Dynamic core hole screening in small-diameter conducting carbon nanotubes: A cluster density functional study

Statistics of work and orthogonality catastrophe in discrete level systems: an application to fullerene molecules and ultra-cold trapped Fermi gases

“…On the other hand, the numerical shake-up response of the harmonically trapped Fermi gas is in excellent agreement with In the C 60 case, P γ is the zero-temperature distribution broadened by a Lorentzian of width γ = 0.05 eV; P γ,σ is obtained by convoluting P(W) with a Voigt distribution [18,19], whose Gaussian standard deviation σ = 0.172 eV and Lorentzian width γ = 0.068 eV are adjusted to some measurements on thick fullerene films. The experimental data are taken from [12,13] and plotted on the same arbitrary unit scale [18,19]. The theoretical distributions are computed with the DFT approach outlined in Section 2.1, using both the PBE and the B3LYP functionals.…”

“…The former is expressed by the photo-current probability, involving the initial core state and the final photo electron state. The latter is manifested by the work distribution in Equation 2, which can be interpreted as the probability density that the work is used to excite valence electrons at the expense of the kinetic energy of the photoelectron, ε [17][18][19]. Indeed, P(W) accounts for the N − 1 electrons that do not directly participate in the ionization process.…”

“…The corresponding kinetic energy spectrum was observed to have an asymmetric peak at the binding energy of the core level with a power-law singularity, which has then become known as the Fermi edge singularity [7]. Similar patterns were afterwards identified in a large number of coreionized systems [8,9], including organic molecules [10] and carbon-based nanomaterials [11][12][13][14][15][16][17][18][19], where an additional signature of the Anderson orthogonality catastrophe are the secondary peaks, or shake-up satellites, in the core level spectra. Despite the diversity of contexts in which Fermi edge resonance and Anderson orthogonality catastrophe occur [20][21][22][23][24][25][26][27][28][29][30], the same generic physics has been recently observed in the controllable domain of ultra-cold trapped gases, as a response to the embedding of a single probe qubit, i.e., a two-level impurity [31,32].…”

“…To depict the rearrangement of the valence electronic structure, we use a DFT approach in which we replace the core electrons of a specific atom in the molecule with an effective core potential (ECP) of the Stevens-Basch-Krauss (SBK) type [40], whose parameters are adjusted to describe neutral and core-ionized atomic carbon [10]. The valence electrons in this reference atom are described by a d-polarized double split-valence pseudo-basis, being specifically designed for the considered ECP and optimized for the neutral (C 60 ) and ionized ( ) clusters [18,19]. As for the core and valence electrons of all other atoms in the compound, we select the d-polarized triple split-valence basis set denoted 6-311G* [41].…”

“…In the fullerene case, another source of broadening is given by the core-hole lifetime. Besides, to cope with real photoemission experiments a further Gaussian term due to experimental uncertainties is needed [18,19]. Working at low thermal energies, we can therefore set , with B(W) denoting a broadening function, which includes the "thermal" Gaussian of standard deviation δ β .…”