Full capacitance matrix of coupled quantum dot arrays: static and dynamical effects

We numerically calculated the full capacitance matrices for both one-dimensional (1D) and two-dimensional (2D) quantum-dot arrays. We found it is necessary to use the full capacitance matrix in modeling coupled quantum dot arrays due to weaker screening in these systems in comparison with arrays of normal metal tunnel junctions. The static soliton potential distributions in both 1D and 2D arrays are well approximated by the unscreened (1/r) coulomb potential, instead of the exponential fall-off expected from the often used nearest neighbor approximation. The Coulomb potential approximation also provides a simple expression for the full inverse capacitance matrix of uniform quantum dot arrays. In terms of dynamics, we compare the current-voltage (I-V) characteristics of voltage biased 1D arrays using either the full capacitance matrix or its nearest neighbor approximation. The I-V curves show clear differences and the differences become more pronounced when larger arrays are considered.Comment: 8 pages preprint format, 3 PostScript figure

Geometrically Induced Multiple Coulomb Blockade Gaps

We have theoretically investigated the transport properties of a ring-shaped array of small tunnel junctions, which is weakly coupled to the drain electrode. We have found that the long range interaction together with the semi-isolation of the array bring about the formation of stable standing configurations of electrons. The stable configurations break up during each transition from odd to even number of trapped electrons, leading to multiple Coulomb blockade gaps in the the $I-V$ characteristics of the system.Comment: 4 Pages (two-columns), 4 Figures, to be published in Physical Review Letter

Optical Conductivity in Mott-Hubbard Systems

We study the transfer of spectral weight in the optical spectra of a strongly correlated electron system as a function of temperature and interaction strength. Within a dynamical mean field theory of the Hubbard model that becomes exact in the limit of large lattice coordination, we predict an anomalous enhancement of spectral weight as a function of temperature in the correlated metallic state and report on experimental measurements which agree with this prediction in $V_2O_3$. We argue that the optical conductivity anomalies in the metal are connected to the proximity to a crossover region in the phase diagram of the model.Comment: 12 pages and 4 figures, to appear in Phys. Rev. Lett., v 75, p 105 (1995

Interplay of Mott Transition and Ferromagnetism in the Orbitally Degenerate Hubbard Model

A slave boson representation for the degenerate Hubbard model is introduced. The location of the metal to insulator transition that occurs at commensurate densities is shown to depend weakly on the band degeneracy M. The relative weights of the Hubbard sub-bands depend strongly on M, as well as the magnetic properties. It is also shown that a sizable Hund's rule coupling is required in order to have a ferromagnetic instability appearing. The metal to insulator transition driven by an increase in temperature is a strong function of it.Comment: 5 pages, revtex, 5 postscript figures, submitted to Phys. Rev.

Resonant-Cavity-Induced Phase Locking and Voltage Steps in a Josephson Array

We describe a simple dynamical model for an underdamped Josephson junction array coupled to a resonant cavity. From numerical solutions of the model in one dimension, we find that (i) current-voltage characteristics of the array have self-induced resonant steps (SIRS), (ii) at fixed disorder and coupling strength, the array locks into a coherent, periodic state above a critical number of active Josephson junctions, and (iii) when $N_a$ active junctions are synchronized on an SIRS, the energy emitted into the resonant cavity is quadratic with $N_a$. All three features are in agreement with a recent experiment [Barbara {\it et al}, Phys. Rev. Lett. {\bf 82}, 1963 (1999)]}.Comment: 4 pages, 3 eps figures included. Submitted to PRB Rapid Com

A Universal Phase Diagram for PMN-xPT and PZN-xPT

The phase diagram of the Pb(Mg1/3Nb2/3)O3 and PbTiO3 solid solution (PMN-xPT) indicates a rhombohedral ground state for x < 0.32. X-ray powder measurements by Dkhil et al. show a rhombohedrally split (222) Bragg peak for PMN-10%PT at 80 K. Remarkably, neutron data taken on a single crystal of the same compound with comparable q-resolution reveal a single resolution-limited (111) peak down to 50 K, and thus no rhombohedral distortion. Our results suggest that the structure of the outer layer of these relaxors differs from that of the bulk, which is nearly cubic, as observed in PZN by Xu et al.Comment: Replaced Fig. 3 with better versio

Full capacitance-matrix effects in driven Josephson-junction arrays

We study the dynamic response to external currents of periodic arrays of Josephson junctions, in a resistively capacitively shunted junction (RCSJ) model, including full capacitance-matrix effects}. We define and study three different models of the capacitance matrix $C_{\vec{r},\vec{r}'}$: Model A includes only mutual capacitances; Model B includes mutual and self capacitances, leading to exponential screening of the electrostatic fields; Model C includes a dense matrix $C_{\vec{r},\vec{r}'}$ that is constructed approximately from superposition of an exact analytic solution for the capacitance between two disks of finite radius and thickness. In the latter case the electrostatic fields decay algebraically. For comparison, we have also evaluated the full capacitance matrix using the MIT fastcap algorithm, good for small lattices, as well as a corresponding continuum effective-medium analytic evaluation of a finite voltage disk inside a zero-potential plane. In all cases the effective $C_{\vec{r},\vec{r}'}$ decays algebraically with distance, with different powers. We have then calculated current voltage characteristics for DC+AC currents for all models. We find that there are novel giant capacitive fractional steps in the I-V's for Models B and C, strongly dependent on the amount of screening involved. We find that these fractional steps are quantized in units inversely proportional to the lattice sizes and depend on the properties of $C_{\vec{r},\vec{r}'}$. We also show that the capacitive steps are not related to vortex oscillations but to localized screened phase-locking of a few rows in the lattice. The possible experimental relevance of these results is also discussed.Comment: 12 pages 18 Postscript figures, REVTEX style. Paper to appear in July 1, Vol. 58, Phys. Rev. B 1998 All PS figures include

Transfer of Spectral Weight in Spectroscopies of Correlated Electron Systems

We study the transfer of spectral weight in the photoemission and optical spectra of strongly correlated electron systems. Within the LISA, that becomes exact in the limit of large lattice coordination, we consider and compare two models of correlated electrons, the Hubbard model and the periodic Anderson model. The results are discussed in regard of recent experiments. In the Hubbard model, we predict an anomalous enhancement optical spectral weight as a function of temperature in the correlated metallic state which is in qualitative agreement with optical measurements in $V_2O_3$. We argue that anomalies observed in the spectroscopy of the metal are connected to the proximity to a crossover region in the phase diagram of the model. In the insulating phase, we obtain an excellent agreement with the experimental data and present a detailed discussion on the role of magnetic frustration by studying the $k-$resolved single particle spectra. The results for the periodic Anderson model are discussed in connection to recent experimental data of the Kondo insulators $Ce_3Bi_4Pt_3$ and $FeSi$. The model can successfully explain the different energy scales that are associated to the thermal filling of the optical gap, which we also relate to corresponding changes in the density of states. The temperature dependence of the optical sum rule is obtained and its relevance for the interpretation of the experimental data discussed. Finally, we argue that the large scattering rate measured in Kondo insulators cannot be described by the periodic Anderson model.Comment: 19 pages + 29 figures. Submitted to PR

Dynamics of a Josephson Array in a Resonant Cavity

We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B {\bf 63}, 144522 (2001); Phys. Rev. B {\bf 64}, 179902 (E)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman {\it et al} [Phys. Rev. Lett. {\bf 79}, 2371 (1997)] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions, that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's), that when $N_a$ active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in $N_a$, and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.Comment: 15 pages, 10 eps figures, submitted to Phys. Rev.

Redesign of plates by large admissible perturbations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76482/1/AIAA-12089-360.pd