Theory of the spin-galvanic effect and the anomalous phase-shift φ0\varphi_{0} in superconductors and Josephson junctions with intrinsic spin-orbit coupling

Due to the spin-orbit coupling (SOC) an electric current flowing in a normal metal or semiconductor can induce a bulk magnetic moment. This effect is known as the Edelstein (EE) or magneto-electric effect. Similarly, in a bulk superconductor a phase gradient may create a finite spin density. The inverse effect, also known as the spin-galvanic effect, corresponds to the creation of a supercurrent by an equilibrium spin polarization. Here, by exploiting the analogy between a linear-in-momentum SOC and a background SU(2) gauge field, we develop a quasiclassical transport theory to deal with magneto-electric effects in superconducting structures. For bulk superconductors this approach allows us to easily reproduce and generalize a number of previously known results. For Josephson junctions we establish a direct connection between the inverse EE and the appearance of an anomalous phase-shift $\varphi_{0}$ in the current-phase relation. In particular we show that $\varphi_{0}$ is proportional to the equilibrium spin-current in the weak link. We also argue that our results are valid generically, beyond the particular case of linear-in-momentum SOC. The magneto-electric effects discussed in this study may find applications in the emerging field of coherent spintronics with superconductors.Comment: v1: article version of the preprints arXiv:1408.4533 and arXiv:1409.4563 in letter format, with far more results and details. v2: some typos and mistakes corrected, new presentation of the derivation at all temperature in the ballistic regime (section VI), including a new fig.2 to illustrate this section. v3: accepted version, with extra reference

Ballistic Josephson junctions in the presence of generic spin dependent fields

Ballistic Josephson junctions are studied in the presence of a spin-splitting field and spin-orbit coupling. A generic expression for the quasi-classical Green's function is obtained and with its help we analyze several aspects of the proximity effect between a spin-textured normal metal (N) and singlet superconductors (S). In particular, we show that the density of states may show a zero-energy peak which is a generic consequence of the spin-dependent couplings in heterostructures. In addition we also obtain the spin current and the induced magnetic moment in a SNS structure and discuss possible coherent manipulation of the magnetization which results from the coupling between the superconducting phase and the spin degree of freedom. Our theory predicts a spin accumulation at the S/N interfaces, and transverse spin currents flowing perpendicular to the junction interfaces. Some of these findings can be understood in the light of a non-Abelian electrostatics.Comment: published versio

Nanoengineering a library of metallic nanostructures using a single microfluidic reactor

Microfluidic synthesis in a microfabricated reactor enables fast and facile synthesis of a wide library of metallic nanostructures: monometallic, bimetallic, anisotropic growth and heterostructures. Specific nanostructures are realized by selection of flow pattern and synthesis parameters. The technique is shown to have advantages over conventional batch technologies. Not only does it allow faster scalable synthesis, but also realization of nanostructures hitherto not reported such as Pt-Ru, Pt-Ni and Pt-Co nanodendrites, Pt-Pd heterostructures, Ag-Pd core-shell NPs, Au-Pd nanodumbbells and Au-Pd nanosheets

On Nichols algebras over SL(2,Fq) and GL(2,Fq)

We compute necessary conditions on Yetter-Drinfeld modules over the groups SL(2,Fq) and GL(2,Fq) to generate finite dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with a group of group-likes isomorphic to one of these groups.Comment: Major exposition revision, including referees remarks. To appear in J. Math. Phys. 13 page

Gravitino Dark Matter and Neutrino Masses in Partial Split Supersymmetry

Partial Split Supersymmetry with bilinear R-parity violation allows to reproduce all neutrino mass and mixing parameters. The viable dark matter candidate in this model is the gravitino. We study the hypothesis that both possibilities are true: Partial Split Supersymmetry explains neutrino physics and that dark matter is actually composed of gravitinos. Since the gravitino has a small but non-zero decay probability, its decay products could be observed in astrophysical experiments. Combining bounds from astrophysical photon spectra with the bounds coming from the mass matrix in the neutrino sector we derive a stringent upper limit for the allowed gravitino mass. This mass limit is in good agreement with the results of direct dark matter searches.Comment: 22 pages, 3 figure

Theory of magnetic response in finite two-dimensional superconductors

We present a theory of magnetic response in a finite-size two-dimensional superconductors with Rashba spin-orbit coupling. The interplay between the latter and an in-plane Zeeman field leads on the one hand to an out-of-plane spin polarization which accumulates at the edges of the sample over the superconducting coherence length, and on the other hand, to circulating supercurrents decaying away from the edge over a macroscopic scale. In a long finite stripe of width W both, the spin polarization and the currents, contribute to the total magnetic moment induced at the stripe ends. These two contributions scale with W and W2 respectively, such that for sufficiently large samples it can be detected by current magnetometry techniques.Comment: 6 pages, 3 figures; typos correcte

Special issue: Fractal functions and applications

This volume gathers some important advances in the fields of fractional calculus and fractal curves and functions. Fractional derivatives and integrals play an increasingly important role in applied science, and these types of models are ubiquitous in the current scientific literature. The references [1, 2] are devoted to fractional calculus and an application of it to a coronavirus spreading model. The first one studies three procedures of inverse Laplace Transforms: A Sinc–Thiele approximation, a Sinc and a Sinc–Gaussian (SG) method. Both Sinc versions are exact methods of inverse Laplace Transforms. The author proves that SG-based transformations present some advantages over the pure Sinc version regarding stability and convergence properties. The convergence is of exponential type. All the methods presented are applied to Mittag-Leffler functions depending on one, two and three parameters, and the author proves that the representation of this kind of functions is very effective. The author concludes that even for variable-order fractional differential or integral equations, the Sinc–Gaussian method is a powerful procedure..

Optimizing edge state transfer in a Su-Schrieffer-Heeger chain via hybrid digital-analog strategies

Su-Schrieffer-Heeger (SSH) chain, serving as a paradigmatic model for comprehending topological phases and their associated edge states, plays a pivotal role in advancing our understanding of quantum materials and quantum information processing and technology. In this paper, we introduce a hybrid analog-digital protocol designed for the non-adiabatic yet high-fidelity transfer of edge states in a SSH chain, featuring two sublattices A and B. The core of our approach lies in harnessing the approximate time-dependent counter-diabatic (CD) interaction, derived from adiabatic gauge potentials. However, to enhance transfer fidelity, particularly in long-distance chains, higher-order nested commutators become crucial. To simplify experimental implementation and navigate computational complexities, we identify the next-to-nearest-neighbour (NNN) hopping terms between sublattice A as dominant CD drivings, and further optimize them by using variational quantum circuits. Through digital quantum simulation, our protocol showcases the capability to achieve rapid and robust solutions, even in the presence of disorder. This analog-digital transfer protocol, an extension of quantum control methodology, establishes a robust framework for edge state transfer. Importantly, the optimal CD drivings identified can be seamlessly implemented across various quantum registers, highlighting the versatility of our approach

Distributed formation control with time and connectivity constraints

[Abstract] In this paper, we propose a distributed control law for non-holonomic vehicles that guarantees to achieve the desired formation and location before a given deadline, while maintaining the connectivity of the group. The group is commanded by a a selected subset of the agents, which know the location of the desired objective, while the rest of the vehicles only have information about their relative desired positions respect their set of neighbors. The analytical results are illustrated with a simulation example.[Resumen] En este documento, proponemos una ley de control distribuido para vehículos no holonómicos que garantiza alcanzar la formación y ubicación deseadas antes de un plazo determinado, mientras se mantiene la conectividad del grupo. El grupo está comandado por un subconjunto seleccionado de agentes, que conocen la ubicación del objetivo deseado, mientras que el resto de los vehículos solo tienen información sobre sus posiciones relativas deseadas con respecto a su conjunto de vecinos. Los resultados analíticos se ilustran con un ejemplo de simulación

Índices de escasez y de calidad del agua para la priorización de cuerpos de agua en los planes de ordenación del recurso hídrico. Aplicación en la jurisdicción de CORANTIOQUIA

En el marco de la formulación del Plan de Ordenamiento del Recurso Hídrico(PORH) para las direcciones territoriales Tahamíes y Zenufaná de la jurisdicción deCORANTIOQUIA (Corporación Autónoma Regional del Centro de Antioquia), sehizo la priorización de corrientes a partir del índice de calidad del agua y del índicede escasez, para corrientes receptoras de vertimientos y para corrientes abastecedorasde agua de suministro. Se presentan los resultados obtenidos para las 22 corrientesabastecedoras evaluadas a través del índice de escasez, y 39 corrientes receptoras devertimientos evaluadas, mediante el índice de calidad del agua. Estos resultadossirvieron como base para la definición de medidas de manejo del recurso hídrico