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 experiment. We show evidence for understanding the decrease of the single-electron tunneling rates in terms of the behavior of the ω→0 spectral weight function. DOI: http://dx.doi.org/10.1103/PhysRevB.50.5760 © 1994 The American Physical Society

The interplay between the Kondo effect and the interdot magnetic interaction in a coupled-dot system is studied. An exact result for the transport properties at zero temperature is obtained by diagonalizing a cluster, composed by the double dot and its vicinity, which is connected to leads. It is shown that the system goes continuously from the Kondo regime to an antiferromagnetic state as the interdot interaction is increased. The conductance, the charge at the dots, and the spin-spin correlation are obtained as a function of the gate potential.

The persistent current through a quantum dot inserted in a mesoscopic ring of length $L$ is studied. A cluster representing the dot and its vicinity is exactly diagonalized and embedded into the rest of the ring. It is shown that the persistent current at the Kondo regime is enhanced relative to the current flowing either when the dot is at resonance or along a perfect ring of the same length. In the Kondo regime, the current scales as $L^{-1/2\mathrm{}}$, unlike the $L^{-1\mathrm{}}$ scaling of a perfect ring. We discuss the possibility of detection of the Kondo effect by means of a persistent current measurement.

The geometric Berry’s phase of the many-body wave function can be used to characterize changes in the electric polarization at quantum phase transitions that take place as one parameter of the Hamiltonian is adiabatically changed. Transitions which involve a discontinuous change in macroscopic polarization are of topological nature, and occur whenever the system exhibits planes of inversion symmetry. We have applied these ideas to a variety of strongly correlated lattice fermion models in one and two dimensions; in particular, the three-band Hubbard model in ${\mathrm{CuO}}_2$ planes in the parent compounds of high-temperature superconductors. For spin-1/2 fermions, we find that the transition between a quantum paramagnet and an antiferromagnet is one of those topological transitions, thus establishing an interesting relation between electric polarization and antiferromagnetism. Interesting consequences emerge when one considers insulators separated by domain walls: A net accumulation of charge at the interface results, which is easily calculated from the Berry’s phase change at the domain wall. We discuss the connection to the recently proposed (and experimentally observed) ‘‘microscopic stripes’’ in nickelate and insulating cuprate materials. © 1996 The American Physical Society.

The conductance $G$ of graphene stripes (of width $W$ and length $L$) with surface disorder and near the Dirac point is investigated numerically. Incoherent metallic leads are attached to the sample ends across its width. In samples of $W∕L⩾1$, the system behaves diffusively with $G\to (2∕\pi )(W∕L)\times 2e^2∕h$, for $L\to \infty$, as found in the clean limit, although with a sharply reduced shape dependence. The conductance in elongated samples, $L⪢W$, decays exponentially with $L$, indicating localization. A similar behavior is found in clean elongated systems due to the existence of minigaps near the Dirac point. Average decay lengths are larger in the presence of disorder. A magnetic field does not appreciably change the conductance unless the flux per unit cell is significant. The distribution of conductances is almost flat between lower and upper cutoffs. Away from the Dirac point, we find the standard ballistic behavior characteristic of systems with rough edges.

Total energies of charge and spin states of a specifically designed target molecule 2,5,8-trihydro-phenalenyl ($3{\text{H-C}}_{13}{\text{H}}_9$ from here on), calculated by means of multiconfigurational self-consistent-field (MCSCF) and density-functional-theory-B3LYP methods, have been fitted by means of interacting Pariser-Parr-Pople (PPP) (intrasite and intersite Coulomb interactions) and Hubbard Hamiltonians for $\pi$ electrons. Numerically exact many-body solutions for these models were obtained by a variant of the Lanczos algorithm. Our calculation shows that the combination MCSCF-PPP with a hopping integral $t=-2.63\text{eV}$ and a local Coulomb repulsion $U=10.51\text{eV}$ produces the best results. Both model parameters are close to values frequently used in the literature, sometimes just for the Hubbard model. The fit of MCSCF energies by the Hubbard model is not as satisfactory (root-mean-square deviation is larger and $t=-4.83\text{eV}$ and $U=21.27\text{eV}$ parameters are far from common values). Neither of both models is able to accurately reproduce B3LYP energies. On the other hand, the value of the ratio $\left|U/t\right|$ is always close to 4 indicating the proximity to a magnetic phase transition in extended systems. Additionally, we find that Lieb’s theorem for the Hubbard model on bipartite lattices applies to neutral $3{\text{H-C}}_{13}{\text{H}}_9$ since all ab initio methods and model Hamiltonians predict a fivefold spin-degenerate ground state. DOI: http://dx.doi.org/10.1103/PhysRevB.81.085120 © 2010 The American Physical Society