Raman scattering fingerprints of the charge density wave state in one-dimensional NbTe$_4$

TL;DR

The study probes the charge-density wave state in NbTe4 using resonant and polarization-resolved Raman scattering, supported by room-temperature X-ray diffraction and DFT phonon calculations. It identifies 25 Raman-active phonon modes at 5 K and 15 at 300 K under backscattering, with clear polarization selection revealing strong symmetry coupling to the crystal axes. Temperature-dependent measurements show a ICDW to CCDW transition with pronounced hysteresis around 45–90 K and a warming-rate dependent transition temperature, indicating finite CDW-domain nucleation kinetics. The findings assign a structural link between the observed Raman features and the P4/ncc to P4/mcc phase transition and highlight potential relevance for memory-device applications due to the kinetic control of the CDW phases.

Abstract

Charge-density waves (CDWs) are ordered quantum states of conduction electrons accompanied by periodic lattice distortions. Raman scattering (RS) spectroscopy is therefore well suited for probing CDW-induced structural modulations. We investigate the CDW state in quasi-one-dimensional NbTe$_4$ using RS spectroscopy. At $T$=5~K, the resonantly enhanced Raman spectrum exhibits 25 phonon modes. Polarization-dependent measurements reveal a strong coupling between phonon-mode symmetry and crystallographic symmetry, with modes polarized parallel or perpendicular to the crystallographic $c$-axis, along which the one-dimensional structure is elongated. Temperature-dependent RS measurements identify a transition between commensurate and incommensurate CDW phases, accompanied by pronounced thermal hysteresis, with transition temperatures of approximately 45~K upon cooling and 90~K upon warming. The hysteresis width depends on the warming rate, indicating a finite nucleation rate of CDW domains and suggesting potential relevance for memory-device applications.

Figures (11)

• Figure 1: The crystal structures of NbTe$_4$ in the $P4/mcc$ and $P4/ncc$ phases. Green (yellow) spheres represent Nb (Te) atoms. Panels (a) and (b) show views along the crystallographic $c$ axis, while panels (c) and (d) show views perpendicular to the $c$ axis. In panels (c) and (d), horizontal dashed lines are included to more clearly highlight the displacement of Nb atoms in the $P4/ncc$ structure. Panels (e) and (f) shows the calculated phonon dispersion of NbTe$_4$ in the $P4/mcc$ and $P4/ncc$ space-group symmetry, respectively.
• Figure 2: (a) False-color map of low-temperature ($T$=5 K) Raman scattering (RS) spectra of the NbTe$_4$ crystal in the co-linear configuration, shown as a function of the angle of linear polarization with respect to the crystallographic orientation of the material, under 1.58 eV laser light excitation. (b) RS spectra at two orthogonal detection angles, 20 $^{\circ}$ and 110 $^{\circ}$, extracted from the map in panel (a). The inset shows the RS spectrum around 68 cm$^{-1}$, where phonon modes P$_2$ and P$_3$ are present. (c)-(j) Polar plots of the integrated intensities of phonon modes P$_1$, P$_2$ and P$_3$, P$_8$, P$_{16}$, P$_{20}$, P$_{21}$, P$_{22}$, and P$_{25}$, respectively. For clarity, the integrated intensity of phonon mode P$_{2}$ is multiplied by 3 in panel (d).
• Figure 3: (a) RS spectra of NbTe$_4$ under 785 nm (1.58 eV) excitation with 1 mW laser power at low ($T$ = 5 K) and room ($T$ = 300 K) temperatures. The spectra are vertically shifted for clarity. False-color maps of RS spectra as a function of temperature during warming from 5 K to 300 K (b) and cooling from 300 K to 5 K (c). (d-k) Temperature evolution of the Raman shifts during warming and cooling for the P$_1$, P$_2$ and P$_3$, P$_8$, P$_{16}$, P$_{20}$, P$_{21}$, P$_{22}$, P$_{25}$ phonon modes, respectively. The isnsets in panels (j, k) focus on the hysteresis.
• Figure 4: Temperature evolution of the Raman shifts with warming rates 1.30 K/min and 0.95 K/min for P$_1$ at panel (a) and P$_2$, P$_3$ at panel (b).
• Figure S1.1: Powder X-ray diffraction (XRD) pattern of NbTe$_4$ sample. The inset shows a photograph of the NbTe$_4$ single crystals.