X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot

The quasi-bound states of a superconducting quantum dot that is weakly coupled to a normal metal appear as resonances in the Andreev reflection probability, measured via the differential conductance. We study the evolution of these Andreev resonances when an external parameter (such as magnetic field or gate voltage) is varied, using a random-matrix model for the $N\times N$ scattering matrix. We contrast the two ensembles with broken time-reversal symmetry, in the presence or absence of spin-rotation symmetry (class C or D). The poles of the scattering matrix in the complex plane, encoding the center and width of the resonance, are repelled from the imaginary axis in class C. In class D, in contrast, a number $\propto\sqrt{N}$ of the poles has zero real part. The corresponding Andreev resonances are pinned to the middle of the gap and produce a zero-bias conductance peak that does not split over a range of parameter values (Y-shaped profile), unlike the usual conductance peaks that merge and then immediately split (X-shaped profile).Comment: Contribution for the JETP special issue in honor of A.F. Andreev's 75th birthday. 9 pages, 8 figure

HFR Code: A Flexible Replication Scheme for Cloud Storage Systems

Fractional repetition (FR) codes are a family of repair-efficient storage codes that provide exact and uncoded node repair at the minimum bandwidth regenerating point. The advantageous repair properties are achieved by a tailor-made two-layer encoding scheme which concatenates an outer maximum-distance-separable (MDS) code and an inner repetition code. In this paper, we generalize the application of FR codes and propose heterogeneous fractional repetition (HFR) code, which is adaptable to the scenario where the repetition degrees of coded packets are different. We provide explicit code constructions by utilizing group divisible designs, which allow the design of HFR codes over a large range of parameters. The constructed codes achieve the system storage capacity under random access repair and have multiple repair alternatives for node failures. Further, we take advantage of the systematic feature of MDS codes and present a novel design framework of HFR codes, in which storage nodes can be wisely partitioned into clusters such that data reconstruction time can be reduced when contacting nodes in the same cluster.Comment: Accepted for publication in IET Communications, Jul. 201

Quantum theory of the charge stability diagram of semiconductor double quantum dot systems

We complete our recently introduced theoretical framework treating the double quantum dot system with a generalized form of Hubbard model. The effects of all quantum parameters involved in our model on the charge stability diagram are discussed in detail. A general formulation of the microscopic theory is presented, and truncating at one orbital per site, we study the implication of different choices of the model confinement potential on the Hubbard parameters as well as the charge stability diagram. We calculate the charge stability diagram keeping three orbitals per site and find that the effect of additional higher-lying orbitals on the subspace with lowest-energy orbitals only can be regarded as a small renormalization of Hubbard parameters, thereby justifying our practice of keeping only the lowest-orbital in all other calculations. The role of the harmonic oscillator frequency in the implementation of the Gaussian model potential is discussed, and the effect of an external magnetic field is identified to be similar to choosing a more localized electron wave function in microscopic calculations. The full matrix form of the Hamiltonian including all possible exchange terms, and several peculiar charge stability diagrams due to unphysical parameters are presented in the appendix, thus emphasizing the critical importance of a reliable microscopic model in obtaining the system parameters defining the Hamiltonian.Comment: 19 pages, 15 figure

Implementation of a color-capable optofluidic microscope on a RGB CMOS color sensor chip substrate

We report the implementation of a color-capable on-chip lensless microscope system, termed color optofluidic microscope (color OFM), and demonstrate imaging of double stained Caenorhabditis elegans with lacZ gene expression at a light intensity about 10 mW/cm^2

Classifying Pattern Formation in Materials via Machine Learning

Scanning probe experiments such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) on strongly correlated materials often reveal complex pattern formation that occurs on multiple length scales. We have shown in two disparate correlated materials that the pattern formation is driven by proximity to a disorder-driven critical point. We developed new analysis concepts and techniques that relate the observed pattern formation to critical exponents by analyzing the geometry and statistics of clusters observed in these experiments and converting that information into critical exponents. Machine learning algorithms can be helpful correlating data from scanning probe experiments to theoretical models of pattern formation. We analyze the use of machine learning algorithms for the identification of critical behavior and universality underlying scanning probe data sets taken from correlated materials. This method has complementary strengths to the cluster analysis methods. The cluster techniques have a clear physical interpretation while machine learning algorithms require less expertise from the user and are faster to implement. The complementary nature of the two techniques further facilitates our understanding of correlated materials. The training of machine learning algorithms has been done through artificial neural networks. The neural net was trained using data from theoretical simulations of percolation and Ising models. The trained net had a 3.00% average classification error during testing. This proves that machine learning algorithms can successfully distinguish whether the complex pattern formation of a specific novel material is governed by uncorrelated percolation or by an interaction model fixed point

Wigner-Poisson statistics of topological transitions in a Josephson junction

The phase-dependent bound states (Andreev levels) of a Josephson junction can cross at the Fermi level, if the superconducting ground state switches between even and odd fermion parity. The level crossing is topologically protected, in the absence of time-reversal and spin-rotation symmetry, irrespective of whether the superconductor itself is topologically trivial or not. We develop a statistical theory of these topological transitions in an N-mode quantum-dot Josephson junction, by associating the Andreev level crossings with the real eigenvalues of a random non-Hermitian matrix. The number of topological transitions in a 2pi phase interval scales as sqrt(N) and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory.Comment: 12 pages, 15 figures; v2 to appear in PRL, with appendix in the supplementary materia