Coherent control through phonon anharmonicity

TL;DR

This work directly probes phonon anharmonicity in a single Raman mode by combining double pump-probe spectroscopy with a DECP framework in SnTe and SnSe. By isolating trailing-pump contributions and modeling the excitation with multiple electronic/thermal channels, the authors extract mode-specific electron-phonon couplings and reveal light-induced anharmonicity through frequency shifts that depend on oscillation amplitude. The approach disentangles electronic, thermal, and intrinsic anharmonic effects via their distinct temporal fingerprints, capturing both monotonic softening at high fluence and nonmonotonic, chirp-like dynamics at ultrafast timescales. The results have implications for thermoelectric material engineering and offer a general tool to study optically induced phase transitions and nonlinear phononics in solids.

Abstract

Anharmonic lattice vibrations play a key role in many physical phenomena. They govern the heat conductivity of solids, strongly affect the phonon spectra, play a prominent role in soft mode phase transitions, allow ultrafast engineering of material properties and more. The most direct evidence for anharmonicity is to measure the oscillation frequency changing as a function of the oscillation amplitude. For lattice vibrations, this is not a trivial task, and anharmonicity is probed indirectly through its effects on thermodynamic properties and spectral features or through coherent decay of one mode to another. However, measurement and control of the anharmonicity of a single Raman mode is still lacking. We show that ultrafast double pump-probe spectroscopy could be used to directly observe frequency shifts of Raman phonons as a function of the oscillation amplitude and disentangle the coherent contributions from quasi-harmonic sources such as temperature and changes to the carrier density in the thermoelectric materials SnTe and SnSe. Moreover, we show that coherent displacive phononic excitations in tandem with electron-phonon coupling is a pathway to dynamically control phonon anharmonicity. Our results have dramatic implications for the material engineering of future thermoelectrics. Moreover, our methodology could be used to isolate the basic mechanisms driving optically induced phase transitions and other nonlinear phenomena based on their unique timestamps.

Figures (14)

• Figure 1: (a) $\Delta R/R$ of SnTe with an incident pump fluence of 0.684 $[mJ/cm^2]$. The blue line is the data, and the black curve is its fit. The red, green, and yellow solid lines are the decomposition of the fit to its exponential and oscillatory components. The inset illustrates the DECP process. As a result of the optical excitation the potential energy landscape $U(Q)$ for the phonons is displaced along the phonon coordinate $Q$ which initiates the oscillatory motion of the phonon (b) Fluence dependence of the $\Delta R/R$. Data is shown in color, and fits are shown as thin black lines. The dashed black lines are guides to the eye through the oscillatory peaks. Data is vertically shifted for clarity. Incident fluences are specified in units of $mJ/cm^2$. (c) Frequencies extracted from the fits to the data shown in panel (b) as a function of the applied pump fluence. The star marks the frequency measured by Raman scattering. In the inset, Raman scattering measurement. A star marks the stokes and anti-stokes peaks corresponding to the same mode measured using the pump-probe technique.
• Figure 2: (a) $\Delta R/R$ data taken with single pump excitation. The blue curve is taken only with the trailing pump whereas the red curve is taken only with the leading pump. (b) $\Delta R/R$ data taken with both pumps incident on the sample with $\Delta t_{pp}$ = 3.31[ps]. The blue curve was taken with the chopper modulating both pump beams and the orange curve corresponds to a measurement in which only the trailing pump is modulated by the chopper. (c) Color map of the double pump $\Delta R/R$ data. Colors represent the magnitude of $\Delta R/R$, the horizontal axis is the time delay between the probe and the trailing pump whereas the vertical axis is $\Delta t_{pp}$.
• Figure 3: Phonon frequency as a function of $\Delta t_{pp}$. Black line is a fit to our oscillator model. In the left inset the blue dots show the data on short timescales for which the horizontal axis represents $\Delta t_{pp}$. The orange curve is the oscillatory component of $\Delta R/R$ of the leading pump for which the horizontal axis represents the time delay between the pump and probe pulses, and the black line is a fit to our model. In the inset on the right, an illustration of the DECP process in the presence of electron-phonon coupling. At early times after the photoexcitation, the phonon potential is soft due to the increased electron density (top curve) depicted by the shallow parabola. As time goes by the excited electron density exponentially decays towards its equilibrium value and with it the parabola shifts towards its original position and curvature.
• Figure 4: (a) $\Delta R/R$ data in SnSe, taken with single pump excitation. The blue curve is taken only with the trailing pump, whereas the red curve is taken only with the leading pump. (b) Color map of the double pump $\Delta R/R$ data for SnSe. Colors represent the magnitude of $\Delta R/R$, the horizontal axis is the time delay between the probe and the trailing pump, whereas the vertical axis is $\Delta t_{pp}$. In panels (c) and (d), similar plots to that presented in Figure \ref{['Figure 3']} are presented, corresponding to two of the $A_g$ phonons of SnSe. In both panels, the blue curves show the phonons' frequency as a function of $\Delta t_{pp}$, the black curves show fit to our model, and the orange curves are the corresponding oscillatory component of $\Delta R/R$ of the leading pump, which were extracted by fitting to the pump-probe data shown in panel (a), as a function of the time delay between the pump and the probe pulses.
• Figure S1: Schematic of the optical setup used in this work. Unlabeled components are silver mirrors.