14
M. I. Stockman
by the boundaries of the plasmonic system. A more advanced approach to nonlocality
in nanoplasmonics, albeit treatable only for very small, R 1 nm, nanoparticles, is
based on an ab initio quantum-chemical approach of time-dependent density functional theory (usually abbreviated as TD-DFT) [103–109].
It shows that while for larger particles and relatively large spacing between them
(1 nm), the semi-phenomenological models work quite well; for smaller nanoparticles and gaps the predicted local fields are significantly smaller. This is understandable because in ab initio theories there are phenomena that are important in the
extremely small nanosystem such as a significant dephasing due to the stronger coupling between the collective plasmon and one-particle electron degrees of freedom,
discreetness of the one-electron spectrum, spill-out of the conduction-band electrons
(extension of their wave function outside of the lattice region) and the corresponding
undescreening of the d-band electrons, and simply the discreetness of the lattice.
In the latest set of publications, e.g., [108, 109], this approach is called quantum
nanoplasmonics. We would argue that this approach is traditionally called quantum
chemistry because what is found from the TD-DFT quantum-mechanically is the
dielectric response (susceptibility or polarizability) of the nanosystems. However,
even to calculate theoretically the permittivity of a bulk method, one has to employ
quantum-mechanical many-body approaches such as the random-phase approximation, self-consistent random-phase approximation (or GW-aproximation), or TDDFT, etc. The only difference from the above-sited works is that for bulk metals the
size effects are absent. Therefore permittivities can be adopted from experimental
measurements such as Ref. [32, 110].
Based on the arguments of the preceding paragraph, we would reserve the therm
“quantum plasmonics” for the subfields of nanoplasmonics studying phenomena
related to quantum nature and behavior SPs and SPPs. This term has been proposed
in our 2003 paper [31] introducing the spaser as a quantum generator of nanolocalized
optical fields—see Sect. 1.5 and references sited therein. A related field of studies
devoted to quantum behavior of single SPPs also can reasonably be called quantum
plasmonics as proposed later in Refs. [111, 112].
While the decay of SP excitations is usually a parasitic phenomenon, there are
some effects that completely depend on it. One of them is the SPIDER [93] mentioned
above in Sect. 1.2.4.1. It is based on the transfer of the energy and momentum from
SPPs to the conduction electrons, which microscopically occurs through the decay
of the SPPs into electron-hole pairs leading to production of hot electrons.
Yet another range of phenomena associated with a plasmon-dephasing decay into
incoherent electron-hole pairs (Landau damping) has come to the forefront recently.
This is the plasmon-assisted and enhanced generation of a dc electric current due to
rectification in Schottky diodes involving hot electrons [61, 113–115]. This phenomenon is promising for applications to photodetection and solar energy conversion.
Note that the use of the Schottky contacts between the plasmonic metal and a semiconductor permits one to eliminate a requirement that the photon energy ω is greater
that the band gap. This is replaced by a much weaker requirement that ω is greater
than a significantly lower Schottky-barrier potential [116].
M. I. Stockman
by the boundaries of the plasmonic system. A more advanced approach to nonlocality
in nanoplasmonics, albeit treatable only for very small, R 1 nm, nanoparticles, is
based on an ab initio quantum-chemical approach of time-dependent density functional theory (usually abbreviated as TD-DFT) [103–109].
It shows that while for larger particles and relatively large spacing between them
(1 nm), the semi-phenomenological models work quite well; for smaller nanoparticles and gaps the predicted local fields are significantly smaller. This is understandable because in ab initio theories there are phenomena that are important in the
extremely small nanosystem such as a significant dephasing due to the stronger coupling between the collective plasmon and one-particle electron degrees of freedom,
discreetness of the one-electron spectrum, spill-out of the conduction-band electrons
(extension of their wave function outside of the lattice region) and the corresponding
undescreening of the d-band electrons, and simply the discreetness of the lattice.
In the latest set of publications, e.g., [108, 109], this approach is called quantum
nanoplasmonics. We would argue that this approach is traditionally called quantum
chemistry because what is found from the TD-DFT quantum-mechanically is the
dielectric response (susceptibility or polarizability) of the nanosystems. However,
even to calculate theoretically the permittivity of a bulk method, one has to employ
quantum-mechanical many-body approaches such as the random-phase approximation, self-consistent random-phase approximation (or GW-aproximation), or TDDFT, etc. The only difference from the above-sited works is that for bulk metals the
size effects are absent. Therefore permittivities can be adopted from experimental
measurements such as Ref. [32, 110].
Based on the arguments of the preceding paragraph, we would reserve the therm
“quantum plasmonics” for the subfields of nanoplasmonics studying phenomena
related to quantum nature and behavior SPs and SPPs. This term has been proposed
in our 2003 paper [31] introducing the spaser as a quantum generator of nanolocalized
optical fields—see Sect. 1.5 and references sited therein. A related field of studies
devoted to quantum behavior of single SPPs also can reasonably be called quantum
plasmonics as proposed later in Refs. [111, 112].
While the decay of SP excitations is usually a parasitic phenomenon, there are
some effects that completely depend on it. One of them is the SPIDER [93] mentioned
above in Sect. 1.2.4.1. It is based on the transfer of the energy and momentum from
SPPs to the conduction electrons, which microscopically occurs through the decay
of the SPPs into electron-hole pairs leading to production of hot electrons.
Yet another range of phenomena associated with a plasmon-dephasing decay into
incoherent electron-hole pairs (Landau damping) has come to the forefront recently.
This is the plasmon-assisted and enhanced generation of a dc electric current due to
rectification in Schottky diodes involving hot electrons [61, 113–115]. This phenomenon is promising for applications to photodetection and solar energy conversion.
Note that the use of the Schottky contacts between the plasmonic metal and a semiconductor permits one to eliminate a requirement that the photon energy ω is greater
that the band gap. This is replaced by a much weaker requirement that ω is greater
than a significantly lower Schottky-barrier potential [116].