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 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.