G. Chiappe

Capacitance spectroscopy in quantum dots: Addition spectra and decrease of tunneling rates

A theoretical study of single electron capacitance spectroscopy in quantum dots is presented. Exact diagonalizations and the unrestricted Hartree-Fock approximation have been used to shed light over some of the unresolved aspects. The addition spectra of up to 15 electrons is obtained and compared with the experiment. We show evidence for understanding the decrease of the single electron tunneling rates in terms of the behavior of the ! → 0 spectral weight function. Single electron capacitance spectroscopy (SECS) [1,2] has been a breakthrough in the experimental knowledge of the electronic structure of a quantum dot (QD). Ashoori and co-workers [1,2] have been able to determine the energies required to introduce electrons one by one, from 0 to 50, into a QD. The electrons tunnel into the QD by means of a vertical gate bias, and change the capacitance of the device. The measurement of that capacitance as a function of the Fermi energy EF in one electrode shows a discrete set of almost equally spaced peaks of different intensities. A peak appears whenever EF = � (N) = E0(N) − E0(N − 1), with E0(N) being the ground state (GS) energy of N electrons in the QD. In this way,

Magnetic molecules created by hydrogenation of Polycyclic Aromatic Hydrocarbons

Present routes to produce magnetic organic-based materials adopt a common strategy: the use of magnetic species (atoms, polyradicals, etc.) as building blocks. We explore an alternative approach which consists of selective hydrogenation of Polycyclic Aromatic Hydrocarbons. Self-Consistent-Field (SCF) (Hartree‐Fock and DFT) and multi-configurational (CISD and MCSCF) calculations on coronene and corannulene, both hexahydrogenated, show that the formation of stable high spin species is possible. The spin of the ground states is discussed in terms of the Hund rule and Lieb’s theorem for bipartite lattices (alternant hydrocarbons in this case). This proposal opens a new door to magnetism in the organic world.

Can model Hamiltonians describe the electron-electron interaction in π-conjugated systems? PAH and graphene.

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser-Parr-Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree-Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree-Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an effective Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

Classical trajectories in quantum transport at the band center of bipartite lattices with or without vacancies

Here we report on several anomalies in quantum transport at the band center of a bipartite lattice with vacancies that are surely due to its chiral symmetry, namely: no weak localization effect shows up, and, when leads have a single channel the transmission is either one or zero. We propose that these are a consequence of both the chiral symmetry and the large number of states at the band center. The probability amplitude associated to the eigenstate that gives unit transmission ressembles a classical trajectory both with or without vacancies. The large number of states allows to build up trajectories that elude the blocking vacancies explaining the absence of weak localization.

Herringbone Pattern and CH–π Bonding in the Crystal Architecture of Linear Polycyclic Aromatic Hydrocarbons

The herringbone pattern is a pervasive structural motive found in most molecular crystals involving aromatic compounds. A plot of the experimental sublimation enthalpies of members of increasing size of the acene, phenacene and p-phenyl families versus the number of carbons uncovers a linear relationship between the two magnitudes, suggesting a major role of CH-π bonding. In this work we undertake the task of evaluating the relevance of the edge-to-face interaction (or CH-π bond) in the overall reticular energy of the crystal, to quantitatively assess the importance of this structural element. Following a heuristic approach, we considered the series of acenes, phenacenes and p-phenyls and analyzed the edge-to-face interaction between the molecules as they occur in the experimental crystal network. Isolation of the relevant molecular dimers allows to incorporate some of the most sophisticated tools of quantum chemistry and get a reliable picture of the isolated bond. When compared to the experimental sublimation energy, our results are conclusive: this sole interaction is the largest contribution to the lattice energy, and definitively dictates the crystal architecture in all the studied cases. Elusive enough, the edge-to-face interaction is mainly dominated by correlation interactions, specifically in the form of dispersion and, to a less extent, of charge-transfer terms. A suggestive picture of the bond has been obtained by displaying the differences in local electron densities calculated by either correlated or non-correlated methods.

Exact momentum distribution of theU=∞ Hubbard model on a 4×4 cluster

The Lanczos method has been used to obtain the evolution after hole doping of the momentum distribution of a one-band Hubbard model of infinite U on a 4×4 cluster of the square lattice. Our results show that the corner of the Brillouin zone is progressively emptied as holes are introduced into the halt-filled system because only one electron per k point is allowed in this situation

The Wavefunction Renormalization Constant for the One- and Two-Band Hubbard Hamiltonians in Two Dimensions

The normal state of the recently discovered high-T c superconductors [1], exhibits many exotic properties that are not yet fully understood. A picture that is gaining acceptance assumes that the normal state is not a normal Fermi liquid [2–5] but rather it shows unconventional properties somewhat similar to those of the Hubbard model in 1D [6], namely: i) an unrenor-malizable Fermi-surface phase shift, which implies a vanishing wavefunction renormalization constant (Z), ii) a one-particle spectral density that shows a strong peak at the Fermi energy, iii) a Fermi surface that obeys Luttinger’s theorem [7], and, iv) charge and spin separation.

Effect of Disorder on Several Properties of the One-Band Hubbard Model in 2D

In this work, we continue the study of the Hubbard model with infinite U that has been reported previously [1, 2]. Ground state quantum numbers, momentum distribution, magnetic structure factor, overlap of the exact wavefunction with the Gutzwiller wavefunction and, several electronic correlations have been obtained for a 4 × 4 cluster of the square lattice. In particular, the possible existence of a phase transition from a perturbative region where the overlap between the non-interacting Fermi sea and the correlated wavefunction is large to a non perturbative region where this overlap is negligible, has been carefully examined. Although non conclusive due to the size limitations, we have shown that the momentum distribution for a small density of holes closely resembles that of spinless fermions.