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

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 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.