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We introduce a new computational method to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce GGA+U results when ignoring inter-orbital Coulomb repulsion $U$ and Hund exchange $J$. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra, and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN$_4$ centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, $U$ changes the relative position of the peaks in the density of states, particularly on the iron $d_{z^2}$ orbital, which is expected to greatly affect the binding of ligands.
The low-energy (intraband) range of the third harmonic generation of graphene in the terahertz regime is governed by the damping terms induced by the interactions. A controlled many-body description of the scattering processes is thus a compelling an
We develop the plasmon-pole approximation (PPA) theory for calculating the carrier self-energy of extrinsic graphene as a function of doping density within analytical approximations to the $GW$ random phase approximation ($GW$-RPA). Our calculated se
We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magneto-phonon resonances, we extract
We investigate the many-body properties of graphene on top of a piezoelectric substrate, focusing on the interaction between the graphene electrons and the piezoelectric acoustic phonons. We calculate the electron and phonon self-energies as well as
We make use of micro-magneto Raman scattering spectroscopy to probe magneto-phonon resonances (MPR) in suspended mono- to penta-layer graphene. MPR correspond to avoided crossings between zone-center optical phonons (G-mode) and optically-active inte