(Nanowerk Spotlight) A theory analysis of energy/momentum conservation laws in a spatially confined coupled system of nearly free electrons and phonons hints that the absorption of electromagnetic waves by a metallic nano-object hosting longitudinal vibration modes may allow channeling the absorbed energy either into heat or into terahertz radiation, depending on the nano-objects’ shape and size. This offers an explanation for the size selectivity of small nanoparticles in radio frequency hyperthermia, and suggests design for novel terahertz radiation sources.The concepts elaborated in condensed matter physics for treating bulk metals remain to some extent valid when applied to metallic nano-objects. For example, longitudinal vibration modes of ions in an infinite crystal can be reasonably casted into an image of a compression waves propagating along a confined path; the nearly-free-electron states roughly maintain their dispersion relation as they get discretized according to the Kubo formula applicable to small metal particles.Prof. Andrei Postnikov of the Université de Lorraine, France and Dr. Kamil Moldosanov of the Kyrgyz-Russian Slavic University, Kyrgyzstan, made use of these concepts in order to address, within simple theory considerations, the process of absorption of electromagnetic (EM) energy by metallic nano-objects. The crucial assumption hereby was that the Fermi electrons within the nano-object can simultaneously absorb a longitudinal phonon and an EM quantum.This assumption can be argued for in the following way. As a longitudinal vibration wave propagates throughout the metallic nano-object, the ions get displaced from their equilibrium positions, giving rise to spatial variations of ionic density and, hence, to alternate positively and negatively charged regions. In the intermediate domains between the two, the resulting electric field may accelerate the Fermi electrons.If a nano-object is irradiated by an EM wave, the Fermi electrons are subject to acceleration by the corresponding external field as well. As the energy levels of both electrons and longitudinal phonons are quantized, the specific manifestation of the conservation laws (for energy and momenta) would vary depending on the size and shape of the nano-object. A scheme of a simultaneous absorption of a longitudinal phonon and of an EM photon by a Fermi electron, with the energies of the corresponding quasiparticles indicated, is shown in the Figure. A possible relaxation scheme for the excited electron, via an emission of a terahertz (THz) photon, is also shown.
(Fig.1 of Ref. [2]) Scheme of absorption of microwave radiation hνRF by an electron at EF, assisted by an absorption of a longitudinal phonon, with subsequent emission of a terahertz quantum hνTHz. The corresponding dispersion laws are indicated.
These new insights became a breakthrough idea because they made it possible, by boosting the one or the other channel for an excited electron to relax in the nano-object of a given shape, (i) to explain the size effect in the radio-frequency (RF) hyperthermia [1], (ii) to suggest a novel design of a THz radiation source [2], (iii) to suggest (patent pending) a terahertz-to-infrared converter for THz imaging the human skin cancer, as well as the low frequency (~0.1–0.5 THz) THz radiation source for detecting hidden and concealed goods.The preferential relaxation mechanism of the excited electron can be somehow pre-selected by the nano-object’s shape, that, in its turn, is dictated by the task: if the nano-object is intended to serve for heating, as in the case for RF hyperthermia [1], or for the terahertz-to-infrared conversion, it should be chosen as a nearly spherical nano-ball. However, for the nano-object to work as an emitter of THz radiation, its shape must be that of nano-bar, or nano-ring [2].The relaxation of an excited electron may occur either (a) via an emission of a longitudinal phonon with the energy superior to that of the "auxiliary" phonon absorbed along with the RF photon [1], or (b) via the scattering at the nano-object’s surface [2], or (c) on intentionally added impurity atoms, chosen among such elements that develop high density of electronic states at the Fermi level of the nano-object.For instance, in case of gold nano-objects the impurities of Fe or Ta seem to be good candidates in this sense [3]. Such way of relaxation (as additional one to scattering at the nano-object’s surface) has been chosen in the low frequency THz radiation source. The skin depth in gold at frequencies 0.1–0.5 THz exceeds the sizes of the nano-objects considered, therefore the THz photons emitted in the course of electronic relaxation would leave the nano-object without being reabsorbed.
References
[1] Postnikov, A. and Moldosanov, K. Phonon-Assisted Radiofrequency Absorption by Gold Nanoparticles Resulting in Hyperthermia.
A preprint is available here.
In Fundamental and Applied Nano-Electromagnetics (NATO Science for Peace and Security Series B: Physics and Biophysics)
; Maffucci, A.; Maksimenko, S. A., Eds.; NATO Science for Peace and Security Series B: Physics and Biophysics; Springer: Dordrecht, The Netherlands, 2016; pp. 171–201. doi: 10.1007/978-94-017-7478-9_9. Proceedings of the NATO Advanced Research Workshop on Fundamental and Applied Nano-Electromagnetics, Minsk, Belarus, May 25–27, 2015.[2] Moldosanov K. and Postnikov A. A terahertz-vibration to terahertz-radiation converter based on gold nanoobjects: a feasibility study, Beilstein J. Nanotechnol. 2016, 7, 983-989 (open access).
[3] Postnikov, A. V. and Moldosanov, K. A. Non-plasmonic hyperthermia: prerequisites for realization and materials, J. Nanophoton. 2012, 6, 061709.By Kamil Moldosanov, Kyrgyz-Russian Slavic University (altair1964@yandex.ru) and Andrei Postnikov Université de Lorraine (andrei.postnikov@univ-lorraine.fr)
Read more: Longitudinal acoustic vibrational modes favour new applications of metallic nano-objects
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