A charge density wave (CDW) is a macroscopic quantum state in which the electron density and the lattice are periodically modulated. In the transition metal dichalcogenide TiSe₂, the CDW emerges below about 200 K and has a number of unusual properties: strong fluctuations, possible chirality, hidden phases, and ultrafast switching. Femtosecond spectroscopy has already made it possible to observe CDW melting and coherent oscillations of the amplitude mode, but it remained unclear how these oscillations and photoexcited carriers are linked to optical transitions. This work fills that gap by using spectral resolution of the probe near an important transition at 1.5 eV, which is often employed in ultrafast measurements.
The measurements were performed using time- and spectrum-resolved optical pump-probe spectroscopy. A titanium-sapphire oscillator was used with a central wavelength of 825 nm, a pulse duration of 35 fs, and a repetition rate of 80 MHz. To isolate narrow spectral components of the reflected probe, a home-built monochromator with a diffraction grating and 500 µm slits was used, giving a resolution of less than 7 nm. The TiSe₂ sample was cooled to 4.8 K in a closed-cycle cryostat. The absorbed pump energy density was 3.45 µJ/cm², which is below the CDW melting threshold. The non-oscillatory part of the signal was isolated by fitting a biexponential function with a constant offset, and the oscillatory modes were analyzed using a fast Fourier transform.
The spectrally resolved signal ΔR/R shows a sign change near a probe energy of 1.52 eV: positive on the low-energy side and negative on the high-energy side. This feature is explained by a red shift of the optical transition energy at the M point of the Brillouin zone, caused by photoexcited carriers and lattice heating. The relaxation times of the non-oscillatory part were τ₁ = 608 fs and τ₂ = 6.0 ps, consistent with carrier lifetimes measured by tr-ARPES. In the oscillatory response, four modes were identified: the A₁g optical phonon at 6.2 THz and three CDW-related modes: the amplitude mode (AM) at 3.5 THz and two zone-folded phonon modes (ZFP1 at 3.4 THz and ZFP2 at 5.2 THz). The amplitudes of the CDW modes peak near 1.48 eV, whereas the amplitude of the A₁g phonon is suppressed in this region and increases at the edges of the spectrum. This indicates different coupling strengths to the optical transition at the M point.
The work demonstrates that different coherent vibrations in the CDW state of TiSe₂ interact differently with optical transitions. The A₁g optical phonon modulates the transition energy at the M point via the deformation potential, which leads to a derivative-like shape of the spectral dependence. The CDW-related modes appear to be more strongly coupled to transitions sensitive to the CDW order parameter rather than to the transition at the M point. This opens a path to selective optical control of individual vibrational modes in layered materials and deepens our understanding of the microscopic details of ultrafast processes in CDW systems.
A promising direction is the theoretical calculation of optical transitions in TiSe₂ taking electron-phonon interaction into account, in order to determine precisely which transitions are modulated by each mode. It would also be interesting to study how the coupling depends on temperature and doping level, and to extend the method to other CDW materials, such as tantalum or niobium dichalcogenides. Two-dimensional samples could be used to enhance the effects and to study the influence of dimensionality.
The results may be useful for developing ultrafast optical switches and CDW-based devices, as well as for controlling coherent phonons in optoelectronics.
Plans include performing calculations of the band structure and reflectance spectra taking specific phonon modes into account, as well as carrying out measurements with a broader range of probe energies to identify other transitions.
In CDW physics, the question of the CDW formation mechanism and the role of excitonic correlations remains unresolved. This work links the dynamics of the order parameter to specific optical transitions, which may help distinguish an excitonic mechanism from a purely electronic one. It also clarifies how coherent phonons affect the electronic structure near the transition, which is important for understanding nonequilibrium phases.
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What the work does
This work investigates the dynamics of the charge-density wave (CDW) in TiSe₂ using femtosecond pump-probe spectroscopy with probe-spectrum resolution. The authors found a sign change in the non-oscillatory part of the signal near 1.5 eV, which they interpret as a red shift of the optical transition at the M point, and showed that the amplitudes of the coherent modes (A₁g and three CDW modes) have different spectral dependences, indicating mode-selective coupling to this transition.
Where its strength is
The strength of the work lies in its spectrally resolved approach, which made it possible to directly link specific coherent vibrations to the optical transition at the M point. This provides a microscopic basis for understanding how photoexcitation controls the CDW state in TiSe₂.
Where it could go next
Worth trying
Why this may matter
Understanding how different coherent vibrations interact with optical transitions in CDW materials could open routes to ultrafast control of quantum states in layered materials, which matters for future applications in optoelectronics and quantum technologies.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.54, against a usual 0.64. It looks like few have drilled nearby.
The temperature of 4.8 K at which the measurements were performed is only slightly above the boiling point of liquid helium (4.2 K). At this temperature, the amplitude of coherent phonons is maximal and the CDW state is stable, which makes it possible to resolve even closely spaced modes that differ by only 0.1 THz.