arXiv subjects

Richard Berkovits

Publications and source records attributed to Richard Berkovits.

66 records · Page 4Linked to original sources

arXiv1999

Statistics of Coulomb Blockade Peak Spacings within the Hartree-Fock Approximation

We study the effect of electronic interactions on the addition spectra and on the energy level distributions of two-dimensional quantum dots with weak disorder using the self-consistent Hartree-Fock approximation for spinless electrons. We show that the distribution of the conductance peak spacings is Gaussian with large fluctuations that exceed, in agreement with experiments, the mean level spacing of the non-interacting system. We analyze this distribution on the basis of Koopmans' theorem. We show furthermore that the occupied and unoccupied Hartree-Fock levels exhibit Wigner-Dyson statistics.

cond-mat.mes-hall↗

arXiv1999

Delocalization of tightly bound excitons in disordered systems

The localization length of a low energy tightly bound electron-hole pair (excitons) is calculated by exact diagonalization for small interacting disordered systems. The exciton localization length (which corresponds to the thermal electronic conductance) is strongly enhanced by electron-electron interactions, while the localization length (pertaining to the charge conductance) is only slightly enhanced. This shows that the two particle delocalization mechanism widely discussed for the electron pair case is more efficient close to the Fermi energy for an electron-hole pair. The relevance to experiment is also discussed.

cond-mat.mes-hall↗

arXiv1999

The addition spectrum of interacting electrons: Parametric dependence

The addition spectrum of a disordered stadium is studied for up to 120 electrons using the self consistent Hartree-Fock approximation for different values of the dimensionless conductance and in the presence and absence of a neutralizing background. In all cases a Gaussian distribution of the addition spectrum is reached for $r_s \leq 1$. An empirical scaling for the distribution width in the presence of a neutralizing background is tested and seems to describe rather well its dependence on the dimensionless conductance.

cond-mat.mes-hall↗

arXiv1999

Fluctuation of Conductance Peak Spacings in Large Semiconductor Quantum Dots

Fluctuation of Coulomb blockade peak spacings in large two-dimensional semiconductor quantum dots are studied within a model based on the electrostatics of several electron islands among which there are random inductive and capacitive couplings. Each island can accommodate electrons on quantum orbitals whose energies depend also on an external magnetic field. In contrast with a single island quantum dot, where the spacing distribution is close to Gaussian, here the distribution has a peak at small spacing value. The fluctuations are mainly due to charging effects. The model can explain the occasional occurrence of couples or even triples of closely spaced Coulomb blockade peaks, as well as the qualitative behavior of peak positions with the applied magnetic field.

cond-mat.mes-hall↗

arXiv1998

Fluctuations of addition spectra of independent quantum systems

Motivated by recent experiments on large quantum dots, we consider the energy spectrum in a system consisting of $N$ particles distributed among $K<N$ independent sub-systems, such that the energy of each sub-system is a quadratic function of the number of particles residing on it. On a large scale, the ground state energy E(N) of such a system grows quadratically with $N$, but in general there is no simple relation such as $E(N)=a N +b N^{2}$. The deviation of E(N) from exact quadratic behavior implies that its second difference (the inverse compressibility) $χ_{N} \equiv E(N+1)-2 E(N)+E(N-1)$ is a fluctuating quantity. Regarding the numbers $χ_{N}$ as values assumed by a certain random variable $χ$, we obtain a closed-form expression for its distribution $F(χ)$. Its main feature is that the corresponding density $P(χ)=\frac{dF(χ)} {dχ}$ has a maximum at the point $χ=0$. As $K \to \infty$ the density is Poissonian, namely, $P(χ) \to e^{-χ}$.

cond-mat↗

arXiv1998

Absence of bimodal peak spacing distribution in the Coulomb blockade regime

Using exact diagonalization numerical methods, as well as analytical arguments, we show that for the typical electron densities in chaotic and disordered dots the peak spacing distribution is not bimodal, but rather Gaussian. This is in agreement with the experimental observations. We attribute this behavior to the tendency of an even number of electrons to gain on-site interaction energy by removing the spin degeneracy. Thus, the dot is predicted to show a non trivial electron number dependent spin polarization. Experimental test of this hypothesis based on the spin polarization measurements are proposed.

cond-mat.mes-hall↗

arXiv1998

Plastic flow of persistent currents in two dimensional strongly interacting systems

The local persistent current in two dimensional strongly interacting systems is investigated. As the interaction strength is enhanced the current in the sample undergoes a transition from diffusive to ordered flow. The strong interacting flow has the characteristics of a plastic flow through dislocations in the pinned charge density wave which develops in the system at low densities.

cond-mat.mes-hall↗

arXiv1998

Spin and interaction effects on charge distribution and currents in one-dimensional conductors and rings within the Hartree-Fock approximation

Using the self--consistent Hartree-Fock approximation for electrons with spin at zero temperature, we study the effect of the electronic interactions on the charge distribution in a one-dimensional continuous ring containing a single $δ$ scatterer. We reestablish that the interaction suppresses the decay of the Friedel oscillations. Based on this result, we show that in an infinite one dimensional conductor containing a weak scatterer, the current is totally suppressed because of a gap opened at the Fermi energy. In a canonical ensemble of continuous rings containing many scatterers, the interactions enhance the average and the typical persistent current.

cond-mat.mes-hall↗

arXiv1996

The effect of electron-electron interactions on the average polarizability of a mesoscopic system

A comparison between an analytical calculation of the polarizability of a mesoscopic interacting system in the random phase approximation and numerical exact diagonalization results is presented. While for weak interactions the analytical calculation fits the numerical results rather well, deviations appear for stronger interactions. This is the result of the appearance of intermediate range correlations in the electron density, which suppresses the polarizability below its classical value. The relevance to quantum dot systems is discussed.

cond-mat↗

arXiv1996

Spectral statistics near the quantum percolation threshold

The statistical properties of spectra of a three-dimensional quantum bond percolation system is studied in the vicinity of the metal insulator transition. In order to avoid the influence of small clusters, only regions of the spectra in which the density of states is rather smooth are analyzed. Using finite size scaling hypothesis, the critical quantum probability for bond occupation is found to be $p_q=0.33\pm.01$ while the critical exponent for the divergence of the localization length is estimated as $ν=1.35\pm.10$. This later figure is consistent with the one found within the universality class of the standard Anderson model.

cond-mat↗

arXiv1995

Interacting electrons in disordered potentials: Conductance versus persistent currents

An expression for the conductance of interacting electrons in the diffusive regime as a function of the ensemble averaged persistent current and the compressibility of the system is presented. This expression involves only ground-state properties of the system. The different dependencies of the conductance and persistent current on the electron-electron interaction strength becomes apparent. The conductance and persistent current of a small system of interacting electrons are calculated numerically and their variation with the strength of the interaction is compared. It is found that while the persistent current is enhanced by interactions, the conductance is suppressed.

cond-mat↗

arXiv1995

Spectral Statistics in the Lowest Landau Band

We study the spectral statistics in the center of the lowest Landau band of a 2D disordered system with smooth potential and strong transverse magnetic field. Due to the finite size of the system, the energy range in which there are extended states is finite as well. The behavior in this range can be viewed as the analogue of the Anderson metal-insulator transition for the case of the Hall system. Accordingly, we verify recent predictions regarding the exponent of the asymptotic power law of $Σ^2 (\bar N)$, $γ$, and that of the stretched exponential dominating the large $s$ behavior of the spacings distribution, $α$. Both the relations, $α= 1- γ$, and $γ= 1 - {1\over{νd}}$ where $ν$ is the critical exponent of the localization length and $d$ is the dimension, are found to hold within the accuracy of our computations. However, we find that none of several possible models of the entire spacings distribution correctly describes our situation. Finally, for very large $\bar N$, $\bar N > 60$, we find a new regime in which $Σ^2 (\bar N)$ behaves as a power law with an unexpectedly large power, $γ_1 = 1.38 \pm 0.02$.

cond-mat↗