Coulomb blockade in one-dimensional arrays of high conductance tunnel junctions

Properties of one-dimensional (1D) arrays of low Ohmic tunnel junctions (i.e. junctions with resistances comparable to, or less than, the quantum resistance $R_{\rm q}\equiv h/e^2\approx 25.8$ k$\Omega$) have been studied experimentally and theoretically. Our experimental data demonstrate that -- in agreement with previous results on single- and double-junction systems -- Coulomb blockade effects survive even in the strong tunneling regime and are still clearly visible for junction resistances as low as 1 k$\Omega$. We have developed a quasiclassical theory of electron transport in junction arrays in the strong tunneling regime. Good agreement between the predictions of this theory and the experimental data has been observed. We also show that, due to both heating effects and a relatively large correction to the linear relation between the half-width of the conductance dip around zero bias voltage, $V_{1/2}$, and the measured electronic temperature, such arrays are inferior to those conventionally used in the Coulomb Blockade Thermometry (CBT). Still, the desired correction to the half-width, $\Delta V_{1/2}$, can be determined rather easily and it is proportional to the magnitude of the conductance dip around zero bias voltage, $\Delta G$. The constant of proportionality is a function of the ratio of the junction and quantum resistances, $R/R_{\rm q}$, and it is a pure strong tunneling effect.Comment: LaTeX file + five postscript figure

Thermoelectricity in Nanowires: A Generic Model

By employing a Boltzmann transport equation and using an energy and size dependent relaxation time ($\tau$) approximation (RTA), we evaluate self-consistently the thermoelectric figure-of-merit $ZT$ of a quantum wire with rectangular cross-section. The inferred $ZT$ shows abrupt enhancement in comparison to its counterparts in bulk systems. Still, the estimated $ZT$ for the representative Bi$_2$Te$_3$ nanowires and its dependence on wire parameters deviate considerably from those predicted by the existing RTA models with a constant $\tau$. In addition, we address contribution of the higher energy subbands to the transport phenomena, the effect of chemical potential tuning on $ZT$, and correlation of $ZT$ with quantum size effects (QSEs). The obtained results are of general validity for a wide class of systems and may prove useful in the ongoing development of the modern thermoelectric applications.Comment: 15 pages, 6 figures; Dedicated to the memory of Amirkhan Qezell

Single-charge escape processes through a hybrid turnstile in a dissipative environment

We have investigated the static, charge-trapping properties of a hybrid superconductor---normal metal electron turnstile embedded into a high-ohmic environment. The device includes a local Cr resistor on one side of the turnstile, and a superconducting trapping island on the other side. The electron hold times, t ~ 2-20s, in our two-junction circuit are comparable with those of typical multi-junction, N >= 4, normal-metal single-electron tunneling devices. A semi-phenomenological model of the environmental activation of tunneling is applied for the analysis of the switching statistics. The experimental results are promising for electrical metrology.Comment: Submitted to New Journal of Physics 201

Effect of quantum noise on Coulomb blockade in normal tunnel junctions at high voltages

We have investigated asymptotic behavior of normal tunnel junctions at voltages where even the best ohmic environments start to look like RC transmission lines. In the experiments, this is manifested by an exceedingly slow approach to the linear behavior above the Coulomb gap. As expected on the basis of the quantum theory taking into account interaction with the environmental modes, better fits are obtained using 1/sqrt{V}- than 1/V- dependence for the asymptote. These results agree with the horizon picture if the frequency-dependent phase velocity is employed instead of the speed of light in order to determine the extent of the surroundings seen by the junction.Comment: 9 pages, 4 figures, submitted to Phys. Rev.

Primary thermometry in the intermediate Coulomb blockade regime

We investigate Coulomb blockade thermometers (CBT) in an intermediate temperature regime, where measurements with enhanced accuracy are possible due to the increased magnitude of the differential conductance dip. Previous theoretical results show that corrections to the half width and to the depth of the measured conductance dip of a sensor are needed, when leaving the regime of weak Coulomb blockade towards lower temperatures. In the present work, we demonstrate experimentally that the temperature range of a CBT sensor can be extended by employing these corrections without compromising the primary nature or the accuracy of the thermometer.Comment: 8 pages, 4 figure

Electron transport through interacting quantum dots

We present a detailed theoretical investigation of the effect of Coulomb interactions on electron transport through quantum dots and double barrier structures connected to a voltage source via an arbitrary linear impedance. Combining real time path integral techniques with the scattering matrix approach we derive the effective action and evaluate the current-voltage characteristics of quantum dots at sufficiently large conductances. Our analysis reveals a reach variety of different regimes which we specify in details for the case of chaotic quantum dots. At sufficiently low energies the interaction correction to the current depends logarithmically on temperature and voltage. We identify two different logarithmic regimes with the crossover between them occurring at energies of order of the inverse dwell time of electrons in the dot. We also analyze the frequency-dependent shot noise in chaotic quantum dots and elucidate its direct relation to interaction effects in mesoscopic electron transport.Comment: 21 pages, 4 figures. References added, discussion slightly extende

Charging Ultrasmall Tunnel Junctions in Electromagnetic Environment

We have investigated the quantum admittance of an ultrasmall tunnel junction with arbitrary tunneling strength under an electromagnetic environment. Using the functional integral approach a close analytical expression of the quantum admittance is derived for a general electromagnetic environment. We then consider a specific controllable environment where a resistance is connected in series with the tunneling junction, for which we derived the dc quantum conductance from the zero frequency limit of the imaginary part of the quantum admittance. For such electromagnetic environment the dc conductance has been investigated in recent experiments, and our numerical results agree quantitatively very well with the measurements. Our complete numerical results for the entire range of junction conductance and electromagnetic environmental conductance confirmed the few existing theoretical conclusions.Comment: 7 pages, 3 ps-figure

Missing Features Reconstruction Using a Wasserstein Generative Adversarial Imputation Network

Missing data is one of the most common preprocessing problems. In this paper, we experimentally research the use of generative and non-generative models for feature reconstruction. Variational Autoencoder with Arbitrary Conditioning (VAEAC) and Generative Adversarial Imputation Network (GAIN) were researched as representatives of generative models, while the denoising autoencoder (DAE) represented non-generative models. Performance of the models is compared to traditional methods k-nearest neighbors (k-NN) and Multiple Imputation by Chained Equations (MICE). Moreover, we introduce WGAIN as the Wasserstein modification of GAIN, which turns out to be the best imputation model when the degree of missingness is less than or equal to 30%. Experiments were performed on real-world and artificial datasets with continuous features where different percentages of features, varying from 10% to 50%, were missing. Evaluation of algorithms was done by measuring the accuracy of the classification model previously trained on the uncorrupted dataset. The results show that GAIN and especially WGAIN are the best imputers regardless of the conditions. In general, they outperform or are comparative to MICE, k-NN, DAE, and VAEAC.Comment: Preprint of the conference paper (ICCS 2020), part of the Lecture Notes in Computer Scienc

Multiple Imputation Ensembles (MIE) for dealing with missing data

Missing data is a significant issue in many real-world datasets, yet there are no robust methods for dealing with it appropriately. In this paper, we propose a robust approach to dealing with missing data in classification problems: Multiple Imputation Ensembles (MIE). Our method integrates two approaches: multiple imputation and ensemble methods and compares two types of ensembles: bagging and stacking. We also propose a robust experimental set-up using 20 benchmark datasets from the UCI machine learning repository. For each dataset, we introduce increasing amounts of data Missing Completely at Random. Firstly, we use a number of single/multiple imputation methods to recover the missing values and then ensemble a number of different classifiers built on the imputed data. We assess the quality of the imputation by using dissimilarity measures. We also evaluate the MIE performance by comparing classification accuracy on the complete and imputed data. Furthermore, we use the accuracy of simple imputation as a benchmark for comparison. We find that our proposed approach combining multiple imputation with ensemble techniques outperform others, particularly as missing data increases

Fuzzy min-max neural networks for categorical data: application to missing data imputation

The fuzzy min–max neural network classifier is a supervised learning method. This classifier takes the hybrid neural networks and fuzzy systems approach. All input variables in the network are required to correspond to continuously valued variables, and this can be a significant constraint in many real-world situations where there are not only quantitative but also categorical data. The usual way of dealing with this type of variables is to replace the categorical by numerical values and treat them as if they were continuously valued. But this method, implicitly defines a possibly unsuitable metric for the categories. A number of different procedures have been proposed to tackle the problem. In this article, we present a new method. The procedure extends the fuzzy min–max neural network input to categorical variables by introducing new fuzzy sets, a new operation, and a new architecture. This provides for greater flexibility and wider application. The proposed method is then applied to missing data imputation in voting intention polls. The micro data—the set of the respondents’ individual answers to the questions—of this type of poll are especially suited for evaluating the method since they include a large number of numerical and categorical attributes