Dynamics of Charge-Density-Wave puddles in 2$H$-NbSe$_2$

Abstract

Electronic phases in quantum materials are often governed by nanoscale inhomogeneity, where local order develops within spatially confined regions or puddles. A prominent example is an incommensurate charge-density-wave (I-CDW) that comprises locally commensurate domains. In 2$H$-NbSe$_2$, such an I-CDW state persists alongside lattice anharmonicity and superconductivity, raising fundamental questions about the dynamical stabilization of CDW order in puddles. Here, we probe the puddle-dynamics in 2$H$-NbSe$_2$. Raman scattering reveals a strong Fano-coupling between the interlayer shear vibration and the CDW amplitude mode. Time-resolved reflectivity measurement shows a low-frequency ~0.15 THz coherent overdamped oscillation onsetting within the CDW regime at ~17 K, pointing towards a so far unexplored transition. This we identify as a Fano-coupled phonon-CDW hybrid emerging from the collective dynamics of CDW puddles. These dynamics highlight how lattice pinning and electronic correlations in layered materials affect the CDW order, which is crucial for the design of novel Van der Waals devices.

Figures (4)

• Figure 1: Fano-coupled phonon-CDW response. (a) Raman susceptibility, $\chi"$ measured in unpolarized backscattering configuration on a mechanically exfoliated bulk-flake (thickness $\sim60$ nm) of NbSe$_2$ on Si/SiO$_2$ substrate at 14 K is shown. The arrow points to a broad shoulder at $\sim40$ cm$^{-1}$. The green solid line shows a fit to the data using a Fano resonance model, as sketched in the right inset of Fig. 1a. Left inset: Optical image of the flake of NbSe$_2$, with the red dot pointing the point of Raman measurements. Right inset: Fano coupling between two discrete oscillators, modelled by Lorentzian lineshapes (blue and red solid curves), leads to the Breit-Wigner Fano lineshape (green solid line). The black arrow represents the shoulder, which is analogous to the data in (a). (b) Time-resolved reflectivity change ($\Delta R / R_0$), normalized with respect to its peak value, of NbSe$_2$ single crystals measured at $T\sim2$ K with 40 $\mu$J/cm$^2$ of 1.2 eV pump fluence is shown. $R_0$ is the reflectivity at zero pump-probe time delay ($t_{pp}$). The data is fitted by a convolution of three distinct components, which are shown separately by the dashed, dotted, and dashed-dotted lines, respectively and discussed further in the main text. (Inset:) The schematic depicts CDW puddles (represented by regions marked with red solid lines). The blue arrows indicate the interlayer shear vibration that couples with the CDW. The colour maps in the square sheets, indicating the layers, are CDW modulations measured via STM experiments reproduced from Ref. pasztor2021multiband.
• Figure 2: Temperature-dependent ultrafast dynamics in bulk NbSe$_2$: (a) The time-resolved reflectivity, $\Delta R/R_0$ is shown at different temperatures ($T$s) from 1.9 K-100 K. The open points are the measured data and the solid lines are the respective fits using the model discussed in Fig. 1(b). (b) Representative $T$-dependent four-probe resistance, $R$ of the NbSe$_2$ crystals is shown. $R$ jumps to nearly zero resistance ($\approx1$ n$\Omega$) at $T_c\sim7$ K, indicating the superconducting transition. The data shows a kink at the CDW transition temperature, $T_{\mathrm{CDW}}\sim28$ K, marked by the solid arrow. The blue and beige regions are marked based on these transition temperatures. (c)-(e) show the $T$-dependence of the long-lived reflectivity, i.e.$\Delta R/R_0$ at $t_{pp}\sim13$ ps, the relaxation time, $\tau_{\mathrm{decay}}$, and overdamped oscillation frequency, $f_0$, estimated from the fits, respectively.
• Figure 3: Temperature dependence of the Raman susceptibility of bulk NbSe$_2$. (a) Raman susceptibility ($\chi^"$) is measured at different $T$s on bulk flakes of NbSe$_2$. The inset plots the value of $\chi^"$ at the frequencies marked by the dashed and dotted lines. (b) $\chi^"$ is plotted at three distinct $T\sim24,~32,~\mathrm{and}~100$ K. The solid lines represent fits to the data. At 100 K, the data is fitted with additive contributions from three distinct lorentzian lineshapes, depicted by the dahed lines, which represent the interlayer shear phonon peak at $\sim29$ cm$^{-1}$, CDW amplitude mode at $\sim35$ cm$^{-1}$, and another peak at 25 cm$^{-1}$, that is identified with a split E$_{2g}$ peak of the interlayer shear vibration. The data at 32 K is fitted by a Fano lineshape, as we discuss further in the text.
• Figure 4: Temperature-dependence of the Fano coupling factor$\nu$, estimated from the fits of the Raman susceptibility, $\chi^"$ at different $T$s is plotted on the left-axis. The grey-shaded region represents the fitting error. The right-axis plots the overdamped oscillation frequency, $f_0$, obtained from the ultrafast response. Blue and beige shaded regions are marked based on the superconducting and CDW transition temperatures, characterized from electrical transport in Fig. 2(a). The red region marks, the onset of $\nu$ as discussed further in the text.