Controlling the movement of plasmonic nanoparticles with fast electron beams

Abstract

The possibility of moving plasmonic nanoparticles in a controllable way with fast electron beams, like those typically used in electron microscopy, is now open. We have recently published results, both theoretically and experimentally, showing that it is possible to induce movement on a small metallic nanoparticle (1-2 nanometers in radius), shifting it towards the electron beam or away of it. In our calculations of the momentum transfer from the electron to plasmonic nanoparticles we consider full relativistic effects. The attractive interaction between a plasmonic nanoparticle and a fast electron beam, occurring at large enough impact parameters, is what intuitively will be expected from the interaction of the electron and the positive induced charge in the closest region of the nanoparticle to the electron trajectory (excitation of dipolar plasmon mode mainly). However, it is well known that for small enough impact parameters, the dipolar plasmon mode of the nanoparticle is not the most strongly excited mode, so that the higher-energy multipolar modes play a predominant role. Under this circumstance, we have shown that the interaction between the electron and the nanoparticle turns out to be repulsive, that is, the electron beam expels the nanoparticle away. Thus, by controlling the impact parameter of the electron beam to the nanoparticles, it is possible for example to induce coalescence between pair of particles, as has been observed and studied experimentally, or avoid that two nanoparticles approach each other. The repulsive behavior at small impact parameters is predicted by theoretical calculations from classical electrodynamics, however other processes might be present in the experiment such as secondary electron emission and surface charging. Although the repulsive behavior between a swift electron and a silver nanoparticle was theoretically found by Garca de Abajo and studied in detail, no fully satisfactory theoretical explanation has been given. We propose, as a suitable explanation based on classical electrodynamics, that the repulsion effect is due to the recoil of the particle produced by the momentum carried on the electromagnetic field radiated away by the particle. In this sense, when the electron beam is traveling far from the nanoparticle, the distribution of the induced charges within the particle (mainly dipolar) will produce a symmetric spatial radiation pattern, with no net momentum. On the other hand, for close electron trajectories, the electron excites higher multipolar plasmon modes producing a constructive interference and resulting in a confined induced charge within the nanoparticle, giving to the radiation (and electromagnetic momentum) a specific direction. Even though the theoretical calculations predict attraction and repulsion effects with transition metals, a simpler analysis has been done with Drude-like metals, where the electromagnetic properties of the excitations are determined by the plasma frequency and the damping.