Plasmon-in-a-Box: On the Physical Nature of Few-Carrier Plasmon Resonances

Abstract

Recent demonstrations in doped semiconductor nanocrystals establish that a plasmon resonance can be sustained by a handful of charge carriers, much smaller in number than conventionally thought. This finding raises questions about the physical nature of such a collective resonance, a fundamental question in condensed matter and many-body physics, which the author addresses here by means of a plasmon-in-a-box model. A small number of carriers confined within a nanocrystal exhibit multiple transitions of individual carriers between quantized states. However, as carriers are progressively added, spectral lines associated with single-carrier excitations evolve into a band representing a collective resonance. This evolution is gradual, and it involves an intermediate regime where single-carrier excitations and few-carrier collective excitations coexist, until, at high carrier numbers, a purely classical collective resonance involving all carriers in the nanocrystal is sustained. The author finds that the emergence of the plasmon resonance is a density-driven transition; at high enough carrier densities, the Coulomb repulsion between carriers becomes strong enough to allow individual carriers to overcome their confinement to the nanocrystal lattice and to participate in a collective excitation within the mean Coulomb field of other carriers. The findings represent deeper insight into the physical picture of a plasmon resonance and serve as a potential design guide for nanoscale optoelectronic components and photocatalytic plasmonic clusters.

Impacts of surface depletion on the plasmonic properties of doped semiconductor nanocrystals

“…Fitting of extinction spectrum with Mie theory based on the Drude dielectric function (table S1) indicates that the carrier concentration in the samples varies in between 3.48x 10 20 and 11.2x10 20 cm -3 , increasing with Sn content. The presence of a high initial number of free carriers in our NCs and NC size greater than 7 nm excludes any significant contribution due to quantum effects, thus supporting the continuum analysis and modeling employed later in this work 55,56 . To study the role of applied potential on LSPR properties, uniform thin films of NCs were spin coated from NC dispersions on conductive Sn:In 2 O 3 -coated glass substrates and assembled into a custom-designed multi-layer sandwich cell for in situ FTIR SEC measurements (see the methods and Figure S3-S6).…”

Plasmonic doped semiconductor nanocrystals: Properties, fabrication, applications and perspectives

“…[12,44,45] The regulation of the carrier density to ultralow levels in quantum confined systems enables the study of quantum plasmonics. [46][47][48] The combination of different functionalities in one material via the chemical incorporation of dopant atoms with specific physical properties, such as magnetism, enables the fabrication of switchable magnetic probes. [49] The chemical reactivity of some of these compound semiconductors, for example the ability of copper chalcogenide to lose or acquire copper ions, or yet to exchange them in part or in total with other ions, with concomitant changes in the plasmonic response, makes them interesting for various applications, including sensing.…”

“…by a transition from the size-quantization regime to the classical regime of plasmon oscillations as carriers are progressively added [46]. Jain et al[47] established a plasmon-in-a-box model to describe such limiting cases and found that intraband transitions of single carriers between levels dominate the optical response, while collective excitations begin when the carrier density reaches critical values, because Coulomb interactions between carriers begin to overcome the confinement of Fermi level carriers to the lattice. Notably, the authors found a transition regime between quantum plasmons and classical plasmons, where both excitations coexist in an intermediate regime [47].…”

“…Jain et al[47] established a plasmon-in-a-box model to describe such limiting cases and found that intraband transitions of single carriers between levels dominate the optical response, while collective excitations begin when the carrier density reaches critical values, because Coulomb interactions between carriers begin to overcome the confinement of Fermi level carriers to the lattice. Notably, the authors found a transition regime between quantum plasmons and classical plasmons, where both excitations coexist in an intermediate regime [47]. These results together highlight the fundamental difference of this new class of plasmonic material with respect to noble metals, as the number of carriers can be precisely controlled to limiting cases, having important consequences for both the understanding and future applications of degenerately doped semiconductor NCs [46][47][48].…”

Synthetic Strategies for Semiconductor Nanocrystals Expressing Localized Surface Plasmon Resonance

“…[3] The ongoing efforts involvings ynthesis studies of improved or novel QD types [4] speaks to their profound chemical adaptability,a nd from time to time also resultsi nt he formation of new subfields within the community.O ne such recent example is the topic of plasmonics in doped QDs. [5][6][7][8][9] Reports of plasmonic modesi nS CN Cs were first published in 2009 with regards to relativelyp olydisperse Cu 2Àx SN Cc lusters by Burda and co-workers, [10] as well as aw ide-bandgapm etal oxide (indium tin oxide)b yT eranishi, et al [11] Am ore controlled QD system of the same Cu 2-x Sc rystal type was reported in 2011i n as eminal manuscript by Alivisatos and co-workers. [12] Prior to these studies, the topic of plasmonic NCs was essentially exclusively relegated to metals such as gold and silver.L ocalized surfacep lasmon resonance (LSPR) frequencies on these particles, although geometrically tunable, are in the UV/Vis regime and are relatively static because of the fixed carrierc oncentrations associatedw ith these metals.…”