) Fermi surface at $k_y=0$. Red and green lines approximately indicate sections of FS formed by $5p$ orbitals from the single and double Te layers, respectively. Arrows indicate the on-axis lattice modulation wave vector expressed in the reduced BZ, ${\vec{q}}^{\prime }=c^{*}-\vec{q}\sim (1∕3)c^{*}$ observed in SADP for ${\mathrm{Nd}}_2{\mathrm{Te}}_5$, ${\mathrm{Sm}}_2{\mathrm{Te}}_5$, and ${\mathrm{Gd}}_2{\mathrm{Te}}_5$.

Figure 6

(Color online) Color scale for all panels: red high, blue low. (a) The Lindhard susceptibility, $\chi \left(\vec{q}\right)={\sum }_{n{n}^{\prime }}{\chi }_{n{n}^{\prime }}\left(\vec{q}\right)$ at $q_y=0$, summed for all the bands including inter single-double layer pairs. (b) ${\chi }_D\left(\vec{q}\right)$: contribution to $\chi \left(\vec{q}\right)$ from the double Te layers. On-axis wave vectors for all three compounds lie on the global maximum. Inset: A line cut following the dashed line, illustrating the resonant enhancement of the mixed harmonics ${\vec{q}}_0+{\vec{q}}_1$ and ${\vec{q}}_0-2{\vec{q}}_1+2{\vec{G}}_x$ for ${\mathrm{Sm}}_2{\mathrm{Te}}_5$. (c) ${\chi }_S\left(\vec{q}\right)$: contribution to $\chi \left(\vec{q}\right)$ from the single Te layers. Symbols represent first harmonics of the off-axis modulation vectors for all three compounds and second harmonics for ${\mathrm{Gd}}_2{\mathrm{Te}}_5$. Upper inset: A line cut following the horizontal dashed line. The off-axis modulation lies close to the global maximum of ${\chi }_S\left(\vec{q}\right)$ for ${\mathrm{Sm}}_2{\mathrm{Te}}_5$. Lower inset: A line cut following the vertical dashed line, showing the resonant enhancement of the commensurate off-axis lattice modulation for ${\mathrm{Gd}}_2{\mathrm{Te}}_5$.