Universal Parametric Correlations of Conductance Peaks in Quantum Dots

We compute the parametric correlation function of the conductance peaks in chaotic and weakly disordered quantum dots in the Coulomb blockade regime and demonstrate its universality upon an appropriate scaling of the parameter. For a symmetric dot we show that this correlation function is affected by breaking time-reversal symmetry but is independent of the details of the channels in the external leads. We derive a new scaling which depends on the eigenfunctions alone and can be extracted directly from the conductance peak heights. Our results are in excellent agreement with model simulations of a disordered quantum dot.Comment: 12 pages, RevTex, 2 Postscript figure

Mesoscopic Fluctuations of Elastic Cotunneling in Coulomb Blockaded Quantum Dots

We report measurements of mesoscopic fluctuations of elastic cotunneling in Coulomb blockaded quantum dots. Unlike resonant tunneling on Coulomb peaks, cotunneling in the valleys is sensitive to charging effects. We observe a larger magnetic field scale for the cotunneling (valley) fluctuations compared to the peaks, as well as an absence of "weak localization" (reduced conductance at B = 0) in valleys. Cotunneling fluctuations remain correlated over several valleys while peak conductance correlations decreases quickly.Comment: 9 pages, postscript (includes 4 figs). To be published in PR

Semiclassical analysis of the quantum interference corrections to the conductance of mesoscopic systems

The Kubo formula for the conductance of a mesoscopic system is analyzed semiclassically, yielding simple expressions for both weak localization and universal conductance fluctuations. In contrast to earlier work which dealt with times shorter than $O(\log \hbar^{-1})$, here longer times are taken to give the dominant contributions. For such long times, many distinct classical orbits may obey essentially the same initial and final conditions on positions and momenta, and the interference between pairs of such orbits is analyzed. Application to a chain of $k$ classically ergodic scatterers connected in series gives the following results: $-{1 \over 3} [ 1 - (k+1)^{-2} ]$ for the weak localization correction to the zero--temperature dimensionless conductance, and ${2 \over 15} [ 1 - (k+1)^{-4} ]$ for the variance of its fluctuations. These results interpolate between the well known ones of random scattering matrices for $k=1$, and those of the one--dimensional diffusive wire for $k \rightarrow \infty$.Comment: 53 pages, using RevTeX, plus 3 postscript figures mailed separately. A short version of this work is available as cond-mat/950207

Statistical Analysis of Magnetic Field Spectra

We have calculated and statistically analyzed the magnetic-field spectrum (the ``B-spectrum'') at fixed electron Fermi energy for two quantum dot systems with classically chaotic shape. This is a new problem which arises naturally in transport measurements where the incoming electron has a fixed energy while one tunes the magnetic field to obtain resonance conductance patterns. The ``B-spectrum'', defined as the collection of values ${B_i}$ at which conductance $g(B_i)$ takes extremal values, is determined by a quadratic eigenvalue equation, in distinct difference to the usual linear eigenvalue problem satisfied by the energy levels. We found that the lower part of the ``B-spectrum'' satisfies the distribution belonging to Gaussian Unitary Ensemble, while the higher part obeys a Poisson-like behavior. We also found that the ``B-spectrum'' fluctuations of the chaotic system are consistent with the results we obtained from random matrices

Ions in mixed dielectric solvents: density profiles and osmotic pressure between charged interfaces

The forces between charged macromolecules, usually given in terms of osmotic pressure, are highly affected by the intervening ionic solution. While in most theoretical studies the solution is treated as a homogeneous structureless dielectric medium, recent experimental studies concluded that, for a bathing solution composed of two solvents (binary mixture), the osmotic pressure between charged macromolecules is affected by the binary solvent composition. By adding local solvent composition terms to the free energy, we obtain a general expression for the osmotic pressure, in planar geometry and within the mean-field framework. The added effect is due to the permeability inhomogeneity and nonelectrostatic short-range interactions between the ions and solvents (preferential solvation). This effect is mostly pronounced at small distances and leads to a reduction in the osmotic pressure for macromolecular separations of the order 1--2 nm. Furthermore, it leads to a depletion of one of the two solvents from the charged macromolecules (modeled as planar interfaces). Lastly, by comparing the theoretical results with experimental ones, an explanation based on preferential solvation is offered for recent experiments on the osmotic pressure of DNA solutions.Comment: 13 pages, 8 figure

Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots

We show that the parametric correlations of the conductance peak amplitudes of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime become universal upon an appropriate scaling of the parameter. We compute the universal forms of this correlator for both cases of conserved and broken time reversal symmetry. For a symmetric dot the correlator is independent of the details in each lead such as the number of channels and their correlation. We derive a new scaling, which we call the rotation scaling, that can be computed directly from the dot's eigenfunction rotation rate or alternatively from the conductance peak heights, and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the universal distributions of the average level width velocity for various values of the scaled parameter. The universality is illustrated in an Anderson model of a disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure

The Thermopower of Quantum Chaos

The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a non-Gaussian distribution, in agreement with simulations using Random Matrix Theory. We observe no contributions from weak localization or short trajectories in the thermopower.Comment: 4 pages, 3 figures, corrected: accidently omitted author in the Authors list, here (not in the article

Transport spectroscopy in a time-modulated open quantum dot

We have investigated the time-modulated coherent quantum transport phenomena in a ballistic open quantum dot. The conductance $G$ and the electron dwell time in the dots are calculated by a time-dependent mode-matching method. Under high-frequency modulation, the traversing electrons are found to exhibit three types of resonant scatterings. They are intersideband scatterings: into quasibound states in the dots, into true bound states in the dots, and into quasibound states just beneath the subband threshold in the leads. Dip structures or fano structures in $G$ are their signatures. Our results show structures due to 2$\hbar\omega$ intersideband processes. At the above scattering resonances, we have estimated, according to our dwell time calculation, the number of round-trip scatterings that the traversing electrons undertake between the two dot openings.Comment: 8 pages, 5 figure

Distributions of the Conductance and its Parametric Derivatives in Quantum Dots

Full distributions of conductance through quantum dots with single-mode leads are reported for both broken and unbroken time-reversal symmetry. Distributions are nongaussian and agree well with random matrix theory calculations that account for a finite dephasing time, $\tau_\phi$, once broadening due to finite temperature $T$ is also included. Full distributions of the derivatives of conductance with respect to gate voltage $P(dg/dV_g)$ are also investigated.Comment: 4 pages (REVTeX), 4 eps figure

Signatures of Chaos in the Statistical Distribution of Conductance Peaks in Quantum Dots

Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained using random matrix theory and are valid in general for any number of non-equivalent and correlated channels, assuming that the underlying classical dynamic of the electrons in the dot is chaotic or that the dot is weakly disordered. The results are expressed in terms of the channel correlation matrix which for chaotic systems is given in closed form for both point-like contacts and extended leads. We study the dependence of the distributions on the number of channels and their correlations. The theoretical distributions are in good agreement with those computed in a dynamical model of a chaotic billiard.Comment: 19 pages, RevTex, 11 Postscript figure