Ultrafast broadband optical spectroscopy for quantifying subpicometric coherent atomic displacements in WTe2

Elettra Highlights 2019-2020; pp. 82-83

Original Paper: D. Soranzio et al., Phys. Rev. Research 1, 032033 (2019); DOI: 10.1103/PhysRevResearch.1.032033

Several fundamental properties of materials, including the electrical and thermal conductivities, are impacted by collective atomic vibrations, also known as phonons, characterized by their amplitude, frequency, phase and symmetry. If a material is perturbed by suitable light pulses, then lattice oscillations with particular frequency and symmetry may become synchronized over extended spatial regions, leading to the so-called coherent phonon modes. The characteristic time and length scales of such vibrations are of the order of picoseconds and fractions of picometers, respectively, requiring lengthy experiments with setups almost exclusive of large-scale facilities, e.g. x-ray or electron diffraction, to detect and characterize them with high precision and accuracy. An efficient alternative is to measure the time-resolved reflectivity, in which periodic damped oscillations provide the fingerprint of coherent phonons. Along this line, we report here on a novel approach to estimate the non-equilibrium atomic displacements associated to coherent phonon modes. The method consists of analyzing the modulations induced in the time-resolved reflectivity of a white light probe, comprising wavelengths from the near infrared (~0.85 eV, 1450 nm) to the visible (~2.25 eV, 550 nm), by perturbing the sample with a ~50-femtosecond near-infrared pump pulse (~1.55 eV, 800 nm) and comparing them to first principles quantomechanical simulations. At present, our strategy is applied to tungsten ditelluride (WTe₂), a layered transition metal dichalcogenide that has recently gained interest for showcasing unusually high and non-saturating magnetoresistance at low temperatures, room-temperature ferroelectricity, quantum spin hall effect and Weyl-like electrons. Furthermore, it has been shown that various of its properties are influenced by strain forces, which can be induced through non-equilibrium light perturbations allowing for an ultrafast control of its functionalities.

Figure 1: Normalized non-equilibrium reflectivity (DR/R), measured with light polarized along the (a) x (η||x) and (b) y (η||y) crystal axes, as a function of the time delay between pump and probe pulses and of the white-light probe photon energy at ~710 µJ/cm² fluence (absorbed) and T=295 K.

The normalized non-equilibrium reflectivity (DR/R), defined as the probe reflectivity difference between non-equilibrium and equilibrium conditions normalized to the equilibrium one, is shown in Fig. 1 using linearly polarized probe light along each of the two in-plane crystallographic axes of WTe₂, pre-oriented by using LEED. After time-zero (the condition at which pump and probe pulses arrive simultaneously at the sample), the DR/R amplitude and sign depend on the wavelength and polarization of the probe light. Concerning the time-domain, superimposed on an exponential decay of the signal, multiple periodic oscillations are resolved. These oscillations are due to coherent phonons. We focused on the two most prominent coherent optical phonon modes with ~8 cm^-1 and ~80 cm^-1 frequency. The former is a uniform in-layer shift of the atoms, while the latter involves both in-layer and out-of-layer displacements which depend on the specific atom (Fig. 2(a)). The quantification of the amplitude of these vibrations has been achieved by combining experiments and computer simulations. Experimentally, the magnitude of each mode was extracted from spectral profiles of the out-of-equilibrium reflectivity, taken at time delays of a few picoseconds after the excitation. Here, the electronic system reaches a quasi-equilibrium state perturbed by the coherent phonon modes. Together with a wavelength-dependent incoherent component of the DR/R, the cosine-like behavior of the atomic modulations is transferred to the optical properties in the investigated spectral region (Fig. 2(b)), which periodically reach a maximum (0 phase) and a minimum (π phase) with large damping times for both the 8 cm^-1 (~77 ps) and 80 cm^-1 (~12 ps) modes. The difference between the spectral profiles provides the spectral fingerprint of each phonon mode. These results were compared with the result of quantum-mechanical simulations based on the density functional theory (DFT). The coherent phonon modes and the anisotropic reflectivity of the material were calculated ab-initio and then combined to reproduce the oscillatory features of the reflectivity. The outcome is an accurate description of the effect of coherent phonons on the optical properties of the material, including the dependence on wavelength and polarization of the white light. The two phonons’ fingerprints are shown in Fig. 2(c) for light polarized along the x crystal axis.


Figure 2: (a) Representation of the coherent phonon modes; the arrow orientation indicates the direction of the displacements, while the arrow length indicated the relative shifts of the different atoms (tungsten in blue, tellurium in yellow). (b) Spectral profiles extracted from the map reported in Fig. 1(a) for probe polarization parallel to x (η||x). The 0 and Π phases labels refer to the maximum and minimum of the oscillation in the DR/R signal; the inset shows the time delays at which the curves were extracted. (c) Comparison between the experimental and calculated DR/R signal difference between the 0 and Π phases, showcasing the effects of the optical phonons for η||x.

Finally, the agreement between the results from experiment and theory has been the key to quantify the magnitude of the coherent atomic displacements. We estimate in ~350 femtometers the atomic displacements by the uniform ~8 cm^-1 coherent phonon mode and in a few tens of femtometers, depending on the specific atom, for the ~80 cm^-1 vibration in a low-fluence condition (230 μJ/cm² , absorbed). Experiments were carried out for different pump fluences, photon energies and temperature conditions. While features due to other coherent phonon modes become more relevant at low temperature, the spectral shapes of the two examined coherent phonon effects are robust as the experimental parameters were modified. Our approach allows to evaluate the atomic shifts with a precision of a few femtometers without free tuning parameters, except a scaling factor determined by an overall magnitude comparison between experimental data and numerical simulations. The method is not system-specific and in principle can be extended to any crystalline material, provided that its high-energy optical properties are affected by the coherent motion of atoms. In perspective, our findings provide a useful and reliable method to design tailored devices in which the amplitude of the coherent lattice motion is exploited to finely tune the functional properties of semiconducting and metallic systems.