Disentangling multipole contributions to collective excitations in fullerenes

Abstract

Angular resolved electron energy-loss spectroscopy (EELS) gives access to the momentum and the energy dispersion of electronic excitations and allows to explore the transition from individual to collective excitations. Dimensionality and geometry play thereby a key role. As a prototypical example we analyze theoretically the case of Buckminster fullerene C 60 using ab initio calculations based on the time-dependent density-functional theory. Utilizing the non-negative matrix factorization method, multipole contributions to various collective modes are isolated, imaged in real space, and their energy and momentum dependencies are traced. A possible experiment is suggested to access the multipolar excitations selectively via EELS with electron vortex (twisted) beams. Furthermore, we construct an accurate analytical model for the response function. Both the model and the ab initio cross sections are in excellent agreement with recent experimental data. PACS numbers: 79.20.Uv,36.40.Gk Plasmonics, a highly active field at the intersection of nanophotonics, material science and nanophysics [1], has a long history dating back to the original work of Gustav Mie on light scattering from spherical colloid particles [2,3]. For extended systems the plasmon response occurs at a frequency set by the carrier density while in a finite system topology and finite-size quantum effects play a key role. E.g., for a nanoshell [4][5][6] in addition to the volume mode, two coupled ultraviolet surface plasmons arise having significant contributions from higher multipoles, as demonstrated below. Such excitations can be accessed by optical means as well as by electron energy-loss spectroscopy (EELS) [7,8]. Particle-hole (p-h) excitations and collective modes may "live" in overlapping momentum-energy domains and couple in a size-dependent way that cannot be understood classically [9][10][11]. Giant plasmon resonances were measured in buckminster fullerene C 60 [12][13][14][15][16][17] and explained, e.g., by assuming C 60 to have a constant density of electrons confined to a shell with inner (R 1 ) and outer (R 2 ) radii (the spherical shell model) [18][19][20]. Refinements in terms of a semi-classical approximation (SCA) incorporate the quantum-mechanical density extending out of the shell R 1 < r < R 2 (so-called spill-out density [21]). Time-dependent density functional theory (TDDFT) [21][22][23] was also employed in a number of calculations [24][25][26], however, most of them use the jellium model, i.e., the ionic structure is smeared out to a uniform positive background. We present here, to our knowledge, the first atomistic fullfledge TDDFT calculations for EELS from C 60 at finite momentum transfer. We demonstrate the necessity of the full ab-initio approach by unraveling the nature of the various contributing plasmonic modes and their multipolar character. This is achieved by analyzing and categorizing the ab initio results by means of the non-negative matrix factorization method [27]. The results are in line with recent experi...

Quantitative first-principles calculations of valence and core excitation spectra of solidC60

“…This was shown, for instance, in an earlier study of the momentum-transfer dependence of the EELS spectrum by Sohmen et al 55 However, it can play an important role in angle-resolved EELS and photoemission. 68–70 Our BSE calculations assume the Fm3 crystal structure. At ambient conditions there is molecular orientational disorder and the system has a 240-atom unit cell Pa3 structure below 260 K. 71 Preliminary calculations and measurements only show slight changes in spectra with such structural changes.…”

Femtosecond dynamics of correlated many-body states in C60fullerenes

“…The matrix element (12) can thus be evaluated in terms of a superposition of matrix elements with respect to the KS orbitals. The scattering states ñ |k were computed with respect to the spherically averaged KS potential [28], which is known to be an adequate approximation for angleintegrated quantities. Asymptotic corrections ensuring ther 1 behavior are incorporated by smoothly interpolating between the short-range and long-range regimes.…”

“…In particular for optimization and control of the charge flow and energy dissipation, rigorous dynamic studies on the fs time scale using ultrafast lasers are indispensable but, still in their infancy [26,27]. Additionally, time-dependent densityfunctional theory (TDDFT) calculations of the absorption and photoelectron spectra, accounting for full structural analysis, were performed [28,29] and constitute the basis for the further development presented below.…”

“…Accessing energy dissipation upon the excitation of correlated many-body states in gas phase C 60 became feasible recently which allows to connect the coherent quantum [28,30], classical and statistical mechanisms [31]. It is known from experiments with optical lasers that electron thermalization mediated by inelastic electron-electron collisions takes place on a time scale of 50-100 fs (see [11] and references therein).…”

Photoionization of multishell fullerenes studied by ab initio and model approaches*

“…A particular attention has been paid to ionization of a C 60 fullerene under the photon, electron, and ion impact [7][8][9][10][11][12][13][14]. Because of their high symmetry and stability, these molecules have been of significant fundamental interest aimed at better understanding the photon-and chargedparticle-induced processes in complex many-particle systems.…”