Quantifying wave-function overlaps in inhomogeneous Majorana nanowires

A key property of Majorana zero modes is their protection against local perturbations. In the standard picture, this protection is guaranteed by a high degree of spatial nonlocality of the Majoranas, namely a suppressed wave-function overlap, in the topological phase. However, a careful characterization of resilience to local noise goes beyond mere spatial separation and must also take into account the projection of wave-function spin. By considering the susceptibility of a given zero mode to different local perturbations, we find the relevant forms of spin-resolved wave-function overlaps that measure its resilience. We quantify these overlaps and study their dependence with nanowire parameters in several classes of experimentally relevant configurations. These include nanowires with inhomogeneous depletion and induced pairing, barriers, and quantum dots. Smooth inhomogeneities have been shown to produce near-zero modes, so-called pseudo-Majoranas, below the critical Zeeman field in the bulk. Surprisingly, their resilience is found to be comparable or better than that of topological Majoranas in realistic systems. We further study how accurately their overlaps can be estimated using a purely local measurement on one end of the nanowire, accessible through conventional transport experiments. In uniform nanowires, this local estimator is remarkably accurate. In inhomogeneous cases, it is less accurate but can still provide reasonable estimates for potential inhomogeneities of the order of the superconducting gap. We further analyze the zero-mode wave-function structure, spin texture, and spectral features associated with each type of inhomogeneity. All our results highlight the strong connection between internal wave-function degrees of freedom, nonlocality, and protection in smoothly inhomogeneous nanowiresWe acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through Grants No. FIS2015-65706-P, No. FIS2015-64654-P, and No. FIS2016-80434-P (AEI/FEDER, EU), the Ramón y Cajal programme, Grants No. RYC-2011-09345 and No. RYC-2013-14645, and the “María de Maeztu” Programme for Units of Excellence in Research and Development (MDM-2014-0377

Zero-energy pinning from interactions in Majorana nanowires

Majorana zero modes at the boundaries of topological superconductors are charge-neutral, an equal superposition of electrons and holes. This ideal situation is, however, hard to achieve in physical implementations, such as proximitized semiconducting nanowires of realistic length. In such systems Majorana overlaps are unavoidable and lead to their hybridization into charged Bogoliubov quasiparticles of finite energy, which, unlike true zero modes, are affected by electronic interactions. We here demonstrate that these interactions, particularly with bound charges in the dielectric surroundings, drastically change the non-interacting paradigm. Remarkably, interactions may completely suppress Majorana hybridization around parity crossings, where the total charge in the nanowire changes. This effect, dubbed zero-energy pinning, stabilizes Majoranas back to zero energy and charge, and leads to electronically incompressible parameter regions wherein Majoranas remain insensitive to local perturbations, despite their overlapWe thank K. Flensberg for illuminating discussions. We acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through the Ramón y Cajal program RYC-2013-14645 and RYC-2011-09345, grant Nos. FIS2012-33521, FIS2013-47328-C2-1-P, FIS2014-55486-P, FIS2015-65706-P, FIS2015-64654-P (MINECO/FEDER), and the “María de Maeztu” Program for Units of Excellence in R&D (MDM-2014-0377

El Extintor como preventivo recurso didáctico

Un dels accidents més freqüents que es produeixen als laboratoris i a les llars és el que s'origina pel foc. Per sufocar un conat d'incendi existeixen extintors estratègicament situats i identificats, però sabem quin és el tipus d'extintor més adient per a cada foc?, els sabem utilitzar correctament? La difusió de les característiques dels extintors i la pràctica del seu correcte ús aconseguiran un entorn més segur, a la vegada que mostraran la utilitat de les substàncies químiques en la vida quotidiana.Fire is the main cause of accidents, not only in laboratories, but also in homes. Every fire, during its initial stage, can be effectively controlled by using fire extinguishers properly. In fact, fire extinguishers are identified and strategically placed in order to control the fire. But, how do we know which kind of extinguisher is the most appropriate for each situation? Do we know how to use them correctly? Information about the different types of fire extinguishers and how to use them properly helps us to be safe and at the same time it shows us how useful some chemical substances are in our daily life.Uno de los accidentes más frecuentes que se producen en los laboratorios y en los hogares es el originado por el fuego. Para sofocar un conato de incendio existen extintores estratégicamente situados e identificados, pero ¿conocemos cuál es el tipo de extintor más adecuado para cada fuego?, ¿sabemos utilizarlo correctamente? La difusión de las características de los extintores y la práctica de su uso adecuado conseguirán un entorno más seguro, a la vez que mostrarán la utilidad de las sustancias químicas en la vida cotidiana

The amazing chemistry of controlled deflagrations

Las deflagraciones realizadas en condiciones controladas y con pequeñas cantidades de combustibles (etanol, acetileno y polvo de licopodio) proporcionan un fructífero recurso didáctico para que el profesorado consiga aumentar la atención del alumnado y su interés en aprender química.Deflagrations under controlled conditions and with small amounts of fuels (ethanol, acetylene and lycopene powder) provide a fruitful teaching resource for the teacher to increase the attention of students and their interest in learning chemistry

Petardos, coetes y mucha química

Els espectaculars efectes que produeixen els petards i coets estan relacionats amb la ciència, per la qual cosa poden ser aprofitats com un inusual i atractiu recurs didàctic per a la química. Amb això es pretén aconseguir augmentar l'interès dels estudiants cap a la ciència, alhora que ampliar el coneixement sobre les reaccions químiques relacionades amb la vida quotidiana. Les experiències proposades han estat realitzades per estudiants davant un públic molt variat en fires de ciència divulgatives.The spectacular effects produced by firecrackers and rockets are based on the science. They can therefore be used as an unusual and attractive didactic resource for chemistry learning. What we intend is to extend scientific knowledge and to increase the interest of students towards chemical reactions related to daily life situations. The suggested experiments have been carried out by students and presented to varied audiences in science fairs.Los espectaculares efectos que producen petardos y cohetes están relacionados con la ciencia, por lo que pueden ser aprovechados como un inusual y atractivo recurso didáctico para la química. Con esto se pretende conseguir aumentar el interés de los estudiantes hacia la ciencia, a la vez que ampliar el conocimiento sobre las reacciones químicas relacionadas con su vida cotidiana. Las experiencias propuestas han sido realizadas por estudiantes ante un público muy variado en ferias de ciencia divulgativas

El Fuego como luminoso recurso didáctico

Desde que el hombre primitivo domesticó el fuego hasta los modernos fuegos artificiales que culminan fiestas y espectáculos en todo el mundo, han pasado miles de años, si bien los principios químicos utilizados siguen siendo los mismos. El fuego está rodeado de un halo mágico que genera un gran poder de atención y admiración, es por ello que puede ser utilizado como un recurso didáctico que atraiga al estudiante hacia el fascinante mundo de la química.Many centuries have past since primitive men first took control of fire and the modern fireworks that end celebrations across the world. However, the chemical laws involved in the two processes are still the same. Fire is surrounded by magical aura that powerfully catches people attention. In this sense, it can be properly used as a didactic resource, attracting our students towards the fascinating world of chemistry

Propuestas prácticas en la docencia de Dº Mercantil y Dº Procesal para la adquisición de competencias de ejercicio de la abogacía

One of the key indicators of EHEA is the employability of graduated law students. Along with the new regulation concerning becoming a lawyer in Spain, precisely the acquisition of such skills and competences is essential in the design and implementation of the new degrees. We analyse this issues regarding the teaching of two subjects: Commercial Law and Procedural Law.Uno de los indicadores clave de la calidad en el EEES es la inserción de los egresados en el mercado laboral. Existe un nuevo marco legal habilitante para colegiarse, y cuyo elemento clave son precisamente las habilidades y competencias adquiridas en los estudios de Grado y Postgrado. Sobre la base de la docencia del Derecho Procesal y el Derecho Mercantil, y la implementación de experiencias prácticas de innovación docente, se proponen una serie de pautas en este sentido

Linear stability of a plane front in solid combustion at large heat of reaction

The existence and linear stability of a uniformly propagating plane front in solid combustion are considered under the assumption of a large heat of reaction, which is of interest in pyrotechnic mixtures. The Zel'dovich number is not necessarily large, and the chemical reaction is not confined to a reaction sheet for typical values of the parameters. Thus the effective calculation of the fronts and the analysis of their stability rely on qualitative methods and on some numerics. It is seen that there is always a minimum burning rate and that the front is stable only if the heat of reaction is sufficiently large. A comparison is made with analytical results obtained from a phenomenological delta-function model

Partitioning approach for large wind farms: active power control for optimizing power reserve

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Nowadays, large wind farms are expected to guarantee stability of the electrical grid contributing with ancillary services, such as frequency support. To this end, wind farm controllers must set the power generation of each turbine to compensate generation and demand imbalances. With the aim of optimizing primary frequency support, this paper proposes a partitioning approach to split large wind farms into several disjoint subsets of turbines according to the wake propagations through the wind farm. The partitioning problem is solved as a mixed-integer multi-objective optimization problem stated to maximize the strength of the coupling among the turbines due to the wake effect. Thus, no additional information sharing related to the wake propagations needs to be considered between the subsets. Different control tasks are assigned to the local controller of each subset, such that the total power generated meets the power demanded by the grid while the power reserve for enhancing primary frequency support is maximized. Finally, as an application of the proposed model, a decentralized wind farm control strategy is designed and compared with a centralized approach.Peer ReviewedPostprint (author's final draft