arXiv subjects

R. Berkovits

Publications and source records attributed to R. Berkovits.

At least 19 recordsLinked to original sources

arXiv2018

Entanglement entropy distribution in the strongly disordered one-dimensional Anderson model

The entanglement entropy distribution of strongly disordered one dimensional spin chains, which are equivalent to spinless fermions at half-filling on a bond (hopping) disordered one-dimensional Anderson model, has been shown to exhibit very distinct features such as peaks at integer multiplications of $\ln(2)$, essentially counting the number of singlets traversing the boundary. Here we show that for a canonical Anderson model with box distribution on-site disorder and repulsive nearest-neighbor interactions the entanglement entropy distribution also exhibits interesting features, albeit different than the distribution seen for the bond disordered Anderson model. The canonical Anderson model shows a broad peak at low entanglement values and one narrower peak at $\ln(2)$. Density matrix renormalization group (DMRG) calculations reveal this structure and the influence of the disorder strength and the interaction strength on its shape. A modified real space renormalization group (RSRG) method was used to get a better understanding of this behavior. As might be expected the peak centered at low values of entanglement entropy has a tendency to shift to lower values as disorder is enhanced. A second peak appears around the entanglement entropy value of $\ln(2)$,this peak is broadened and no additional peaks at higher integer multiplications of $\ln(2)$ are seen. We attribute the differences in the distribution between the canonical model and the broad hopping disorder to the influence of the on-site disorder which breaks the symmetry across the boundary.

cond-mat.mes-hall↗

arXiv2016

Transmission Resonances Anomaly in 1D Disordered Quantum Systems

Connections between the electron eigenstates and conductivity of one-dimensional disordered electron systems is studied in the framework of the tight-binding model. We show that for weak disorder only part of the states exhibit resonant transmission and contribute to the conductivity. The rest of the eigenvalues are not associated with peaks in transmission and the amplitudes of their wave functions do not exhibit a significant maxima within the sample. Moreover, unlike ordinary states, the lifetimes of these `hidden' modes either remain constant or even decrease (depending on the coupling with the leads) as the disorder becomes stronger. In a wide range of the disorder strengths, the averaged ratio of the number of transmission peaks to the total number of the eigenstates is independent of the degree of disorder and is close to the value $\sqrt{2/5}$, which was derived analytically in the weak-scattering approximation. These results are in perfect analogy to the spectral and transport properties of light in one-dimensional randomly inhomogeneous media, which provides strong grounds to believe that the existence of hidden, non-conducting modes is a general phenomenon inherent to 1D open random systems, and their fraction of the total density of states is the same for quantum particles and classical waves.

cond-mat.mes-hall↗

arXiv2015

Fractional Coulomb blockade in a coupling controlled metallic quantum dot

We use a novel technique to experimentally explore transport properties through a single metallic nanoparticle with variable coupling to electric leads. For strong dot-lead coupling the conductance is an oscillatory function of the gate voltage with periodicity determined by the charging energy, as expected. For weaker coupling we observe the appearance of additional multi-periodic oscillations of the conductance with the gate voltage. These harmonics correspond to a change of the charge on the dot by a fraction of an electron. This notion is supported by theoretical calculations based on dissipative action theory. Within this framework the multiple periodicity of the conductance oscillations arises due to non-pertubative instanton solutions.

cond-mat.mes-hall↗

arXiv2015

Persistent current in an almost staggered Harper model

In this paper we study the persistent current (PC) of a staggered Harper model, close to the half-filling. The Harper model, which is a quasi-periodic system, is different than other one dimensional systems with uncorrelated disorder in the fact that it can be in the metallic regime. Nevertheless, the PC for a wide range of parameters of the Harper model does not show typical metallic behavior, although the system is in the metallic regime. This is a result of the nature of the central band states, which are a hybridization of Gaussian states localized in superlattice points. When the superlattice is not commensurate with the system length, the PC behaves as in an insulator. Thus even in the metallic regime a typical finite Harper model may exhibit a PC expected from an insulator.

cond-mat.mes-hall↗

arXiv2009

Two gate-voltage periods in a metallic-nanoparticle based single-electron transistor

Systems of quantum dots (QD) connected to leads exhibit periodic conductance peaks as a function of gate voltage arising from the Coulomb blockade effect \cite{review1,review2,review3}. Much effort goes into minimizing the size of QDs and reaching the scale of single molecules \cite{molecular1,molecular2,molecular3} which could serve as nanoelectronic circuit components such as transistors. Connecting molecules or nanoparticles to external leads cannot be achieved by the traditional methods used in semiconductor based QDs, hence, controlling the coupling to nanoparticle QDs is a major technical challenge. Here we present a novel technique by which we can explore electric properties of a metallic nanoparticle while varying the coupling to leads. We find that the conductance through the nanoparticle is characterized by \emph{two} gate voltage periods. The relative strength of the periods depends both on the dot-lead coupling and on the source-drain voltage. These surprising findings may be a general property of strongly coupled metallic nanoparticles.

cond-mat.mes-hall↗

arXiv2007

Driving a first order quantum phase transition by coupling a quantum dot to a 1D charge density wave

The ground state properties of a one-dimensional system with particle-hole symmetry, consisting of a gate controlled dot coupled to an interacting reservoir, are explored using the numerical DMRG method. It was previously shown that the system's thermodynamic properties as a function of the gate voltage in the Luttinger liquid phase are qualitatively similar to the behavior of a non-interacting wire with an effective (renormalized) dot-lead coupling. Here we examine the thermodynamic properties of the wire in the charge density wave phase, and show that these properties behave quite differently. The number of electrons in the system remains constant as a function of the gate voltage, while the total energy becomes linear. Moreover, by tuning the gate voltage on the dot in the charge density wave phase it is possible to drive the wire through a first order quantum phase transition in which the population of each site in the wire is inverted.

cond-mat.str-el↗

arXiv2006

Friedel oscillations in disordered quantum wires: Influence of e-e interactions on the localization length

The Friedel oscillations caused due to an impurity located at one edge of a disordered interacting quantum wire are calculated numerically. The electron density in the system's ground state is determined using the DMRG method, and the Friedel oscillations data is extracted using the density difference between the case in which the wire is coupled to an impurity and the case where the impurity is uncoupled. We show that the power law decay of the oscillations occurring for an interacting clean 1D samples described by Luttinger liquid theory, is multiplied by an exponential decay term due to the disorder. Scaling of the average Friedel oscillations by this exponential term collapses the disordered samples data on the clean results. We show that the length scale governing the exponential decay may be associated with the Anderson localization length and thus be used as a convenient way to determine the dependence of the localization length on disorder and interactions. The localization length decreases as a function of the interaction strength, in accordance with previous predictions.

cond-mat.mes-hall↗

arXiv2005

Localization transition on complex networks via spectral statistics

The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small. The critical index of the transition corresponds to the mean field expectation. When the connectivity is higher, the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity, though a precise transition cannot be identified. The absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks, resulting in a small diameter even for a large number of sites.

cond-mat.mes-hall↗

arXiv2005

The signature of a double quantum-dot structure in the I-V characteristics of a complex system

We demonstrate that by carefully analyzing the temperature dependent characteristics of the I-V measurements for a given complex system it is possible to determine whether it is composed of a single, double or multiple quantum-dot structure. Our approach is based on the orthodox theory for a double-dot case and is capable of simulating I-V characteristics of systems with any resistance and capacitance values and for temperatures corresponding to thermal energies larger than the dot level spacing. We compare I-V characteristics of single-dot and double-dot systems and show that for a given measured I-V curve considering the possibility of a second dot is equivalent to decreasing the fit temperature. Thus, our method allows one to gain information about the structure of an experimental system based on an I-V measurement.

cond-mat.mes-hall↗

arXiv2004

A level coupled to a 1D interacting reservoir : A DMRG study

The influence of interactions in a reservoir coupled to a level on the width of the filling as a function of the chemical potential and the position of the level is studied. The density matrix renormalization group (DMRG) method is used to calculate the ground state of a finite-size interacting reservoir, linked to a single state dot. The influence of the interactions in the lead as well as dot-lead interactions is considered. It is found that interactions in the reservoir result in a decrease in the resonance width, while the dot-lead interaction has an opposite effect. These effects are explained within the random phase approximation as an effective change in the inverse compressibility of the reservoir, while the dot-lead interactions renormalize the position of the level.

cond-mat.mes-hall↗

arXiv2002

Magneto-transport properties of dilute granular ferromagnets

We present magnetoresistance (MR) measurements performed on quench condensed granular Ni thin films which are on the verge of electric continuity. In these systems the electric conductivity is believed to be governed by the resistance between a very small number of grains. The films exihibit sharp resistance jumps as a function of magnetic field. We interpret these findings as being the result of magneto-mechanical distortions that occour in single grains which act as bottlenecks in the dilute percolation network. The observed features provide a unique measure of magnetostriction effects in nano-grain structures as well as being able to shed light on some of the properties of regular granular magnetic films.

cond-mat.mes-hall↗

arXiv2002

The breakdown of the Nagaoka phase in the 2D t-J model

In the limit of weak exchange, J, at low hole concentration, the ground state of the 2D t-J model is believed to be ferromagnetic. We study the leading instability of this Nagaoka state, which emerges with increasing J. Both exact diagonalization of small clusters, and a semiclassical analytical calculation of larger systems show that above a certain critical value of the exchange, Nagaoka's state is unstable to phase separation. In a finite-size system a bubble of antiferromagnetic Mott insulator appears in the ground state above this threshold. The size of this bubble depends on the hole concentration and scales as a power of the system size, N.

cond-mat.str-el↗

arXiv2001

Coherent electron transport in a Si quantum dot dimer

We show that the coherence of charge transfer through a weakly coupled double-dot dimer can be determined by analyzing the statistics of the conductance pattern, and does not require large phase coherence length in the host material. We present an experimental study of the charge transport through a small Si nanostructure, which contains two quantum dots. The transport through the dimer is shown to be coherent. At the same time, one of the dots is strongly coupled to the leads, and the overall transport is dominated by inelastic co-tunneling processes.

cond-mat.mes-hall↗

arXiv2000

Ground state spin and Coulomb blockade peak motion in chaotic quantum dots

We investigate experimentally and theoretically the behavior of Coulomb blockade (CB) peaks in a magnetic field that couples principally to the ground-state spin (rather than the orbital moment) of a chaotic quantum dot. In the first part, we discuss numerically observed features in the magnetic field dependence of CB peak and spacings that unambiguously identify changes in spin S of each ground state for successive numbers of electrons on the dot, N. We next evaluate the probability that the ground state of the dot has a particular spin S, as a function of the exchange strength, J, and external magnetic field, B. In the second part, we describe recent experiments on gate-defined GaAs quantum dots in which Coulomb peak motion and spacing are measured as a function of in-plane magnetic field, allowing changes in spin between N and N+1 electron ground states to be inferred.

cond-mat.mes-hall↗

arXiv1999

Disorder Induced Ferromagnetism in Restricted Geometries

We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite $U$ Hubbard model. We find that for one dimensional systems disorder has no influence, while for two dimensional systems disorder enhances the spin polarization of the system. The tendency of disorder to enhance magnetism in the ground state may be relevant to recent experimental observations of spin polarized ground states in quantum dots and small metallic grains.

cond-mat.mes-hall↗

arXiv1999

Ground State Spin Structure of Strongly Interacting Disordered 1D Hubbard Model

We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite U 1D Hubbard model. We find that the ground state is not ferromagnetic. This is analyzed in terms of the algebraic structure of the spin dependence of the Hamiltonian. A simple explanation is derived for the 1/N periodicity in the persistent current for this model.

cond-mat.mes-hall↗

arXiv1998

Statistics of energy spectra of a strongly disordered system of interacting electrons

Statistics of many particle energy levels of a finite two-dimensional system of interacting electrons is numerically studied. It is shown that the statistics of these levels undergoes a Poisson to Wigner crossover as the strength of the disorder is decreased. This transition occurs at a similar strength of disorder as the one-electron delocalization crossover in a finite 2d system and develops almost simultaneously at all energies. We interpret this crossover in terms of delocalization in the space of occupation numbers of strongly bound and compact electron-hole pairs (excitons).

cond-mat.mes-hall↗

arXiv1998

Transmission through a n interacting quantum dot in the Coulomb blockade regime

The influence of electron-electron (e-e) interactions on the transmission through a quantum dot is investigated numerically for the Coulomb blockade regime. For vanishing magnetic fields, the conductance peak height statistics is found to be independent of the interactions strength. It is identical to the statistics predicted by constant interaction single electron random matrix theory and agrees well with recent experiments. However, in contrast to these random matrix theories, our calculations reproduces the reduced sensitivity to magnetic flux observed in many experiments. The relevant physics is traced to the short range Coulomb correlations providing thus a unified explanation for the transmission statistics as well as for the large conductance peak spacing fluctuations observed in other experiments.

cond-mat.mes-hall↗