arXiv subjects

A. Glatz

Publications and source records attributed to A. Glatz.

At least 19 recordsLinked to original sources

arXiv2021

Large-scale quantum hybrid solution for linear systems of equations

State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are restricted to exploring specific simplified protocols, whereas the implementation of full-scale quantum algorithms aimed at solving concrete large scale problems arising in data analysis and numerical modelling remains a challenge. Here we introduce and implement a hybrid quantum algorithm for solving linear systems of equations with exponential speedup, utilizing quantum phase estimation, one of the exemplary core protocols for quantum computing. We introduce theoretically classes of linear systems that are suitable for current generation quantum machines and solve experimentally a $2^{17}$-dimensional problem on superconducting IBMQ devices, a record for linear system solution on quantum computers. The considered large-scale algorithm shows superiority over conventional solutions, demonstrates advantages of quantum data processing via phase estimation and holds high promise for meeting practically relevant challenges.

quant-ph↗

arXiv2020

Analysis of the Ghost and Mirror Fields in the Nernst Signal Induced by Superconducting Fluctuations

We present a complete analysis of the Nernst signal due to superconducting fluctuations in a large variety of superconductors from conventional to unconventional ones. A closed analytical expression of the fluctuation contribution to the Nernst signal is obtained in a large range of temperature and magnetic field. We apply this expression directly to experimental measurements of the Nernst signal in Nb$_x$Si$_{1-x}$ thin films and a URu$_2$Si$_2$ superconductors. Both magnetic field and temperature dependence of the available data are fitted with very good accuracy using only two fitting parameters, the superconducting temperature $T_{\mathrm{c0}}$ and the upper critical field $H_{\mathrm{c2}}$. The obtained values agree very well with experimentally obtained values. We also extract the ghost lines (maximum of the Nernst signal for constant temperature or magnetic field) from the complete expression and also compare it to several experimentally obtained curves. Our approach predicts a linear temperature dependence for the ghost critical field well above $T_{\mathrm{c0}}$. Within the errors of the experimental data, this linearity is indeed observed in many superconductors far from $T_{\mathrm{c0}}$.

cond-mat.supr-con↗

arXiv2019

Realization of the Werner-Holevo and Landau-Streater quantum channels for qutrits on quantum computers

We realize Landau-Streater (LS) and Werner-Holevo (WH) quantum channels for qutrits on the IBM quantum computers. These channels correspond to interaction between the qutrit and its environment that result in the globally unitarily covariant qutrit transformation violating multiplicativity of the maximal $p$-norm. Our realization of LS and WH channels is based on embedding qutrit states into states of two qubits and using single-qubit and two-qubit CNOT gates to implement the specific interaction. We employ the standard quantum gates hence the developed algorithm suits any quantum computer. We run our algorithm on a 5-qubit and a 20-qubit computer as well as on a simulator. We quantify the quality of the implemented channels comparing their action on different input states with theoretical predictions. The overall efficiency is quantified by fidelity between the theoretical and experimental Choi states implemented on the 20-qubit computer.

quant-ph↗

arXiv2017

Strong-pinning regimes by spherical inclusions in anisotropic type-II superconductors

The current-carrying capacity of type-II superconductors is decisively determined by how well material defect structures can immobilize vortex lines. In order to gain deeper insights into the fundamental pinning mechanisms, we have explored the case of vortex trapping by randomly distributed spherical inclusions using large-scale simulations of the time-dependent Ginzburg-Landau equations. We find that for a small density of particles having diameters of two coherence lengths, the vortex lattice preserves its structure and the critical current $j_c$ decays with the magnetic field following a power-law $B^{-α}$ with $α\approx 0.66$, which is consistent with predictions of strong-pinning theory. For a higher density of particles and/or larger inclusions, the lattice becomes progressively more disordered and the exponent smoothly decreases down to $α\approx 0.3$. At high magnetic fields, all inclusions capture a vortex and the critical current decays faster than $B^{-1}$ as would be expected by theory. In the case of larger inclusions with a diameter of four coherence length, the magnetic-field dependence of the critical current is strongly affected by the ability of inclusions to capture multiple vortex lines. We found that at small densities, the fraction of inclusions trapping two vortex lines rapidly grows within narrow field range leading to a peak in $j_c(B)$-dependence within this range. With increasing inclusion density, this peak transforms into a plateau, which then smooths out. Using the insights gained from simulations, we determine the limits of applicability of strong-pinning theory and provide different routes to describe vortex pinning beyond those bounds.

cond-mat.supr-con↗

arXiv2017

Effect of hexagonal patterned arrays and defect geometry on the critical current of superconducting films

Understanding the effect of pinning on the vortex dynamics in superconductors is a key factor towards controlling critical current values. Large-scale simulations of vortex dynamics can provide a rational approach to achieve this goal. Here, we use the time-dependent Ginzburg-Landau equations to study thin superconducting films with artificially created pinning centers arranged periodically in hexagonal lattices. We calculate the critical current density for various geometries of the pinning centers --- varying their size, strength, and density. Furthermore, we shed light upon the influence of pattern distortion on the magnetic-field-dependent critical current. We compare our result directly with available experimental measurements on patterned molybdenum-germanium films, obtaining good agreement. Our results give important systematic insights into the mechanisms of pinning in these artificial pinning landscapes and open a path for tailoring superconducting films with desired critical current behavior.

cond-mat.supr-con↗

arXiv2016

Toward superconducting critical current by design

We present the new paradigm of critical current by design. Analogous to materials by design, it aims at predicting the optimal defect landscape in a superconductor for targeted applications by elucidating the vortex dynamics responsible for the bulk critical current. To highlight this approach, we demonstrate the synergistic combination of critical current measurements on commercial high-temperature superconductors containing self-assembled and irradiation tailored correlated defects by using large-scale time-dependent Ginzburg-Landau simulations for vortex dynamics.

cond-mat.supr-con↗

arXiv2015

Simulation of the vortex dynamics in a real pinning landscape of YBa$_2$Cu$_3$O$_{7-δ}$ coated conductors

The ability of high-temperature superconductors (HTSs) to carry very large currents with almost no dissipation makes them irreplaceable for high-power applications. The development and further improvement of HTS-based cables requires an in-depth understanding of the superconducting vortex dynamics in presence of complex pinning landscapes. We present a critical current analysis of a real HTS sample in a magnetic field by combining state-of-the-art large-scale Ginzburg-Landau simulations with reconstructive three-dimensional scanning transmission electron microscopy tomography of the pinning landscape in Dy-doped YBa$_2$Cu$_3$O$_{7-δ}$. This methodology provides a unique look at the vortex dynamics in the presence of a complex pinning landscape, responsible for the high current-carrying capacity characteristic of commercial HTS wires. Our method demonstrates very good functional and quantitative agreement of the critical current between simulation and experiment, providing a new predictive tool for HTS wires design.

cond-mat.supr-con↗

arXiv2015

Optimization of vortex pinning by nanoparticles using simulations of time-dependent Ginzburg-Landau model

Introducing nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. We address the problem of optimizing vortex pinning landscape for randomly distributed metallic spherical inclusions using large-scale numerical simulations of time-dependent Ginzburg-Landau equations. We found the size and density of particles for which the highest critical current is realized in a fixed magnetic field. For each particle size and magnetic field, the critical current reaches a maximum value at a certain particle density, which typically corresponds to 15-23% of the total volume being replaced by nonsuperconducting material. For fixed diameter, this optimal particle density increases with the magnetic field. Moreover, we found that the optimal particle diameter slowly decreases with the magnetic field from 4.5 to 2.5 coherence lengths at a given temperature. This result shows that pinning landscapes have to be designed for specific applications taking into account relevant magnetic field scales.

cond-mat.supr-con↗

arXiv2015

Stable large-scale solver for Ginzburg-Landau equations for superconductors

Understanding the interaction of vortices with inclusions in type-II superconductors is a major outstanding challenge both for fundamental science and energy applications. At application-relevant scales, the long-range interactions between a dense configuration of vortices and the dependence of their behavior on external parameters, such as temperature and an applied magnetic field, are all important to the net response of the superconductor. Capturing these features, in general, precludes analytical description of vortex dynamics and has also made numerical simulation prohibitively expensive. Here we report on a highly optimized iterative implicit solver for the time-dependent Ginzburg-Landau equations suitable for investigations of type-II superconductors on massively parallel architectures. Its main purpose is to study vortex dynamics in disordered or geometrically confined mesoscopic systems. In this work, we present the discretization and time integration scheme in detail for two types of boundary conditions. We describe the necessary conditions for a stable and physically accurate integration of the equations of motion. Using an inclusion pattern generator, we can simulate complex pinning landscapes and the effect of geometric confinement. We show that our algorithm, implemented on a GPU, can provide static and dynamic solutions of the Ginzburg-Landau equations for mesoscopically large systems over thousands of time steps in a matter of hours. Using our formulation, studying scientifically-relevant problems is a computationally reasonable task.

cond-mat.supr-con↗

arXiv2015

Detecting vortices in superconductors: Extracting one-dimensional topological singularities from a discretized complex scalar field

In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise positions and motion from discretized numerical simulation data is an important, but challenging task. In the past, vortices have mostly been detected by analyzing the magnitude of the complex scalar field representing the order parameter and visualized by corresponding contour plots and isosurfaces. However, these methods, primarily used for small-scale simulations, blur the fine details of the vortices, scale poorly to large-scale simulations, and do not easily enable isolating and tracking individual vortices. Here we present a method for exactly finding the vortex core lines from a complex order parameter field. With this method, vortices can be easily described at a resolution even finer than the mesh itself. The precise determination of the vortex cores allows the interplay of the vortices inside a model superconductor to be visualized in higher resolution than has previously been possible. By representing the field as the set of vortices, this method also massively reduces the data footprint of the simulations and provides the data structures for further analysis and feature tracking.

cond-mat.supr-con↗

arXiv2014

Hotspots in two-phase conducting media

We study electric properties of random resistor networks consisting of resistors of two kinds numerically, focusing on the power loss across each bond. Tuning the ratio of the resistances $r$ and their respective fraction $α$ we find that at large $r$ the conductance of the network is dominated by a few optimal, percolation-like, conducting paths. We demonstrate that the distribution of the local power losses $P$ is exponential, $\propto\exp(-P/\langle P\rangle)$, and reveal the spatial distribution of hotspots concentrating the main part of the dissipated power.

cond-mat.mes-hall↗

arXiv2014

Interplay of Coulomb Blockade and Ferroelectricity in Nano-Granular Materials

We study electron transport properties of composite ferroelectrics --- materials consisting of metallic grains embedded in a ferroelectric matrix. In particular, we calculate the conductivity in a wide range of temperatures and electric fields, showing pronounced hysteretic behavior. In weak fields, electron cotunneling is the main transport mechanism. In this case, we show that the ferroelectric matrix strongly influences the transport properties through two effects: i) the dependence of the Coulomb gap on the dielectric permittivity of the ferroelectric matrix, which in turn is controlled by temperature and external field; and ii) the dependence of the tunneling matrix elements on the electric polarization of the ferroelectric matrix, which can be tuned by temperature and applied electric field as well. In the case of strong electric fields, the Coulomb gap is suppressed and only the second mechanism is important. Our results are important for i) thermometers for precise temperature measurements and ii) ferrroelectric memristors.

cond-mat.mes-hall↗

arXiv2013

Electron Transport Properties of Composite Ferroelectrics

We study electron transport in composite ferroelectrics --- materials consisting of metallic grains embedded in a ferroelectric matrix. Due to its complex tunable morphology the thermodynamic properties of these materials can be essentially different from bulk or thin-film ferroelectrics. We calculate the conductivity of composite ferroelectrics by taking into account the interplay between charge localization, multiple grain boundaries, strong Coulomb repulsion, and ferroelectric order parameter. We show that the ferroelectricity plays a crucial role on the temperature behavior of the conductivity in the vicinity of the ferroelectric-paraelectric transition.

cond-mat.mes-hall↗

arXiv2013

Low-Bias-Anomaly and Tunnel Fluctuoscopy

Electron tunneling spectroscopy pioneered by Esaki and Giaever offered a powerful tool for studying electronic spectra and density of states (DOS) in superconductors. This led to important discoveries that revealed, in particular, the pseudogap in the tunneling spectrum of superconductors above their critical temperatures. However, the phenomenological approach is insufficient for describing the does not resolve the fine structure of low-bias behavior carrying significant information about electron scattering, interactions, and decoherence effects. Here we construct a complete microscopic theory of electron tunneling into a superconductor in the fluctuation regime. We reveal a non-trivial low-energy anomaly in tunneling conductivity due to Andreev-like reflection of injected electrons from superconducting fluctuations. Our findings enable real-time observation of fluctuating Cooper pairs dynamics by time-resolved scanning tunneling microscopy measurements and open new horizons for quantitative analysis of the fluctuation electronic spectra of superconductors.

cond-mat.supr-con↗

arXiv2013

Dirac Fermions and Superconductivity in Homologous Structures (AgxPb1-xSe)5(Bi2Se3)3m,m = 1,2

A newly discovered topological insulator (AgxPb1-xSe)5(Bi2Se3)3m, m=2, has a band gap of 0.5 eV, the largest value ever reported in topological insulators (TIs). We present a magnetoconductivity study of the Dirac electrons of this compound in the quantum diffusion regime. Two dimensional weak antilocalization was observed and identified as destructive interference caused by the Berry phase of this topological state. We find that the phase coherence length of the Dirac electrons is independent of doping and disorder levels. This provides proof for the absence of backscattering arising from the protection of time reversal invariance in TI (AgxPb1-xSe)5(Bi2Se3)3m, m=2. We further report that the homologous compound (AgxPb1-xSe)5(Bi2Se3)3m, m=1 is a superconductor with a transition temperature Tc = 1.7 K. The related structures of these two phases allow lateral intergrowth of crystals to occur naturally, offering an opportunity to observe the Majorana Fermion state at the boundary of two intergrown crystals.

cond-mat.supr-con↗

arXiv2013

Universality and quantization of the power to heat ratio in nano-granular systems

We study heating and dissipation effects in granular nanosystems in the regime of weak coupling between the grains. We focus on the cotunneling regime and solve the heat-dissipation problem in an array of grains exactly. We show that the power to heat ratio has a universal quantized value, which is geometrically protected: it depends only on the number of grains.

cond-mat.mes-hall↗

arXiv2013

Analytical Description of the Quantum-Mesoscopic-Classical Transition in Systems with Quasi-Discrete Environment

We investigate dynamic properties of inhomogeneous nano-materials, which appear in analytical descriptions typically as series of $δ$-functions with corresponding Gibbs weights. We focus on observables relevant for transport theories of Josephson junction arrays and granular systems near the superconductor -- insulator transition. Furthermore, our description applies to the theory of tunnel junctions exchanging energy with a "bath", the latter having a discrete spectrum. Using the matrix theta-function formalism we find an analytical expression for the transport characteristics capturing the complete temperature driven transition from the quantum to the classical regime.

cond-mat.mes-hall↗

arXiv2012

Pseudogap and zero-bias anomaly due to fluctuation suppression of quasiparticle tunneling

We study the effect of superconducting fluctuations on the tunnel current-voltage characteristics of disordered superconducting films placed in a perpendicular magnetic field, $H$, in the whole $H$-$T$ phase diagram outside the superconducting region. This tunnel-current is experimentally accessible by STM measurements. In the domain of temperatures $T\geq T_{c0}$ and relatively weak fields $H\ll H_{c2}(0)$ we reproduce existing results for the zero-voltage tunneling conductance, but also discover an important nonlinear contribution, which appears due to dynamic fluctuation modes and results in the formation of a strong zero-bias anomaly (ZBA) on the scale $eV\sim k_{\mathrm{B}}(T-T_{c0})$. At large voltages ($eV\sim k_{\mathrm{B}}T_{c0}$) these modes, together with the contribution from static fluctuations, form a pseudogap maximum. At low temperatures, with magnetic field values near $H_{c2}(0)$, fluctuations acquire quantum character and the general picture of the voltage dependent tunneling conductance resembles that one close to $T_{c0}$, where the role of temperature and magnetic field are exchanged. In particular, a gap-like structure appears with maximum at $eV_{\max}\sim Δ_{\mathrm{BCS}}$ and a sharp ZBA on the scale $eV\sim Δ_{\mathrm{BCS}}(H/H_{c2}(0)-1)$. The complete expression for the tunneling current at arbitrary fields and temperatures can be evaluated only numerically, which is presented in detail.

cond-mat.supr-con↗