Charge density waves (CDWs) are the self-organization of electrons into new spatially periodic structure. In condensed matter physics, CDWs and related phenomena have been a long-standing topic. Recent discovery of ubiquitous experimental signatures of CDWs in cuprate high-temperature superconductors have evoked renewed interest in this topic. However, the charge order observed in the cuprates are often short-ranged and coexisting with nanoscale disorder, which does not fit into the conventional understanding of CDWs. Therefore, it is very important to elucidate the role of disorder during the incipience and evolution of CDWs, but such a question lack a thorough understanding even in simple prototypical CDW materials.
In order to experimentally addressing this issue, a proper probing technique is necessary. The interaction between disorder and CDWs may have effects on CDW correlations and domain dynamics, which are expected to occur at the mesoscopic scale. Unfortunately, the majority of experiments carried out to date for addressing disorder effects in CDW materials are either in the macroscopic regime, such as transport and thermodynamic measurements, or in the nanoscale regime, such as scanning probe experiments.
Now, based on state-of-the-art coherent resonant X-ray diffraction, Prof. Yuan Li’s group from ICQM, together with collaborators from Massachusetts Institute of Technology and Brookhaven National Lab, have carried out a study on disorder effects on CDWs in a prototypical material, ZrTe3. The work has been published in Nature Communications on Jan. 7th, 2020.
The high-flux soft X-rays and a high-resolution area detector at Beamline 23-ID-I, NSLS2, Brookhaven National Lab has enabled the research team to achieve high momentum resolution so as to distinguish diffraction signals that are slightly different in momentum space. Meanwhile, the highly coherent X-ray beam enables detecting the mesoscopic CDW domain texture and dynamics via interference patterns known as speckles, generated by X-rays diffracted from different enlightened domains on the sample. This work successfully observed distinct fingerprints of pristine and disorder-perturbed CDWs, and reveals interesting disorder-induced effects in a CDW system.
The study was carried out on a high-quality ZrTe3 crystal, where the density of disorder is low. By scanning and reconstructing the momentum space [Fig. 1 (c)], the researchers found two coexisting diffraction signals [Fig. 1 (a)]: They appear at the same momentum wavevector at the CDW transition temperature TCDW = 64 K, and with cooling, gradually move apart from each other [Fig. 1 (a-b)], with very different temperature dependence [Fig. 1 (d-f)]. A new characteristic temperature can be identified near TLO = 56 K, which indicates the formation of long-range charge order. While the sharp and intense peak is from CDWs, the broad and weak peak is mostly likely due to the charge modulations that are similar in essence to Friedel oscillations induced by disorder, according to the analysis.
After the insertion of a 10-micron pinhole into the X-ray beam’s path about 5 mm upstream from the sample, speckle patterns can be observed due to the interference of the X-rays diffracted from different charge domains [Fig. 2 (a-b)]. The variation of speckle patterns over time characterizes the mesoscopic dynamics of charge domains. The researchers tracked the time variation of speckle patterns at different temperatures [Fig. 2 (c-g)], and found that the charge domains are anomalously stable at 62 K, compared to dynamical behaviors at lower temperatures 47 K and 56 K, which seems strange because thermal activation of CDW domain walls ought to increase with increasing temperatures. The anomalously stable charge domains near TCDW = 64 K are thus attributed to a result of disorder pinning, and a scenario depicting the temperature evolution of charge order in the dilute disorder system is proposed: incipient short-ranged isolated CDWs are stabilized and pinned around disorder sites, then upon further cooling, the correlation length increases so that the disconnected domains merge into long-range CDWs.
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Figure 1. a Reconstructed diffraction signals in the [H, 0, L] reciprocal plane at various temperatures. b Momentum-space trajectory of the two peak centers indicated at the bottom of a. c Schematics of momentum scan in real and reciprocal space. The inset displays how the (H, K, L) volume data were reconstructed and the (H, 0, L) slice extracted. d Temperature dependence of the intensities of the sharp and broad peaks. e, f evolution of the full width at half maximum (FWHM) of the sharp peak in L and H, respectively. Horizontal shaded stripes indicate the FWHM (and its uncertainty) of the broad peak, which is weakly T dependent.
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Figure 2. a, b Images of CDW diffraction signal taken without and with pinhole, b shows the speckle patterns. c–f waterfall plots of the time series of diffraction intensities extracted from a horizontal strip taken near the dashed line in b. g Autocorrelation of speckle patterns at different temperatures. The inset shows fitted values of coherent time that characterizes the rate of domain motion.
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Ph.D. students Li Yue from ICQM, Shangjie Xue and Jiarui Li from Massachusetts Institute of Technology are the first authors of this work. Prof. Riccardo Comin from Massachusetts Institute of Technology and Prof. Yuan Li from ICQM are the corresponding authors. The resonant X-ray scattering experiment was performed at the NSLS-2, Brookhaven National Lab, under a user program. The work at PKU was financially supported by NSFC and MOST of China.
Paper information:
Li Yue, Shangjie Xue, Jiarui Li, Wen Hu, Andi Barbour, Feipeng Zheng, Lichen Wang, Ji Feng, Stuart B. Wilkins, Claudio Mazzoli, Riccardo Comin* & Yuan Li*, “Distinction between pristine and disorderperturbed charge density waves in ZrTe3”, Nature Communications 11, 98 (2020).
https://www.nature.com/articles/s41467-019-13813-y
