Many semimetallic materials exhibit a uniform charge distribution that becomes unstable at low temperatures, leading to charge ordering. This instability is particularly pronounced in quasi-one-dimensional (1D) or two-dimensional (2D) metals, where the electronic susceptibility is sensitive to lattice perturbations. Electron-phonon coupling can induce charge ordering, potentially causing metal-to-insulator transitions. Incommensurate CDWs, where the charge density modulation doesn't match the host lattice periodicity, are of particular interest. These CDWs display collective dynamics associated with amplitude or phase excitations of their order parameter. Incommensurate CDWs are theoretically predicted to exhibit a Nambu-Goldstone mode enabling lossless current via collective phase motion. However, disorder and impurities create spatial heterogeneity within the charge-ordered phase, strongly influencing the collective dynamics and potentially collapsing the collective phase mode into low-energy phason excitations. CDW pinning by defects leads to insulating behavior in some 1D materials and conductivity kinks in 2D materials. While CDW pinning at individual defects has been imaged by STM, the defect-induced low-energy phase dynamics have only been observed using ensemble-averaging techniques like neutron scattering, ultrafast low-energy electron diffraction, and transport measurements. This paper aims to directly observe the low-energy CDW dynamics in real space with atomic resolution, overcoming the limitations of previous ensemble-averaging methods. The use of STM allows for spatially resolved investigation of the CDW response to terahertz excitation, providing insights into the interplay between collective behavior and localized interactions with defects. Understanding the localized nature of these dynamics is crucial for a complete comprehension of CDWs and their behavior in various materials.

Existing studies on charge density wave dynamics have primarily relied on ensemble-averaging techniques that obscure the spatial heterogeneity inherent in real materials. Neutron scattering experiments have detected dispersing phase excitations down to 0.25 THz, while ultrafast low-energy electron diffraction revealed slow phase ordering during the relaxation from an incommensurate to a nearly commensurate CDW. MHz-range noise in transport measurements hints at phase sliding across pinning potentials. Picosecond-scale relaxation attributed to phase fluctuations has been observed using X-ray diffraction and optical spectroscopy. However, these methods lack the spatial resolution necessary to probe the influence of individual defects on the CDW dynamics. Previous STM studies have successfully imaged CDW pinning at individual defects, but they have not been able to directly observe the ultrafast phase dynamics associated with these pinning events. This gap in our understanding highlights the need for a technique capable of probing CDW dynamics with both high temporal and spatial resolution, enabling direct visualization of the interplay between collective excitations and localized defect interactions.

This study utilizes a custom-built low-temperature STM integrated with terahertz (THz) pump-probe spectroscopy. Single-cycle THz pulses, with a time resolution better than 0.4 ps and a peak electric field strength of 130 V cm⁻¹ in the far field, are used to excite and probe the CDW dynamics in 2H-NbSe₂. The THz pulses induce a strong screening current on the NbSe₂ surface, which locally excites the CDW phase. The tip-enhanced electric field in the STM junction (exceeding 1 MV cm⁻¹) is crucial for the nanoscale excitation. A pair of THz pulses is employed; the first excites the CDW, and a time-delayed second pulse probes the resulting dynamics via THz-induced electron tunneling. Sweeping the time delay between the pulses generates a time trace of the junction conductivity, revealing the ultrafast CDW modulation. The THz pulse waveform at the STM tip is measured using electro-optic sampling. To spatially resolve the CDW dynamics, a series of time traces is acquired along a line across the sample surface. Spatially resolved power spectral density (PSD) maps are created by performing a fast Fourier transform (FFT) on these time traces. The dependence of the CDW dynamics on the THz pulse electric field strength is investigated by varying the excitation pulse amplitude. To further confirm the electric-field driven excitation mechanism, measurements are performed with the tip retracted from the surface, significantly reducing tunneling probability. A numerical model based on an extended Ginzburg-Landau model is used to simulate the CDW response to the THz excitation in the presence of a random distribution of atomic-scale defects. The model includes a time- and position-dependent free energy density, incorporating the effects of the screening current and Joule heating from the THz pulse, along with a pinning potential landscape representing the randomly distributed defects. The model is used to understand the emergence of low-frequency CDW dynamics in the disordered pinning potential landscapes.

The researchers observed direct, real-space visualization of low-energy CDW dynamics in 2H-NbSe₂ at frequencies ranging from 0.15 THz to 0.9 THz. Time traces recorded in the CDW phase (20 K) exhibited an ultrafast relaxation (0.6 ps) followed by oscillatory dynamics persisting for at least 20 ps. In contrast, the normal metal phase (150 K) showed a much weaker response. Analysis of the PSD revealed prominent peaks at 0.15 THz and between 0.6 THz and 0.8 THz in the CDW phase, which were absent in the normal metal phase. The low-energy modes were attributed to local phase excitations of the CDW. A strong spatial correlation was found between the defects visible in STM topography and the THz-induced tunnel current, indicating a link between defects and phase excitations. The spatially resolved PSD maps showed that the sub-THz modes varied in frequency and amplitude on a length scale comparable to the average distance between defects. The study found that the ultrafast decay amplitude increased linearly with increasing THz pulse electric field strength, and the decay time constant decreased nonlinearly, consistent with electron bath thermal relaxation. Measurements with the tip retracted indicated that the CDW excitation was driven by the THz electric field rather than tunneling electrons. The PSD of CDW-related modes showed an approximately quadratic increase with increasing electric field strength. The numerical model supported the experimental findings, showing that the low-frequency CDW dynamics originated from phase excitations near atomic defects. The model also predicted a group velocity for phase excitations consistent with theoretically predicted phason velocities. The observed spatial heterogeneity of the sub-THz modes helps explain why such low-frequency oscillations have not been previously detected using far-field optical spectroscopy.

The atomic-scale resolution achieved in this study directly reveals the nanoscale heterogeneity of CDW dynamics and clarifies the role of defects in shaping the collective response. The observed low-frequency modes, previously undetectable with far-field techniques due to spatial averaging, are directly linked to localized phase excitations arising from the interaction of the CDW with atomic-scale defects. The results highlight the interplay between collective behavior and localized interactions in charge-ordered states. The electric-field-driven excitation mechanism suggests a general approach for studying nanoscale dynamics in a wide range of layered materials, providing a path towards imaging phase boundary motion, localized fluctuations, and pair-breaking dynamics in different systems. The observed quadratic scaling of the CDW related peaks with electric field strongly supports the electric field as the driving force for the observed dynamics.

This research demonstrates the capability of STM-based THz spectroscopy to directly image nanoscale CDW dynamics. The low-energy sub-THz modes are attributed to phase excitations localized near atomic defects that pin the CDW. The electric field driven excitation mechanism offers a promising tool for studying nanoscale dynamics in diverse materials, opening avenues for future research in related phenomena such as superconductivity and magnetism.

The numerical model, while providing valuable insights, is a simplification of the complex system. The exact pinning potential landscape of the sample cannot be quantitatively reproduced. The model demonstrates the emergence of low-frequency CDW dynamics in disordered systems but does not aim for quantitative fitting of the experimental data. The study focuses on 2H-NbSe₂, and the generalizability of the findings to other materials requires further investigation. The current method is limited by the intensity and frequency range of the terahertz source, which might limit its application in certain materials with different characteristic frequencies.