General framework for transport in spin-orbit-coupled superconducting heterostructures: Nonuniform spin-orbit coupling and spin-orbit-active interfaces

Electronic spin-orbit coupling (SOC) is essential for various newly discovered phenomena in condensed-matter systems. In particular, one-dimensional topological heterostructures with SOC have been widely investigated in both theory and experiment for their distinct transport signatures indicating the presence of emergent Majorana fermions. However, a general framework for the SOC-affected transport in superconducting heterostructures, especially with the consideration of interfacial effects, has not been developed even regardless of the topological aspects. We hereby provide one for an effectively one-dimensional superconductor-normal heterostructure with nonuniform magnitude and direction of both Rashba and Dresselhaus SOC as well as a spin-orbit-active interface. We extend the Blonder-Tinkham-Klapwijk treatment to analyze the current-voltage relation and obtain a rich range of transport behaviors. Our work provides a basis for characterizing fundamental physics arising from spin-orbit interactions in heterostructures and its implications for topological systems, spintronic applications, and a whole variety of experimental setups.Comment: 8 pages, 4 figure

Use of Triangular Elements for Nearly Exact BEM Solutions

A library of C functions yielding exact solutions of potential and flux influences due to uniform surface distribution of singularities on flat triangular and rectangular elements has been developed. This library, ISLES, has been used to develop the neBEM solver that is both precise and fast in solving a wide range of problems of scientific and technological interest. Here we present the exact expressions proposed for computing the influence of uniform singularity distributions on triangular elements and illustrate their accuracy. We also present a study concerning the time taken to evaluate these long and complicated expressions \textit{vis a vis} that spent in carrying out simple quadratures. Finally, we solve a classic benchmark problem in electrostatics, namely, estimation of the capacitance of a unit square plate raised to unit volt. For this problem, we present the estimated values of capacitance and compare them successfully with some of the most accurate results available in the literature. In addition, we present the variation of the charge density close to the corner of the plate for various degrees of discretization. The variations are found to be smooth and converging. This is in clear contrast to the criticism commonly leveled against usual BEM solvers.Comment: 18 pages, 12 figure

A Study of Three Dimensional Edge and Corner Problems using the neBEM Solver

The previously reported neBEM solver has been used to solve electrostatic problems having three-dimensional edges and corners in the physical domain. Both rectangular and triangular elements have been used to discretize the geometries under study. In order to maintain very high level of precision, a library of C functions yielding exact values of potential and flux influences due to uniform surface distribution of singularities on flat triangular and rectangular elements has been developed and used. Here we present the exact expressions proposed for computing the influence of uniform singularity distributions on triangular elements and illustrate their accuracy. We then consider several problems of electrostatics containing edges and singularities of various orders including plates and cubes, and L-shaped conductors. We have tried to show that using the approach proposed in the earlier paper on neBEM and its present enhanced (through the inclusion of triangular elements) form, it is possible to obtain accurate estimates of integral features such as the capacitance of a given conductor and detailed ones such as the charge density distribution at the edges / corners without taking resort to any new or special formulation. Results obtained using neBEM have been compared extensively with both existing analytical and numerical results. The comparisons illustrate the accuracy, flexibility and robustness of the new approach quite comprehensively.Comment: Submitted to Elsevie

Phenomenology of keV scale sterile neutrino dark matter with S4S_{4} flavor symmetry

We study the possibility of simultaneously addressing neutrino phenomenology and the dark matter in the framework of inverse seesaw. The model is the extension of the standard model by the addition of two right handed neutrinos and three sterile fermions which leads to a light sterile state with the mass in the keV range along with three light active neutrino states. The lightest sterile neutrino can account for a feasible dark matter(DM) candidate. We present a $S_{4}$ flavor symmetric model which is further augmented by $Z_{4}\times Z_{3}$ symmetry to constrain the Yukawa Lagrangian. The structures of the mass matrices involved in inverse seesaw within the $S_{4}$ framework naturally give rise to correct neutrino mass matrix with non-zero reactor mixing angle $\theta_{13}$. In this framework, we conduct a detailed numerical analysis both for normal hierarchy as well as inverted hierarchy to obtain dark matter mass and DM-active mixing which are the key factors for considering sterile neutrino as a viable dark matter candidate. We constrain the parameter space of the model from the latest cosmological bounds on the mass of the dark matter and DM-active mixing.Comment: v3:37+6 pages, 15+3 figures, more analysis added, more references added to appear in JHE

Consistent bosonization-debosonization I: A resolution of the non-equilibrium transport puzzle

We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of a tunneling junction out of equilibrium, we show that the conventional approach gives results that are not consistent with the exact solution of the problem even at the qualitative level. We identify inconsistencies that can adversely affect the results of all types of calculations. We subsequently show a way to avoid these and proceed consistently. The extended framework we develop here should be widely applicable.Comment: 16 pages, 3 figures, 1 tabl

Consistent bosonization-debosonization II: The two-lead Kondo problem and the fate of its non-equilibrium Toulouse point

Following the development of a scheme to bosonize and debosonize consistently [N. Shah and C.J. Bolech, Phys. Rev B 93, 085440 (2016); arXiv:1508.03078], we present in detail the Toulouse-point analytic solution of the two-lead Kondo junction model. The existence and location of the solvable point is not modified, but the calculational methodology and the final expressions for observable quantities change markedly as compared to the existent results. This solvable point is one of the remarkably few exact results for non-equilibrium transport in correlated systems. It yields relatively simple analytical expressions for the current in the full range of temperature, magnetic field and voltage. It also shows precisely, within the limitations of the Toulouse fine-tuning, how the transport evolves depending on the relative strengths of inter-lead and intra-lead Kondo exchange couplings ranging from weak to strong. Thus its improved understanding is an important stepping stone for future research.Comment: 15 pages, 6 figure

Dimensionality Distinguishers

The celebrated Clauser, Horne, Shimony and Holt (CHSH) game model helps to perform the security analysis of many two-player quantum protocols. This game specifies two Boolean functions whose outputs have to be computed to determine success or failure. It also specifies the measurement bases used by each player. In this paper, we generalize the CHSH game by considering all possible non-constant Boolean functions and all possible measurement basis (up to certain precision). Based on the success probability computation, we construct several equivalence classes and show how they can be used to generate three classes of dimension distinguishers. In particular, we demonstrate how to distinguish between dimensions 2 and 3 for a special form of maximally entangled state.Comment: 14 page

Inherent stochasticity of superconductive-resistive switching in nanowires

Hysteresis in the current-voltage characteristic in a superconducting nanowire reflects an underlying bistability. As the current is ramped up repeatedly, the state switches from a superconductive to a resistive one, doing so at random current values below the equilibrium critical current. Can a single phase-slip event somewhere along the wire--during which the order-parameter fluctuates to zero--induce such switching, via the local heating it causes? We address this and related issues by constructing a stochastic model for the time-evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. The model indicates that although, in general, several phase-slip events are necessary to induce switching, there is indeed a temperature- and current-range for which a single event is sufficient. It also indicates that the statistical distribution of switching currents initially broadens, as the temperature is reduced. Only at lower temperatures does this distribution show the narrowing with cooling naively expected for resistive fluctuations consisting of phase slips that are thermally activated.Comment: 5 pages, 4 figure

Transport in multi-terminal superconductor/ferromagnet junctions having spin-dependent interfaces

We study electronic transport in junctions consisting of a superconductor electrode and two ferromagnet (F) leads in which crossed Andreev reflections (CAR) and elastic cotunnelings are accommodated. We model the system using an extended Blonder-Tinkham-Klapwijk treatment with a key modification that accounts for spin-dependent interfacial barriers (SDIB). We compute current-voltage relations as a function of parameters characterizing the SDIB, magnetization in the F leads, geometry of the junction, and temperature. Our results reveal a rich range of significantly altered physics due to a combination of interfering spin-dependent scattering processes and population imbalance in the ferromagnets, such as a significant enhancement in CAR current and a sign change in the relative difference between resistance of two cases having a antiparallel or parallel alignment of the magnetization in the F leads, respectively. Our model accounts for the surprising experimental findings of positive relative resistance by M. Colci et al. [Phys. Rev. B 85, 180512(R) (2012)] as well as previously measured negative relative resistance results, both within sufficiently large parameter regions.Comment: 12 pages, 10 figure

Majorana fermions in an out-of-equilibrium topological superconducting wire: an exact microscopic transport analysis of a p-wave open chain coupled to normal leads

Topological superconductors are prime candidates for the implementation of topological-quantum-computation ideas because they can support non-Abelian excitations like Majorana fermions. We go beyond the low-energy effective-model descriptions of Majorana bound states (MBSs), to derive non-equilibrium transport properties of wire geometries of these systems in the presence of arbitrarily large applied voltages. Our approach involves quantum Langevin equations and non-equilibrium Green's functions. By virtue of a full microscopic calculation we are able to model the tunnel coupling between the superconducting wire and the metallic leads realistically; study the role of high-energy non-topological excitations; predict how the behavior compares for increasing number of odd vs. even number of sites; and study the evolution across the topological quantum phase transition (QPT). We find that the normalized spectral weight in the MBSs can be remarkably large and goes to zero continuously at the topological QPT. Our results have concrete implications for the experimental search and study of MBSs.Comment: 5 pages, 4 figure