arXiv subjects

Victor A. Gopar

Publications and source records attributed to Victor A. Gopar.

At least 19 recordsLinked to original sources

arXiv2024

Four-terminal voltage fluctuations in disordered graphene nanoribbons: Anderson and anomalous localization effects

Voltage is a sensitive quantity to quantum interference in coherent electronic transport. We study the voltage fluctuations in disordered graphene nanoribbons with zigzag and armchair edge terminations in a four-terminal configuration. We show that the average and standard deviation of the voltage oscillates with the separation of the attached voltage probes and depend on the coupling strength of the probes. The voltage fluctuations can be large enough to observe negative voltages for weakly coupled probes. As we numerically verified, the voltage fluctuations are described within a random matrix approach for weakly disordered nanoribbons at energies away from the Fermi energy. However, near the Fermi energy, zigzag nanoribbons exhibit Anderson localization, whereas electrons are anomalously localized in armchair nanoribbons. This distinction leads to different voltage statistics for zigzag and armchair nanoribbons.

cond-mat.mes-hall↗

arXiv2024

Universal and nonuniversal statistics of transmission in thin random layered media

The statistics of transmission through random 1D media are generally presumed to be universal and to depend only upon a single dimensionless parameter-the ratio of the sample length and the mean free path, s = L/l. Here, we show in numerical simulations and optical measurements of random binary systems, and most prominently in systems for which s is less than unity, that the statistics of the logarithm of transmission, ln T, are universal for transmission near the upper cutoff of unity and depend distinctively upon the reflectivity of the layer interfaces and their number near a lower cutoff. The universal segment of the probability distribution function of the logarithm of transmission P (ln T) is manifested with as few as three binary layers. For a given value of s, P (ln T ) evolves towards a universal distribution as the number of layers increases. Optical measurements in stacks of 5 and 20 glass coverslips exhibit statistics at low and moderate values of transmission that are close to those found in simulations for 1D layered media, while differences appear at higher transmission where the transmission time in the medium is longer and the wave explores the transverse nonuniformity of the sample.

cond-mat.dis-nn↗

arXiv2022

Time delay in 1D disordered media with high transmission

We study the time delay of reflected and transmitted waves in 1D disordered media with high transmission. Highly transparent and translucent random media are found in nature or can be synthetically produced. We perform numerical simulations of microwaves propagating in disordered waveguides to show that reflection amplitudes are described by complex Gaussian random variables with the remarkable consequence that the time-delay statistics in reflection of 1D disordered media are described as in random media in the diffusive regime. For transmitted waves, we show numerically that the time delay is an additive quantity and its fluctuations thus follow a Gaussian distribution. Ultimately, the distributions of the time delay in reflection and transmission are physical illustrations of the central limit theorem at work.

cond-mat.dis-nn↗

arXiv2021

Characterizing random 1D media with an embedded reflector via scattered waves

We show in random matrix theory, microwave measurements, and computer simulations that the mean free path of a random medium and the strength and position of an embedded reflector can be determined from radiation scattered by the system. The mean free path and strength of the reflector are determined from the statistics of transmission. The statistics of transmission are independent of the position of the reflector. The reflector's position can be found, however, from the average dwell time for waves incident from one side of the sample.

cond-mat.dis-nn↗

arXiv2021

Statistics of coherent waves inside media with Lévy disorder

Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the study of wave propagation or lasing in such systems requires the consideration of coherent scattering. We consider the distribution of wave energy inside 1D random media in which the spacing between scatterers follow a Lévy $α$-stable distribution characterized by a power-law decay with exponent $α$. We show that the averages of the intensity and logarithmic intensity are given in terms of the average of the logarithm of transmission and the depth into the sample raised to the power $α$. Mapping the depth into the sample to the number of scattering elements yields intensity statistics that are identical to those found for Anderson localization in standard random media. This allows for the separation for the impacts of disorder distribution and wave coherence in random media.

cond-mat.dis-nn↗

arXiv2020

Transition between anomalous and Anderson localization in systems with non-diagonal disorder driven by time-periodic fields

In models of hopping disorder in the absence of external fields and at the band center, the electrons are less localized in space than the standard exponential Anderson localization. A signature of this anomalous localization is the square root dependence of the logarithmic average of the conductance on the system length, in contrast to the linear length dependence for Anderson localized systems. We study the effect of a time-periodic external field in the scaling and distribution of the conductance of a quantum wire with hopping disorder. In the low-frequency regime, we show a transition between anomalous localization and Anderson localization as a function of the parameters of the external field. The Floquet modes mix different energy contributions and standard length dependence of the logarithmic average of the conductance is gradually recovered as we lower the frequency or increase the amplitude of the external field. In the high-frequency regime, the system presents still anomalous localization but the conductance is also renormalized, depending on the parameters of the external field, by interference effects at the coupling to the leads. This allows for a high degree of control of the average of the conductance.

cond-mat.dis-nn↗

arXiv2019

Invariance principle for wave propagation inside inhomogeneously disordered materials

Disorder is more the rule than the exception in natural and synthetic materials. Nonetheless, wave propagation within inhomogeneously disordered materials has received scant attention. We combine microwave experiments and theory to find the spatial variation of generic wave propagation quantities in inhomogeneously disordered materials. We demonstrate that wave statistics within samples of any dimension are independent of the detailed structure of a material and depend only on the net strengths of distributed scattering and reflection between the observation point and each of the boundaries.

cond-mat.mes-hall↗

arXiv2018

Conductance fluctuations in disordered 2D topological insulator wires: From quantum spin-Hall to ordinary quantum phases

Impurities and defects are ubiquitous in topological insulators (TIs) and thus understanding the effects of disorder on electronic transport is important. We calculate the distribution of the random conductance fluctuations $P(G)$ of disordered 2D TI wires modeled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian with realistic parameters. As we show, the disorder drives the TIs into different regimes: metal (M), quantum spin-Hall insulator (QSHI), and ordinary insulator (OI). By varying the disorder strength and Fermi energy, we calculate analytically and numerically $P(G)$ across the entire phase diagram. The conductance fluctuations follow the statistics of the unitary universality class $β=2$. At strong disorder and high energy, however, the size of the fluctutations $δG$ reaches the universal value of the orthogonal symmetry class ($β=1$). At the QSHI-M and QSHI-OI crossovers, the interplay between edge and bulk states plays a key role in the statistical properties of the conductance.

cond-mat.mes-hall↗

arXiv2015

Shot noise fluctuations in disordered graphene nanoribbons near the Dirac point

Random fluctuations of the shot-noise power in disordered graphene nanoribbons are studied. In particular, we calculate the distribution of the shot noise of nanoribbons with zigzag and armchair edge terminations. We show that the shot noise statistics is different for each type of these two graphene structures, which is a consequence of presence of different electron localizations: while in zigzag nanoribbons electronic edge states are Anderson localized, in armchair nanoribbons edge states are absent, but electrons are anomalously localized. Our analytical results are verified by tight binding numerical simulations with random hopping elements, i.e., off diagonal disorder, which preserves the symmetry of the graphene sublattices.

cond-mat.mes-hall↗

arXiv2013

Conductance through disordered graphene nanoribbons: Standard and anomalous electron localization

Conductance fluctuations produced by the presence of disorder in zigzag and armchair graphene nanoribbons are studied. We show that quantum transport in zigzag nanoribbons takes place via edge states which are exponentially localized, as in the standard Anderson localization problem, whereas for armchair nanoribbons the symmetry of the graphene sublattices produces anomalous localization, or delocalization. We show that these two different electron localizations lead to significant differences of the conductance statistics between zigzag and armchair nanoribbons. In particular, armchair nanoribbons show nonconventional large conductance fluctuations relative to those of Anderson-localized electrons. We calculate analytically the complete distribution of conductances for both types of ribbons. Without free fitting parameters, we verify our theoretical results by performing numerical simulations of disordered zigzag and armchair nanoribbons of experimentally achievable lengths and widths.

cond-mat.mes-hall↗

arXiv2012

Conductance of 1D quantum wires with anomalous electron-wavefunction localization

We study the statistics of the conductance $g$ through one-dimensional disordered systems where electron wavefunctions decay spatially as $|ψ| \sim \exp (-λr^α)$ for $0 <α<1$, $λ$ being a constant. In contrast to the conventional Anderson localization where $|ψ| \sim \exp (-λr)$ and the conductance statistics is determined by a single parameter: the mean free path, here we show that when the wave function is anomalously localized ($α<1$) the full statistics of the conductance is determined by the average $<\ln g>$ and the power $α$. Our theoretical predictions are verified numerically by using a random hopping tight-binding model at zero energy, where due to the presence of chiral symmetry in the lattice there exists anomalous localization; this case corresponds to the particular value $α=1/2$. To test our theory for other values of $α$, we introduce a statistical model for the random hopping in the tight binding Hamiltonian.

cond-mat.mes-hall↗

arXiv2012

Photonic heterostructures with Levy-type disorder: statistics of coherent transmission

We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --Lévy-type distribution. Based on recent predictions made for 1D coherent transport with Lévy-type disorder, we show numerically that for a system of length $L$ (i) the average $<-\ln T> \propto L^α$ for $0<α<1$, while $<-\ln T> \propto L$ for $1\leα<2$, $α$ being the exponent of the power-law decay of the layer-thickness probability distribution; and (ii) the transmission distribution $P(T)$ is independent of the angle of incidence and frequency of the electromagnetic wave, but it is fully determined by the values of $α$ and $<\ln T>$.

physics.optics↗

arXiv2011

Conductance through quantum wires with Levy-type disorder: universal statistics in anomalous quantum transport

In this letter we study the conductance G through one-dimensional quantum wires with disorder configurations characterized by long-tailed distributions (Levy-type disorder). We calculate analytically the conductance distribution which reveals a universal statistics: the distribution of conductances is fully determined by the exponent αof the power-law decay of the disorder distribution and the average < ln G >, i.e., all other details of the disorder configurations are irrelevant. For 0< α< 1 we found that the fluctuations of ln G are not self-averaging and < ln G > scales with the length of the system as L^α, in contrast to the predictions of the standard scaling-theory of localization where ln G is a self-averaging quantity and < ln G > scales linearly with L. Our theoretical results are verified by comparing with numerical simulations of one-dimensional disordered wires.

cond-mat.mes-hall↗

arXiv2010

Scattering and transport statistics at criticality

We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth transition from localized to delocalized behavior in the average scattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying $b$ (the effective bandwidth of the PBRM model) from small ($b\ll 1$) to large ($b>1$) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit $b\to \infty$. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with $b \in [0.2,0.4]$ reproduces well the scattering and transport properties of the 3D Anderson model.

cond-mat.dis-nn↗

arXiv2010

Controlling conductance statistics of quantum wires by driving ac fields

We calculate the entire distribution of the conductance P(G) of a one-dimensional disordered system --quantum wire-- subject to a time-dependent field. Our calculations are based on Floquet theory and a scaling approach to localization. Effects of the applied ac field on the conductance statistics can be strong and in some cases dramatic, as in the high-frequency regime where the conductance distribution shows a sharp cut-off. In this frequency regime, the conductance is written as a product of a frequency-dependent term and a field independent term, the latter containing the information on the disorder in the wire. We thus use the solution of the Mel'nikov equation for time-independent transport to calculate P(G) at any degree of disorder. At lower frequencies, it is found that the conductance distribution and the correlations of the transmission Floquet modes are described by a solution of the Dorokhov-Mello-Pereyra-Kumar equation with an effective number of channels. In the regime of strong localization, induced by the disorder or the ac field, P(G) is a log-normal distribution. Our theoretical results are verified numerically using a single-band Anderson Hamiltonian.

cond-mat.mes-hall↗

arXiv2009

Quantum Scattering and Transport in Classically Chaotic Cavities: An Overview of Past and New Results

We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from atomic nuclei to mesoscopic systems and microwave cavities; the main application to be discussed in this contribution is to electronic transport through mesoscopic ballistic structures or quantum dots. The theory describes the regime in which there are two distinct time scales, associated with a prompt and an equilibrated response, and is cast in terms of the matrix of scattering amplitudes S. We construct the ensemble of S matrices using a maximum-entropy approach which incorporates the requirements of flux conservation, causality and ergodicity, and the system-specific average of S which quantifies the effect of prompt processes. The resulting ensemble, known as Poisson's kernel, is meant to describe those situations in which any other information is irrelevant. The results of this formulation have been compared with the numerical solution of the Schroedinger equation for cavities in which the assumptions of the theory hold. The model has a remarkable predictive power: it describes statistical properties of the quantum conductance of quantum dots, like its average, its fluctuations, and its full distribution in several cases. We also discuss situations that have been found recently, in which the notion of stationarity and ergodicity is not fulfilled, and yet Poisson's kernel gives a good description of the data. At the present moment we are unable to give an explanation of this fact.

cond-mat.mes-hall↗

arXiv2009

Effects of Andreev reflection on the conductance of quantum-chaotic dots

We investigate the conductance statistics of a quantum-chaotic dot--a normal-metal grain--with a superconducting lead attached to it. The cases of one and two normal leads additionally attached to the dot are studied. For these two configurations the complete distribution of the conductance is calculated, within the framework of random matrix theory, as a function of the transparency parameter of the Schottky barrier formed at the interface of the normal-metal and superconducting regions. Our predictions are verified by numerical simulations.

cond-mat.mes-hall↗

arXiv2008

Statistical analysis of the transmission based on the DMPK equation: An application to Pb nano-contacts

The density of the transmission eigenvalues of Pb nano-contacts has been estimated recently in mechanically controllable break-junction experiments. Motivated by these experimental analyses, here we study the evolution of the density of the transmission eigenvalues with the disorder strength and the number of channels supported by the ballistic constriction of a quantum point contact in the framework of the Dorokhov-Mello-Pereyra-Kumar equation. We find that the transmission density evolves rapidly into the density in the diffusive metallic regime as the number of channels $N_c$ of the constriction increase. Therefore, the transmission density distribution for a few $N_c$ channels comes close to the known bimodal density distribution in the metallic limit. This is in agreement with the experimental statistical-studies in Pb nano-contacts. For the two analyzed cases, we show that the experimental densities are seen to be well described by the corresponding theoretical results.

cond-mat.mes-hall↗