Quantum shot noise in mesoscopic superconductor-semiconductor heterostructures

Shot noise in a mesoscopic electrical conductor have become one of the most attentiondrawing subject over the last decade. This is because the shot-noise measurements provide a powerful tool to study charge transport in mesoscopic systems [1]. While conventional resistance measurements yield information on the average probability for the transmission of electrons from source to drain, shot-noise provides additional information on the electron transfer process, which can not be obtained from resistance measurements. For example, one can determine the charge ‘q’ of the current carrying quasi-particles in different systems from the Poisson shot noise SI = 2q�I� [2] where �I� is the mean current of the system. For instance, the quasi-particle charge is a fraction of the electron charge ‘e’ in the fractional quantum Hall regime [3, 4, 5]. The multiple charge quanta were observed in an atomic point contact between two superconducting electrodes [6]. Shot-noise also provides information on the statistics of the electron transfer. Shot noise in general is suppressed from its classical value SI = 2e�I�, due to the correlations. In mesoscopic conductors, due to the Pauli principle in fermion statistics, electrons are highly correlated. As a results, the noise is fully suppressed in the limit of a perfect open channel T = 1. For the opposite limit of low transmission T � 1, transmission of electron follows a Poisson process and recovers the Schottky result SI = 2e�I� [2]. For many channel systems, shot-noise is suppressed to 1/2 × 2e�I� for a symmetric double barrier junction [7, 8], to 1/3 in a disordered wire [9, 10, 11, 12, 13, 14] and to 1/4 in an open chaotic cavity [15, 16, 17]. When a superconductor is involved, the shot-noise can be enhanced by virtue of the Andreev reflection process taking place at the interface between a normal metal and a superconductor. In some limiting cases, e.g. in the tunneling and disordered limit, the shot-noise can be doubled with respect to its normal state value [18, 19, 20, 21]. One of the main results of this thesis is an extensive comparison of our experimental data on conductance and shot noise measurements in a S-N junction with various theoretical models. In addition to measure shot-noise in a two-terminal geometry, one can also perform the fluctuation measurements on multi-terminal conductors. Whereas shotnoise corresponds to the autocorrelation of fluctuations from the same leads, crosscorrelation measurements of fluctuations between different leads provide a wealth of new experiments. For example, the exchange-correlations can be measured directly from these geometry [22]. Experimental attempt in mesoscopic electronic device was the correlation measurements [14, 23] on electron beam-splitter geometry [24] which is the analogue to the Hanbury-Brown Twiss (HBT) experiment in optics. In their experiment, Hanbury-Brown and Twiss demonstrated the intensity-intensity correlations of the light of a star in order to determine its diameter [25]. They measured a positive correlations between two different output photon beams as predicted to the particles obeying Bose-Einstein statistics. This behavior is often called ‘bunching’. On the other hand, a stream of the particles obeying Fermi-Dirac statistics is expected to show a anti-bunching behavior, resulting in a negative correlation of the intensity fluctuations. Latter one was confirmed by a Fermionic version of HBT experiments in single-mode, high-mobility semiconductor 2DEG systems [14, 23]. Whereas in a single electron picture, correlations between Fermions are always negative1 (anti-bunching), the correlation signal is expected to become positive if two electrons are injected simultaneously to two arms and leave the device through different leads for the coincident detection in both outputs2. One simple example is the splitting of the cooper pair in a Y-junction geometry in front of the superconductor. Fig.1.1 shows the possible experimental scheme of the correlation measurement as described here and the sample realized in an high-mobility semiconductor heterostructures. Since all three experiments were done3, only one left unfolded, ‘The positive correlations from the Fermionic system’. The main motivation of this thesis work was to find a positive correlations in the device shown in Fig.1.1. In a well defined single channel collision experiment on an electron beam splitter, it has theoretically been shown that the measured correlations are sensitive to the spin entanglement [29, 30]. This is another even more exciting issue and we would like to mention that the experimental quest for positive correlations is important for the new field of quantum computation and communication in the solid state, [31, 32] in which entangled electrons play a crucial role. A natural source of entanglement is found in superconductors in which electrons are paired in a spin-singlet state. A source of entangled electrons may therefore be based on a superconducting injector.[33, 34, 27, 35, 36, 37, 38, 38, 39, 40, 41] Even more so, an electronic beamsplitter is capable of distinguishing entangled electrons from single electrons.[29, 42] However, the positive correlations have not been observed in solid-state mesoscopic devices until today. This thesis is organized as follows. Chapter 2 is devoted to the theoretical background of the electrical transport and the current fluctuations. We introduce the basic concept of electrical transport and the shot noise in normal state and superconductor-normal metal (S-N) junction. We also briefly review the theoretical proposals and arguments about the current-current cross-correlations in threeterminal systems. In Chapter 3, we describe the sample fabrication techniques which have been done in our laboratory such as e-beam lithography, metallization and etching. We present also the characterization of our particular system, niobium (Nb) / InAs-based 2DEG junction. Chapter 4 describes the reliable low-temperature measurement technique for detecting the noise. We characterize our measurement setup using a simple RC-circuit model. In Chapter 5, our main results about the shot noise of S-N junction are presented in detail

Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The result also applies to various sub-models of the stochastic blockmodel found in the literature.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1124 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

ACREAGE RESPONSE, EXPECTED PRICE FUNCTIONS, AND ENDOGENOUS PRICE EXPECTATIONS

Taking the price of futures as a proxy for expected price, this article treats acreage planted to soybean, the price of futures, and other variables as jointly dependent. A futures price equation is embedded in a simultaneous equations model along with the consumption demand and acreage response. The model is estimated using both ordinary and three-stage least squares. Estimated price elasticities for consumption demand, demand for stocks, and acreage response equal, respectively, -.5, -1.8, and +.2 (short run) and +.59 (long run).Crop Production/Industries,

Soft Supersymmetry Breaking in KKLT Flux Compactification

We examine the structure of soft supersymmetry breaking terms in KKLT models of flux compactification with low energy supersymmetry. Moduli are stabilized by fluxes and nonperturbative dynamics while a de Sitter vacuum is obtained by adding supersymmetry breaking anti-branes. We discuss the characteristic pattern of mass scales in such a set-up as well as some features of 4D N=1 supergravity breakdown by anti-branes. Anomaly mediation is found to always give an important contribution and one can easily arrange for flavor-independent soft terms. In its most attractive realization, the modulus mediation is comparable to the anomaly mediation, yielding a quite distinctive sparticle spectrum. In addition, the axion component of the modulus/dilaton superfield dynamically cancels the relative CP phase between the contributions of anomaly and modulus mediation, thereby avoiding dangerous SUSY CP violation.Comment: minor corrections, references added, version accepted in NP

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities

Immigration as Business Strategy: Simplifying American Immigration Law in a Global Economy

Despite immigration law’s notorious complexity, public debate on immigration reform has historically ignored basic questions of why and how the current laws should be simplified. Instead, discussion has often focused on substantive proposals—most commonly regarding legalization and border enforcement—without reference to the impact of these proposals on the legal immigration structure. This article emphasizes that any durable immigration reform must take steps to free the immigration system from the intricacies that define it today. The article begins by overviewing the basic features of the modern global economy, their implications for immigration law, and why these implications compel an immigration system based on simple rules. Then, borrowing from the literature on business strategy and organizational design, the article applies to the current immigration system a basic three-step framework for developing simple rules. In the first step—Setting the Objective—the article argues that family reunification, the primary objective of the current system, does not adequately acknowledge the global economy in which the American immigration system operates. As economic conditions affecting the United States have evolved since fifty years ago when family reunification emerged as the cornerstone of American immigration policy, the focus of the American immigration system must be reoriented towards competing in the global economy. In the second step—Identifying a Bottleneck—the article hones in on the second and third categories of the current five-category preference system for admitting employment-based immigrants. Examining the unique obstacles and complexities facing immigration under the EB-2 and EB-3 categories, the article identifies these categories as a focal point on which any effort to simplify American immigration law should take aim at the outset. Finally, in the third step—Formulating the Rules—the article argues that from the perspective of simplicity, a provisional visa program proposed by many commentators offers a legal system that is user-created, repetitively applicable, and easily adaptable—features that are necessary for the effective practical application of simple rules. As such, provisional visas provide a structurally viable replacement for the procedures currently used to admit immigrants who fall under the EB-2 and EB-3 categories. The overarching purpose of this article is to emphasize that sustainable reform of American immigration law must not only make substantive revisions, but also initiate a process of structural simplification. The article offers a conceptual starting point for this process by applying to the current immigration system a basic business-strategy framework for developing simple rules

Prewhitening Bias in HAC Estimation

HAC estimation commonly involves the use of prewhitening filters based on simple autoregressive models. In such applications, small sample bias in the estimation of autoregressive coefficients is transmitted to the recoloring filter, leading to HAC variance estimates that can be badly biased. The present paper provides an analysis of these issues using asymptotic expansions and simulations. The approach we recommend involves the use of recursive demeaning procedures that mitigate the effects of small sample autoregressive bias. Moreover, a commonly-used restriction rule on the prewhitening estimates (that first order autoregressive coefficient estimates, or largest eigenvalues, greater than 0.97 be replaced by 0.97) adversely interfers with the power of unit root and KPSS tests. We provide a new boundary condition rule that improves the size and power properties of these tests. Some illustrations are given of the effects of these adjustments on the size and power of KPSS testing. Using prewhitened HAC estimates and the new boundary condition rule, the KPSS test is consistent, in contrast to KPSS testing that uses conventional prewhitened HAC estimates (Lee, 1996).Autoregression, Bias, HAC estimator, KPSS testing, Long run variance, Prewhitening, Recursive demeaning