arXiv subjects

Richard Berkovits

Publications and source records attributed to Richard Berkovits.

At least 55 records · Page 3Linked to original sources

arXiv2007

Disorder effect on the Friedel oscillations in a one-dimensional Mott insulator

The Friedel oscillations resulting from coupling a quantum dot to one edge of a disordered one-dimensional wire in the Mott insulator regime, are calculated numerically using the DMRG method. By investigating the influence of the disorder on the Friedel oscillations decay we find that the effect of disorder is reduced by increasing the interaction strength. This behavior is opposite to the recently reported influence of disorder in the Anderson insulator regime, where disorder led to a stronger decay of the Friedel oscillations.

cond-mat.mes-hall↗

arXiv2006

Interference effects in interacting quantum dots

In this paper we study the interplay between interference effects in quantum dots (manifested through the appearance of Fano resonances in the conductance), and interactions taken into account in the self-consistent Hartree-Fock approximation. In the non-interacting case we find that interference may lead to the observation of more than one conductance peak per dot level as a function of an applied gate voltage. This may explain recent experimental findings, which were thought to be caused by interaction effects. For the interacting case we find a wide variety of different interesting phenomena. These include both monotonous and non-monotonous filling of the dot levels as a function of an applied gate voltage, which may occur continuously or even discontinuously. In many cases a combination of the different effects can occur in the same sample. The behavior of the population influences, in turn, the conductance lineshape, causing broadening and asymmetry of narrow peaks, and determining whether there will be a zero transmission point. We elucidate the essential role of the interference between the dot levels in determining these outcomes. The effects of finite temperatures on the results are also examined.

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arXiv2006

Anti-Kondo regime of charge transport through a double dot molecule

The conductance through a serial double dot structure for which the inter-dot tunneling is stronger than the tunneling to the leads is studied using the numerical density matrix renormalization group method and analytic arguments. When the dots are occupied by 1 or 3 electrons the usual Kondo peak is obtained. For the case in which 2 electrons occupy the molecule a singlet is formed. Nevertheless, the conductance in that case has a constant non-zero value, and might even be equal to the maximum conductance of $2 e^2/h$ for certain values of the molecule parameters. We show that this is the result of the subtle interplay between the symmetric and anti-symmetric orbitals of the molecule caused by interactions and interference.

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arXiv2005

Resistance distribution in the hopping percolation model

We study the distribution function, P(rho), of the effective resistance, rho, in two and three-dimensional random resistor network of linear size L in the hopping percolation model. In this model each bond has a conductivity taken from an exponential form σ~ exp(-kappa r), where kappa is a measure of disorder, and r is a random number, 0< r < 1. We find that in both the usual strong disorder regime L/kappa^{nu} > 1 (not sensitive to removal of any single bond) and the extreme disorder regime L/kappa^{nu} < 1 (very sensitive to such a removal) the distribution depends only on L/kappa^{nu} and can be well approximated by a log-normal function with dispersion b kappa^nu/L, where b is a coefficient which depends on the type of the lattice

cond-mat.dis-nn↗

arXiv2004

Theory of charge sensing in quantum-dot structures

Charge sensing in quantum-dot structures is studied by an exactly solvable reduced model and numerical density-matrix renormalization group methods. Charge sensing is characterized by the repeated cycling of the occupation of current-carrying states due to the capacitive coupling to trap states which are weakly coupled to the leads. In agreement with recent experiments, it results in a variety of characteristic behaviors ranging from asymmetric Coulomb-blockade peaks to sawtooth- and dome-like structures. Temperature introduces distinct asymmetric smearing of these features and correlations in the conductance provide a fingerprint of charge-sensing behavior.

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arXiv2004

Discrete charging of a quantum dot strongly coupled to external leads

We examine a quantum dot with $N_{\rm dot}$ levels which is strongly coupled to leads for varying number of channels $N$ in the leads. It is shown both analytically and numerically that for strong couplings between the dot and the leads, at least $N_{\rm dot}-N$ bound states (akin to subradiant states in optics) remain on the dot. These bound states exhibit discrete charging and, for a significant range of charging energies, strong Coulomb blockade behavior as function of the chemical potential. The physics changes for large charging energy where the same (superradiant) state is repeatedly charged.

cond-mat.mes-hall↗

arXiv2004

Spin polarization and effective mass: a numerical study in disordered two dimensional systems

We numerically study the magnetization of small metallic clusters. The magnetic susceptibility is enhanced for lower electronic densities due to the stronger influence of electron-electron interactions. The magnetic susceptibility enhancement stems mainly from an enhancement of the mass for commensurate fillings, while for non-commensurate fillings its a result of an enhancement of the Landé $g$ factor. The relevance to recent experimental measurements is discussed.

cond-mat.mes-hall↗

arXiv2003

Orbital Magnetic Susceptibility of Disordered Mesoscopic Systems

In this paper we study the orbital weak-field susceptibility of two-dimensional diffusive mesoscopic systems. For the previously unstudied regime of temperatures lower than the mean level spacing we find unexpected strong temperature as well as statistical ensemble dependence of the average and typical susceptibilities. An explanation for these features is given in terms of the long tail of the zero-temperature susceptibility distribution, including the parametric form of the temperature dependence. For temperatures higher than the mean level spacing we calculate the difference between the true canonical ensemble and the effective grand-canonical ensemble. We also perform numerical simulations, which seem to generally confirm previous theoretical predictions for this regime of temperatures, although some difficulties arise. The important role of gauge-invariance, especially how it renders Random Matrix Theory inapplicable to the study of orbital susceptibility, is discussed. We conclude by considering interaction effects, giving a new interpretation to previous results as well as demonstrating the influence of in-plane magnetic field on the interaction-induced orbital response.

cond-mat.mes-hall↗

arXiv2003

On-Site Interaction Effects on Localization : Dominance of Non-Universal Contributions

The influence of on-site (Hubbard) electron-electron interaction on disorder-induced localization is studied in order to clarify the role of electronic spin. The motivation is based on the recent experimental indications of a "metal-insulator" transition in two dimensional systems. We use both analytical and numerical techniques, addressing the limit of weak short-range interaction. The analytical calculation is based on Random Matrix Theory (RMT). It is found that although RMT gives a qualitative explanation of the numerical results, it is quantitatively incorrect. This is due to an exact cancellation of short range and long range correlations in RMT, which does not occur in the non-universal corrections to RMT. An estimate for these contributions is given.

cond-mat.mes-hall↗

arXiv2003

Density matrix renormalization group study of the charging of a quantum dot strongly coupled to a single lead

A new application of the density matrix renormalization group (DMRG) method to a system composed of an interacting dot coupled to a infinite one dimensional lead is presented. This method enables one to study the influence of the coupling to an external lead on the thermodynamical properties of the dot. It is shown that this method reproduces known results for a non-interacting dot coupled to a lead, i.e., that for strong coupling discrete states remain in the dot. We show that these states are robust and do not disappear once interactions in the dot are considered. Moreover, due to these discrete states, Coulomb blockade affects the charging of the dot even though its strongly coupled to a lead.

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arXiv2003

Statistical Properties of The First Excited State of an Interacting Many Particle Disordered System

The distribution $P_1$ of the first many-body excitation energy of a weakly and moderately interacting electron gas in a finite conductor (in the diffusive regime) is calculated. As the interaction is increased, $P_1$ crosses over from Wigner-Dyson to Poisson. We characterize this transition through the inverse participation ratio in Hilbert space, and examine its manifestation in a projected 2-dimensional space.

cond-mat.dis-nn↗

arXiv2003

Study of the Localization Transition on a Cayley-tree via Spectral Statistics

The spectral statistics of a Cayley-tree is numerically studied. The statistics are non-universal due to the high ratio of boundary sites. Once the boundary sites are connected to each other in a way that preserves the local structure of the tree the universal statistics of the spectra is recovered. A clear localization transition is observed as function of on-site disorder strength, with a critical disorder $W_c=11.44^{+0.08}_{-0.04}$ and critical index $ν=0.51^{+0.05}_{-0.04}$. The value of $ν$ fits nicely to its mean field value, while the value of $W_c$ is puzzling.

cond-mat.dis-nn↗

arXiv2002

Electron-hole generations: A numerical approach to interacting fermion systems

A new approach, motivated by Fock space localization, for constructing a reduced many-particle Hilbert space is proposed and tested. The self-consistent Hartree-Fock (SCHF) approach is used to obtain a single-electron basis from which the many-particle Hilbert space is constructed. For a given size of the truncated many particle Hilbert space only states with the lowest number of particle-hole excitations are retained and exactly diagonalized. This method is shown to be more accurate than previous truncation methods, while there is no additional computational complexity.

cond-mat.mes-hall↗

arXiv2001

The Parallel Magnetoconductance of Interacting Electrons in a Two Dimensional Disordered System

The transport properties of interacting electrons for which the spin degree of freedom is taken into account are numerically studied for small two dimensional diffusive clusters. On-site electron-electron interactions tend to delocalize the electrons, while long-range interactions enhance localization. On careful examination of the transport properties, we reach the conclusion that it does not show a two dimensional metal insulator transition driven by interactions. A parallel magnetic field leads to enhanced resistivity, which saturates once the electrons become fully spin polarized. The strength of the magnetic field for which the resistivity saturates decreases as electron density goes down. Thus, the numerical calculations capture some of the features seen in recent experimental measurements of parallel magnetoconductance.

cond-mat.mes-hall↗

arXiv2001

Anderson Orthogonality Catastrophe in Disordered Systems

We study the Anderson orthogonality catastrophe (AOC) in finite conductors with diffusive disorder. The disorder averaged logarithm of $χ$, the overlap between the ground states before and after adding a static impurity, is found to depend nonmonotonically on the disorder. In two dimensions $<\lnχ^{-1}> \propto \ln^2 N$ in the weak disorder limit, thus showing a stronger dependence on the number of electrons $N$ than in the canonical AOC. A very broad tail of the distribution of $χ$, found numerically, is a signature of the importance of a few-level statistics at the Fermi energy.

cond-mat.mes-hall↗

arXiv2000

No indications of metal-insulator transition for systems of interacting electrons in two dimensions

The influence of Coulomb interaction on transport properties of spinless electrons in small disordered two dimensional systems is studied within a tight binding model. Spatial correlations, inverse participation ratio, and multifractal spectrum of the zero temperature local tunneling amplitude as well as the DC Kubo conductance are traced as function of the interaction strength $U$. When $U$ is increased, all of the above quantities are shifted rather smoothly towards localized behavior, indicating the absence of an interaction driven insulator-metal transition.

cond-mat.mes-hall↗

arXiv2000

Conductance peak motion due to a magnetic field in weakly coupled chaotic quantum dots

We study the influence of moderate exchange interactions of electrons on the behavior of the peaks in the conductance of single electron transistors. We numerically reproduce recently observed features of both the peak positions and the peak heights magnetic field dependence. These features unambiguously identify the total spin $S$ of each ground state. We evaluate the probability of each $S$ (combination of spontaneous and induced magnetization) as a function of the exchange strength, $J$, and external magnetic field, $B$. The expressions involve only $J$ and $g$-factor as adjustable parameters. Moreover, in a surprisingly broad parameter range these probabilities are determined by certain linear combinations of $J$ and $B$.

cond-mat.mes-hall↗

arXiv2000

Fluctuation of inverse compressibility for electronic systems with random capacitive matrices

This article is concerned with statistics of addition spectra for systems of identical charged particles. A classical model is suggested in order to study fluctuations of Coulomb blockade peak spacings in large two-dimensional semiconductor quantum dots. It is 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 energy depend also on an external magnetic field. | In contrast with a single island quantum dot where the spacing distribution between conductance peaks 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.

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