Disorder-induced suppression of charge density wave order: STM study of Pd-intercalated ${\mathrm{ErTe}}_3$

Pd-intercalated ${\mathrm{ErTe}}_3$ is studied as a model system to explore the effect of increasing disorder on an incommensurate two-component charge density wave (CDW). The ordering vectors of the CDW components lie along the two in-plane principal axes of the nearly tetragonal crystal structure. Using scanning tunneling microscopy (STM), we show that introducing Pd intercalants (i.e., disorder) induces CDW dislocations, which appear to be associated with each CDW component separately. Increasing Pd concentration has a stronger effect on the secondary CDW order, manifested in a higher density of dislocations, and thus increases the anisotropy (nematic character) of the CDW. Suggestive evidence of Bragg glass phases at weak disorder is also discussed.

Figure 1

Phase diagram taken from [13]. Colored points at $x=0$ mark the phase transitions of the pristine sample. Gray points at finite $x$ mark the crossover temperatures identified as features in the electrical resistivity. Vertical arrows mark the three Pd concentrations discussed in this paper. Inset: Calculated Fermi surface of the parent compound ${\mathrm{ErTe}}_3$ (from [15]) with $q_1$ and $q_2$ as nesting vectors.

Figure 2

(a) Topography (cropped) of the 0.3% Pd-intercalation sample. (A full-size 100-nm image is available in Appendix pp1). (b) FFT of (a) with reciprocal lattice points from the Te plane labeled and white lines indicating the line cut directions. (c) The respective line cuts. Here the stronger CDW peaks (red) are along $c^{*}$. (d) Topography (cropped) of the 2% sample. (e) FFT of (d) and (f) the respective line cuts.

Figure 3

CDW defect analysis of the 0.3% and 2% Pd-intercalation samples. (a) The 1000-Å phase plot for the 0.3% secondary CDW showing dislocations. (b) The 2% sample. (c) and (d) Zooms of the highlighted areas showing real-space filtered topography. (e) Autocorrelation plots for the CDW signals.

Figure 4

(a) The 300-Å topography of the 5% Pd-intercalation sample. (b) FFT of (a) and (c) the respective line cuts.

Figure 5

A proposed phase diagram as derived in Appendix pp2.

Figure 6

The 1000-Å topographic images for (a) the 0.3% Pd-intercalation sample and (b) the 2% sample.

Figure 7

The 1000-Å phase plots for (a) the 0.3% Pd-intercalation sample and (b) the 2% sample.

Figure 8

Effect of varying the Fourier filter width around the CDW point when computing autocorrelation. “Medium” filter width is used in the main body of the paper.

Figure 9

Steps in constructing the phase diagram which is the result of the minimization of the different parts of the effective potential (see text).

Figure 10

A conjectured phase diagram as a function of temperature $T$ and disorder strength $\sigma$. Here the inset shows a portion of the clean-limit phase diagram (plotted in the $\alpha \text{−}\gamma$ plane, where $\alpha$ should be considered a proxy for $T$; see text).