Theory of radial oscillations in metal nanoparticles driven by optically induced electron density gradients

Abstract

We provide a microscopic approach to describe the onset of radial oscillation of a silver nanoparticle. Using the Heisenberg equation of motion framework, we find that the coupled ultrafast dynamics of coherently excited electron occupation and the coherent phonon amplitude initiate periodic size oscillations of the nanoparticle. Compared to the established interpretation of experiments, our results show a more direct coupling mechanism between the field intensity and coherent phonons. This interaction triggers a size oscillation via an optically induced electron density gradient occurring directly with the optical excitation. This source is more efficient than the incoherent heating process currently discussed in the literature and well-describes the early onset of the oscillations in recent experiments.

Time-Resolved Single-Particle X-ray Scattering Reveals Electron-Density Gradients As Coherent Plasmonic-Nanoparticle-Oscillation Source

“…Additional power-dependent TA experiments showed no phase change. Our experimental findings were rationalized by calculations, yielding a consistent picture of all observed aspects of the breathing excitation . Two source terms for the lattice dynamics emerge from the calculations: The optically induced spatial gradients of the electron density, including their decay due to their thermalization, act as the main initial driving source for the breathing oscillations, accompanied by time-delayed thermal contributions.…”

“…This is detailed in the Supporting Information (Section 2). To understand the origin of the breathing oscillations, we set up a fundamental microscopic model which extends earlier calculations in ref . to two-band models.…”

“…Our experimental findings were rationalized by calculations, yielding a consistent picture of all observed aspects of the breathing excitation. 24 Two source terms for the lattice dynamics emerge from the calculations: The optically induced spatial gradients of the electron density, including their decay due to their thermalization, act as the main initial driving source for the breathing oscillations, accompanied by time-delayed thermal contributions. The dominance of the direct coupling between the displaced electrons and the lattice can have important consequences for applications harnessing hot electrons 2,3,25−27 and for the general understanding of nanoscale metal dynamics.…”

“…To connect the lattice displacement with the optical excitation, we calculated the equation of motion for the conduction band electron density ρ c ( r , t ) ,− incorporating the electron-light interaction and the electron–phonon interaction from the same Hamiltonian used above. In the limiting case of a short interband dephasing time compared to the pulse width, a rate equation for the electron density can be derived and expanded in orders of the exciting electric field, i.e., ρ = ρ 0 + ρ 1 + ρ 2 + scriptO ( E 3 ) .…”