Progressive Melting of Charge Density Waves Mapped with in situ 4D-STEM

In two dimensions, melting can proceed via exotic intermediate phases, such as hexatic and nematic order, that retain orientational coherence despite the loss of translational symmetry—offering partially ordered states that interpolate between a crystalline and liquid phase [1]. Similar hexatic and nematic order of electronic, quantum, and magnetic states are predicted in low-dimensional materials [2]. Charge density waves (CDWs) represent an electronic analog to classical crystallinity, spontaneously breaking translational symmetry to form periodic modulations in the electronic charge density. CDWs elastically deform and contain topological defects—including dislocations and domain boundaries—that destabilize order [3,4]. We show incommensurate CDWs melt through the proliferation of electronic dislocations. However, there is a departure from classical solid melting by proceeding with localized CDW amplitude collapse near regions of disorder [5]. Here, in situ 4D-STEM (scanning/transmission electron microscopy) provides a map of the CDW amplitude at the nanoscale (Fig. 1) throughout the CDW melting process (373 – 603 K) [5]. This real space observation of CDW melting confirms the proliferation of disorder and decrease in spatial coherence. 4D-STEM directly measures spatial fluctuations and local amplitude [6]. The autocorrelation function is extracted from the amplitude map (Fig. 1c), and the CDW correlation length continuously decreases through the melting process (Fig. 1d). Melting-driven disorder is marked by this decreasing correlation length. The real space observation of increased spatial fluctuations is consistent with superlattice peak broadening observed in diffraction. Unique to electronic melting, there is a concomitant decay of average CDW amplitude across the measured field of view (Fig. 1e). This demonstrates 4D-STEM as a powerful tool to map the evolution of CDWs. We also report the first high temperature Raman spectroscopy study of 2D 1T-TaS2, confirming the CDW amplitude attenuation during melting. High-temperature (77 – 600 K) Raman spectroscopy of 2D 1T-TaS2 shows a continuous decrease in integrated intensity along with a large broadening of the 70 cm-1 Raman peak (Fig. 2) [5]. This Raman mode at 70 cm-1 has been associated with the amplitude mode for nearly commensurate and commensurate phases. Above ∼350K, this 70 cm-1 mode becomes too broad to be resolved clearly, and additionally, only weak, broad A1g modes are observed at ∼300 cm-1 and ∼380 cm-1 (Fig. 2a-c). This suggests that no amplitude mode characteristic to the incommensurate CDW of 1T-TaS2 has been detected by high-temperature Raman spectroscopy. Similar behavior has been observed in other CDW systems such as rare-earth tellurides [7], 1T-TaSe2 [8], 2H-NbSe2 [9], and even bulk 1T-TaS2 [10]. In summary, we observe charge density wave melting through real space disordering using in situ 4D-STEM and broadening and weakening of the A1g mode with high-temperature Raman spectroscopy [5]. CDW melting probed with 4D-STEM. Real space maps (virtual dark field image) of CDW amplitude (b) at 373K (i), 473K (ii), and 603K (iii) with corresponding position averaged convergent beam electron diffraction (CBED) patterns (a). The CDW dramatically decreases in intensity and disorders spatially. Colorbars are normalized to CDW max intensity. At elevated temperatures, the weak superlattice peaks are obfuscated by a rising thermal diffuse background. We average the six first-order Bragg peaks and surrounding superlattice peaks to improve signal-to-noise ratio and fit and subtract the diffuse background. Virtual dark field images (b) are formed by integrating intensities of the background-subtracted superlattice peaks with a pixel size of 8.19 nm and a probe size of 1.7 nm. Because of the endotaxial TaS2 structure, we note that the amplitude map is a projection across several decoupled 2D CDWs [11,12]. Autocorrelation function of CDW real space map plotted across the melting regime (c) showing gradual spatial decoherence. The functional form of the autocorrelation is unresolvable in the subpixel regime. Each autocorrelation function is normalized at “zero distance” (i.e., each image was normalized to its mean intensity level.). The correlation length (d) and average pixel intensity (e) of CDW real space maps decreases continuously through the CDW melting process. Correlation length is defined to be the point where autocorrelation decays to 1/e. Figure recreated from ref. [5]. Temperature-dependent Raman spectroscopy of TaS2 with 2D CDWs. The signature Raman mode tracked throughout heating is located at ∼70 cm−1, with additional weak, broad A1g modes observed at ∼300 and ∼380 cm−1. (a) Zoomed-in spectra of A1g1 (b) and weak, broad A1g2 and A1g3 (c) modes in the IC-CDW regime above 350 K. Vertical bars in a)–c) indicate the magnification factor for each panel. In the incommensurate charge density wave melting regime, the A1g modes observed at ∼70, ∼300, and ∼380 cm−1 broaden and decrease in intensity. Figure recreated from ref. [5].