Hydrodynamic model of the collective electron resonances in C60 fullerene

Abstract

The polarization-response spectrum of the fullerene C 60 modeled as a homogeneous spherical plasma shell is calculated in the framework of the hydrodynamic approach allowing for the spatial dispersion caused by the Fermi-distributed valence electrons. The dipole eigenoscillations spectrum of the shell is found to contain a series of plasmons distinguished by the frequency and the radial structure. The first two of them (whose structures for C 60 is the subject of discussion up to now) pass to the lower and higher surface plasmons of the plasma shell if its thickness is much larger than Tomas-Fermi length. However, under parameters values corresponding to the C 60 molecule, when these lengths are of the same order, both these plasmons (providing the main contribution to the fullerene absorption spectrum) are found to be actually volume ones in their spatial structure, and the frequency of the higher of them becomes larger than the plasma frequency (as with all the higher volume plasmons). The resonance curve of the fullerene absorption cross-section calculated on the basis of the developed model with allowance for the surface losses caused by the reflection of electrons at the shell boundaries agrees satisfactorily with the experimental data.Studies on the dynamical polarizability of the spherical plasma shells interacting with the fields of different external sources are of interest in connection with the problems of the observed scattering and absorption spectra identification of the fullerenes (and, in particular, C 60 molecule), displaying oscillatory features of plasma-like systems due to a great number of the valence (delocalized) electrons [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Related circle of problems arises also when studying metamaterials made on the basis of shell-like structures (for example, semiconductor quantum dots or metal-dielectric nanoparticles) [19][20][21][22][23][24][25][26][27]. The studies described in the references above have allowed to reveal a number of important features and characteristics of the fullerene polarization processes. There was predicted [1] and confirmed experimentally [2-5] the existence of the so-called giant resonance of C 60 molecule in the frequency range ~ 20 -40 eV, associated with the excitation of the dipole surface plasmons. The plasmon resonances spectra of this molecule were studied in different aspects: based on the quantum [5][6][7][8][9][10][11] and semiclassical [12][13][14][15][16][17][18] approaches (including the nonlinear effects in the processes of the one-photon and multi-photon absorption [9]), with the dipole and high multipoles excitations taken into account [6][7][8][14][15][16][17][18], under different manifestation conditions (excitation by the optical radiation [5,[9][10][11][12][13][14][15][16][17][18] and moving electrons [6-8]), and different approximations of electron density distribution (homogeneous [5-10,13,14] or inhomogeneous shells [11,12] and 2D spherical films [15][16][17][18]). Nevertheless, the carr...

Time-dependent orbital-free density functional theory for electronic stopping power: Comparison to the Mermin-Kohn-Sham theory at high temperatures

“…7 accounts for both the static Von-Weizsäcker KED potential and the high frequency limit dynamic KED response, shown below [63]. More specifically it leads to the quantum Bohmian pressure, the continuity equation, and the bulk hydrodynamic response to a potential or pressure, for the "electron liquid" [63][64][65][66][67][68][69]. We refer to the solution of Eq.…”