The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice Sicily in the period June 23 - July 2 , was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium Radiative Majorana Neutrino Masses.
We present new radiative mechanisms for generating Majorana neutrino masses, within an extension of the standard model that successfully generates radiative charged lepton masses, order by order, from heavy sequential leptons. Only the new sequential neutral lepton has a right-handed partner, and its Majorana mass provides the seed for Majorana neutrino mass generation.
The Majorana Experiment. Aalseth, Craig E. The Majorana Collaboration is assembling an array of HPGe detectors to search for neutrinoless double-beta decay in 76Ge. Initially, Majorana aims to construct a prototype module to demonstrate the potential of a future 1-tonne experiment. The design and potential reach of this prototype Demonstrator module are presented. Quantized Majorana conductance. Das; Kouwenhoven, Leo P. Majorana zero-modes - a type of localized quasiparticle - hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool for identifying the presence of Majorana zero-modes, for instance as a zero-bias peak in differential conductance.
Majorana entanglement bridge. We study the concurrence of entanglement between two quantum dots in contact to Majorana bound states on a floating superconducting island. The distance between the Majorana states, the charging energy of the island, and the average island charge are shown to be decisive parameters for the efficiency of entanglement generation.
We find that long-range entanglement with basically distance-independent concurrence is possible over wide parameter regions, where the proposed setup realizes a " Majorana entanglement bridge. Accurate analytical expressions for the concurrence are derived both for the static and the time-dependent cases. Our results indicate that entanglement formation in interacting Majorana devices can be fully understood in terms of an interplay of elastic cotunneling also referred to as "teleportation" and crossed Andreev reflection processes.
Majorana zero-modes—a type of localized quasiparticle—hold great promise for topological quantum computing. The Majorana symmetry protects the quantization against disorder, interactions and variations in the tunnel coupling. The height of our zero-bias peak remains constant despite changing parameters such as the magnetic field and tunnel coupling, indicating that it is a quantized conductance plateau.
We distinguish this quantized Majorana peak from possible non- Majorana origins by investigating its robustness to electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of Majorana zero-modes in the system, consequently paving the way for future braiding experiments that could lead to topological quantum computing. Aguayo Navarrete, Estanislao; Avignone, F. The current, primary focus is the construction of the Majorana Demonstrator experiment, an R and D effort that will field approximately 40 kg of germanium detectors with mixed enrichment levels.
This article provides a status update on the construction of the Demonstrator. Vortex loops and Majoranas. We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We give some general results and then focus on ladder Hamiltonian examples as a test of further ideas. Two methods yield exact results: i A mapping of certain spin Hamiltonians to quartic interactions of Majoranas shows that the spectra of these two examples coincide.
Two additional methods suggest wider applicability of these results: iii Numerical evidence suggests similar behavior for certain systems without reflection symmetry. Magnetic Majorana Fermions. Condensed matter systems provide emergent mini-universes in which quasiparticles may exist which do not correspond to any experimentally detected elementary particle. Topological quantum materials have been particularly productive in this regard, with the present search focussing on Majorana fermions, known theoretically already for decades. Here, we discuss manifestations of magnetic Majorana fermions in the Kitaev model.
We place particular emphasis on their fate when perturbations, such as Heisenberg terms, are added to the ideal model system, and address experimental signatures of their vestiges in phases adjacent to the spin liquid. Boosting Majorana Zero Modes. Full Text Available One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase.
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Their non-Abelian nature allows for processing quantum information by braiding operations that are insensitive to local perturbations, making Majorana zero modes a promising platform for topological quantum computation. Motivated by the ultimate goal of executing quantum-information processing on a finite time scale, we study domain walls moving at a constant velocity.
We exploit an effective Lorentz invariance of the Hamiltonian to obtain an exact solution of the associated quasiparticle spectrum and wave functions for arbitrary velocities. Essential features of the solution have a natural interpretation in terms of the familiar relativistic effects of Lorentz contraction and time dilation. We find that the Majorana zero modes remain stable as long as the domain wall moves at subluminal velocities with respect to the effective speed of light of the system. However, the Majorana bound state dissolves into a continuous quasiparticle spectrum after the domain wall propagates at luminal or even superluminal velocities.
This relativistic catastrophe implies that there is an upper limit for possible braiding frequencies even in a perfectly clean system with an arbitrarily large topological gap. We also exploit our exact solution to consider domain walls moving past static impurities present in the system. Majorana fermion codes. We initiate the study of Majorana fermion codes MFCs. These codes can be viewed as extensions of Kitaev's one-dimensional 1D model of unpaired Majorana fermions in quantum wires to higher spatial dimensions and interacting fermions. The purpose of MFCs is to protect quantum information against low-weight fermionic errors, that is, operators acting on sufficiently small subsets of fermionic modes.
We examine to what extent MFCs can surpass qubit stabilizer codes in terms of their stability properties. A general construction of 2D MFCs is proposed that combines topological protection based on a macroscopic code distance with protection based on fermionic parity conservation. Algebra of Majorana doubling. Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum.
For general nonlinear interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state. Effective Majorana neutrino decay. We study the decay of heavy sterile Majorana neutrinos according to the interactions obtained from an effective general theory. We describe the two- and three-body decays for a wide range of neutrino masses.
The results obtained and presented in this work could be useful for the study of the production and detection of these particles in a variety of high energy physics experiments and astrophysical observations. We show in different figures the dominant branching ratios and the total decay width.
The Majorana Demonstrator. Aguayo, Estanislao; Fast, James E. A brief review of the history and neutrino physics of double beta decay is given. The application of point contact PC detectors to the experiment is discussed, including the effectiveness of pulse shape analysis. Universal Majorana thermoelectric noise. Thermoelectric phenomena resulting from an interplay between particle flows induced by electric fields and temperature inhomogeneities are extremely insightful as a tool providing substantial knowledge about the microscopic structure of a given system. By tuning, e. Even more exciting physics emerges when the system's electronic degrees freedom split to form Majorana fermions which make the thermoelectric dynamics universal.
Here, we propose revealing these unique universal signatures of Majorana fermions in strongly nonequilibrium quantum dots via noise of the thermoelectric transport beyond linear response. It is demonstrated that whereas mean thermoelectric quantities are only universal at large-bias voltages, the noise of the electric current excited by an external bias voltage and the temperature difference of the contacts is universal at any bias voltage. We provide truly universal, i.
Elliott, S. Nuclear Lab. The Majorana Collaboration proposes a design based on using high-purity enriched 76 Ge crystals deployed in ultra- low background electroformed Cu cryostats and using modern analysis techniques that should be capable of reaching the required sensitivity while also being scalable to a 1-tonne size. We plan to deploy and evaluate two different Ge detector technologies, one based on a p-type configuration and the other on n-type.
Majorana box qubits. Quantum information protected by the topology of the storage medium is expected to exhibit long coherence times. Another feature is topologically protected gates generated through braiding of Majorana bound states MBSs. However, braiding requires structures with branched topological segments which have inherent difficulties in the semiconductor—superconductor heterostructures now believed to host MBSs.
In this paper, we construct quantum bits taking advantage of the topological protection and non-local properties of MBSs in a network of parallel wires, but without relying on braiding for quantum gates. The elementary unit is made from three topological wires, two wires coupled by a trivial superconductor and the third acting as an interference arm.
Coulomb blockade of the combined wires spawns a fractionalized spin, non-locally addressable by quantum dots used for single-qubit readout, initialization, and manipulation. We describe how the same tools allow for measurement-based implementation of the Clifford gates, in total making the architecture universal. Proof-of-principle demonstration of topologically protected qubits using existing techniques is therefore within reach.
Majorana Higgses at colliders. Collider signals of heavy Majorana neutrino mass origin are studied in the minimal Left-Right symmetric model, where their mass is generated spontaneously together with the breaking of lepton number. The latter features tri- and quad same-sign lepton final states that break lepton number by four units and have no significant background. In both cases up to four displaced vertices may be present and their displacement may serve as a discriminating variable. The backgrounds at the LHC, including the jet fake rate, are estimated and the resulting sensitivity to the Left-Right breaking scale extends well beyond 10 TeV.
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Quantum computing with Majorana fermion codes. We establish a unified framework for Majorana -based fault-tolerant quantum computation with Majorana surface codes and Majorana color codes. All logical Clifford gates are implemented with zero-time overhead. This is done by introducing a protocol for Pauli product measurements with tetrons and hexons which only requires local 4- Majorana parity measurements. An analogous protocol is used in the fault-tolerant setting, where tetrons and hexons are replaced by Majorana surface code patches, and parity measurements are replaced by lattice surgery, still only requiring local few- Majorana parity measurements.
To this end, we discuss twist defects in Majorana fermion surface codes and adapt the technique of twist-based lattice surgery to fermionic codes. Moreover, we propose a family of codes that we refer to as Majorana color codes, which are obtained by concatenating Majorana surface codes with small Majorana fermion codes. Majorana surface and color codes can be used to decrease the space overhead and stabilizer weight compared to their bosonic counterparts. Majorana Zero Modes in Graphene. Full Text Available A clear demonstration of topological superconductivity TS and Majorana zero modes remains one of the major pending goals in the field of topological materials.
One common strategy to generate TS is through the coupling of an s-wave superconductor to a helical half-metallic system. Numerous proposals for the latter have been put forward in the literature, most of them based on semiconductors or topological insulators with strong spin-orbit coupling. Here, we demonstrate an alternative approach for the creation of TS in graphene-superconductor junctions without the need for spin-orbit coupling.
We show how canted antiferromagnetic ordering in the graphene bulk close to neutrality induces TS along the junction and gives rise to isolated, topologically protected Majorana bound states at either end. We also discuss possible strategies to detect their presence in graphene Josephson junctions through Fraunhofer pattern anomalies and Andreev spectroscopy. The latter, in particular, exhibits strong unambiguous signatures of the presence of the Majorana states in the form of universal zero-bias anomalies.
Remarkable progress has recently been reported in the fabrication of the proposed type of junctions, which offers a promising outlook for Majorana physics in graphene systems. Majorana and Majorana -Weyl fermions in lattice gauge theory. In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. Prescriptions based on the overlap formalism do not remove these difficulties.
We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. Abgrall, N. The tracking implementation takes a novel approach based on the schema-free database technology CouchDB. Transportation, storage, and processes undergone by parts such as machining or cleaning are linked to part records. Tracking parts provide a great logistics benefit and an important quality assurance reference during construction. In addition, the location history of parts provides an estimate of their exposure to cosmic radiation.
A web application for data entry and a radiation exposure calculator have been developed as tools for achieving the extreme radio-purity required for this rare decay search. Diaz; Leviner, L. Yu, C. Searches for neutrinoless double-beta decay are understood to be the only viable experimental method for testing the Majorana nature of the neutrino. Observation of this decay would imply violation of lepton number, that neutrinos are Majorana in nature, and provide information on the neutrino mass.
The experiment achieved a high efficiency of converting raw Ge material to detectors and an unprecedented detector energy resolution of 2. This paper summarizes key construction aspects of the Demonstrator and shows preliminary results from initial data. Majorana Thermosyphon Prototype Experimental Results. The Majorana demonstrator will operate at liquid Nitrogen temperatures to ensure optimal spectrometric performance of its High Purity Germanium HPGe detector modules. In order to transfer the heat load of the detector module, the Majorana demonstrator requires a cooling system that will maintain a stable liquid nitrogen temperature.
This cooling system is required to transport the heat from the detector chamber outside the shield. One approach is to use the two phase liquid-gas equilibrium to ensure constant temperature. This cooling technique is used in a thermosyphon. A prototype of such system has been built at PNNL. This document presents the experimental results of the prototype and evaluates the heat transfer performance of the system. The cool down time, temperature gradient in the thermosyphon, and heat transfer analysis are studied in this document with different heat load applied to the prototype.
Status of the Majorana Demonstrator experiment. Martin, R. An overview and status of the experiment are given. Majorana modes in solid state systems and its dynamics. We review the properties of Majorana fermions in particle physics and point out that Majorana modes in solid state systems are significantly different.
The key reason is the concept of anti-particle in solid state systems is different from its counterpart in particle physics. We define Majorana modes as the eigenstates of Majorana operators and find that they can exist both at edges and in the bulk. According to our definition, only one single Majorana mode can exist in a system no matter at edges or in the bulk.
Kitaev's spinless p-wave superconductor is used to illustrate our results and the dynamical behavior of the Majorana modes. Iterants, Fermions and Majorana Operators. Beginning with an elementary, oscillatory discrete dynamical system associated with the square root of minus one, we study both the foundations of mathematics and physics. Position and momentum do not commute in our discrete physics. Their commutator is related to the diffusion constant for a Brownian process and to the Heisenberg commutator in quantum mechanics.
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We take John Wheeler's idea of It from Bit as an essential clue and we rework the structure of that bit to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We show how the dynamical system for the square root of minus one is essentially the dynamics of a distinction whose self-reference leads to both the fusion algebra and the operator algebra for the Majorana Fermion.
In the course of this, we develop an iterant algebra that supports all of matrix algebra and we end the essay with a discussion of the Dirac equation based on these principles.
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Geometry of Majorana neutrino and new symmetries. Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter--antimatter symmetry and some new ways to understand the baryo-genesis problem in cosmology. In the Majorana -Diraco genesis approach there appears a possibility to check the proton and electron non-stability on the very low energy scale.
This can just support a conjecture about the non-completeness of the SM in terms of Istituto di Zoologia fu diretto da Antonio Carruccio Alto Rio Negro del , guidata da Ettore Biocca. Nel periodo universitario, infatti, il Museo della nuova capitale d? Italia fu oggetto di grande attenzione da parte di privati ed enti, a partire dai Savoia, che donarono le loro collezioni o il materiale raccolto durante le spedizioni effettuate.
Il lavoro di revisione in corso sta mettendo in luce una serie di esemplari meritevoli di ulteriori, dettagliate ricerche. A Direct Road to Majorana Fields. The Majorana formalism which describes massive neutral fermions by the help of two-component or four-component spinors is of fundamental importance for the understanding of mathematical aspects of supersymmetric and other extensions of the Standard Model of particle physics, which may play an increasingly important role at the beginning of the LHC era. The interplay between the two-component and the four-component formalism is highlighted in an introductory way.
Majorana particles are predicted both by grand unified theories, in which these particles are neutrinos, and by supersymmetric theories, in which they are photinos, gluinos and other states. Size constraints on a Majorana beam-splitter interferometer: Majorana coupling and surface-bulk scattering. Topological insulator surfaces in proximity to superconductors have been proposed as a way to produce Majorana fermions in condensed matter physics.
One of the simplest proposed experiments with such a system is Majorana interferometry. Here we consider two possibly conflicting constraints on the size of such an interferometer. Coupling of a Majorana mode from the edge the arms of the interferometer to vortices in the center of the device sets a lower bound on the size of the device. On the other hand, scattering to the usually imperfectly insulating bulk sets an upper bound.
From estimates of experimental parameters, we find that typical samples may have no size window in which the Majorana interferometer can operate, implying that a new generation of more highly insulating samples must be explored. Contributed report: Flavor anarchy for Majorana neutrinos. December physics pp. Majorana spin in magnetic atomic chain systems.
In this paper, we establish that Majorana zero modes emerging from a topological band structure of a chain of magnetic atoms embedded in a superconductor can be distinguished from trivial localized zero energy states that may accidentally form in this system using spin-resolved measurements. To demonstrate this key Majorana diagnostics, we study the spin composition of magnetic impurity induced in-gap Shiba states in a superconductor using a hybrid model.
By examining the spin and spectral densities in the context of the Bogoliubov-de Gennes BdG particle-hole symmetry, we derive a sum rule that relates the spin densities of localized Shiba states with those in the normal state without superconductivity. Extending our investigations to a ferromagnetic chain of magnetic impurities, we identify key features of the spin properties of the extended Shiba state bands, as well as those associated with a localized Majorana end mode when the effect of spin-orbit interaction is included.
We then formulate a phenomenological theory for the measurement of the local spin densities with spin-polarized scanning tunneling microscopy STM techniques. By combining the calculated spin densities and the measurement theory, we show that spin-polarized STM measurements can reveal a sharp contrast in spin polarization between an accidental-zero-energy trivial Shiba state and a Majorana zero mode in a topological superconducting phase in atomic chains.
We further confirm our results with numerical simulations that address generic parameter settings. Phase space methods for Majorana fermions. Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The resulting phase-space of covariance matrices belongs to the symmetry class D, one of the non-standard symmetry classes.
This was originally proposed to study mesoscopic normal-metal-superconducting hybrid structures, which is the type of structure that has led to recent experimental observations of Majorana fermions. Under a unitary transformation, it is possible to express these Gaussian operators using real anti-symmetric matrices and Majorana operators, which are much simpler mathematical objects.
We derive differential identities involving Majorana fermion operators and an antisymmetric matrix which are relevant to the derivation of the corresponding Fokker—Planck equations on symmetric space. These enable stochastic simulations either in real or imaginary time. This formalism has direct relevance to the study of fermionic systems in which there are Majorana type excitations, and is an alternative to using expansions involving conventional Fermi operators.
The approach is illustrated by showing how a linear coupled Hamiltonian as used to study topological excitations can be transformed to Fokker—Planck and stochastic equation form, including dissipation through particle losses. Majorana fermion modulated nonequilibrium transport through double quantum dots.
Nonequilibrium electronic transports through a double-QD- Majorana coupling system are studied with a purpose to extract the information to identify Majorana bound states MBSs. It is found that MBSs can help form various transport processes, including the nonlocal crossed Andreev reflection, local resonant Andreev reflection, and cotunneling, depending on the relative position of two dot levels. These processes enrich the signature of average currents and noise correlations to probe the nature of MBSs. We further demonstrate the switching between the current peaks of crossed Andreev reflection and cotunneling, which is closely related to the nonlocal nature of Majorana fermions.
We also propose effective physical pictures to understand these Majorana -assisted transports. Majorana flat bands in anisotropic systems. It has been recently proposed that topologically protected Majorana flat bands MFBs emerge in superconductors with nodal energy spectrum. In this work we introduce a new class of gapful superconductors, in which MFBs can occur due to strong anisotropy.
Our proposal can be for instance experimentally implemented in topological superconductors engineered from i. By investigating the topological properties of both setups, we show that their unique features render them feasible platforms for manipulating the Majorana fermion bandstructure and realizing MFBs. Background Model for the Majorana Demonstrator. Cuesta, C.
The Majorana Collaboration is constructing a system containing 40 kg of HPGe detectors to demonstrate the feasibility and potential of a future tonne-scale experiment capable of probing the neutrino mass scale in the inverted-hierarchy region. This goal is pursued through a combination of a significant reduction of radioactive impurities in construction materials with analytical methods for background rejection, for example using powerful pulse shape analysis techniques profiting from the p-type point contact HPGe detectors technology. The effectiveness of these methods is assessed using simulations of the different background components whose purity levels are constrained from radioassay measurements.
Conservation of lepton charges, massive majorana and massless neutrinos. It is shown that the necessary and sufficient condition for the presence of k massless and n-k massive nondegenerate Majorana neutrinos in a theory with n neutrino flavours and a neutrino mass term of Majorana type is the existence of k standard and no other conserved lepton charges. Two-loop Majorana mass corrections for neutrinos, massless at tree level, are also briefly discussed. Majorana fermion exchange in strictly one dimensional structures. It is generally thought that adiabatic exchange of two identical particles is impossible in one spatial dimension.
Here we describe a simple protocol that permits adiabatic exchange of two Majorana fermions in a one-dimensional topological superconductor wire. On oscillations of neutrinos with Dirac and Majorana masses. Pontecorvo neutrino beam oscillations are discussed assuming both Dirac and Majorana neutrino mass terms. It is proved that none of possible experiments on neutrino oscillations, including those on effects of CP violation, can distinguish between these two possibilities. Neutrino oscillations with concomitant Dirac and Majorana mass terms are also considered.
Three-dimensional Majorana fermions in chiral superconductors. Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface.
We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles.
Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs 4 Sb 12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions. Landau levels of Majorana fermions in a spin liquid. Majorana fermions were originally proposed as elementary particles acting as their own antiparticles.
In recent years, it has become clear that Majorana fermions can instead be realized in condensed-matter systems as emergent quasiparticles, a situation often accompanied by topological order. Stimulated transitions in resonant atom Majorana mixing. Massive neutrinos demand to ask whether they are Dirac or Majorana particles. Majorana neutrinos are an irrefutable proof of physics beyond the Standard Model. As a mixing between two neutral atoms and the observable signal in terms of emitted two-hole X-rays, the strategy, experimental signature and background are different from neutrinoless double beta decay.
The mixing is resonantly enhanced for almost degeneracy and, under these conditions, there is no irreducible background from the standard two-neutrino channel. We reconstruct the natural time history of a nominally stable parent atom since its production either by nature or in the laboratory. After the time periods of atom oscillations and the decay of the short-lived daughter atom, at observable times the relevant "stationary" states are the mixed metastable long-lived state and the non-orthogonal short-lived excited state, as well as the ground state of the daughter atom.
We find that they have a natural population inversion which is most appropriate for exploiting the bosonic nature of the observed atomic transitions radiation. Among different observables of the atom Majorana mixing, we include the enhanced rate of stimulated X-ray emission from the long-lived metastable state by a high-intensity X-ray beam: a gain factor of can be envisaged at current XFEL facilities. On the other hand, the historical population of the daughter atom ground state can be probed by exciting it with a current pulsed optical laser, showing the characteristic absorption lines: the whole population can be excited in a shorter time than typical pulse duration.
Connecting Majorana phases to the geometric parameters of the Majorana unitarity triangle in a neutrino mass matrix model. We have investigated a possible connection between the Majorana phases and geometric parameters of Majorana unitarity triangle MT in two-texture zero neutrino mass matrix. Such analytical relations can, also, be obtained for other theoretical models viz.
As an example, we have considered the two-texture zero neutrino mass model to obtain a relation between Majorana phases and MT parameters that may be probed in various lepton number violating processes. In particular, we find that Majorana phases depend on only one of the three interior angles of the MT in each class of two-texture zero neutrino mass matrix. Nonvanishing areas and nontrivial orientations of these Majorana unitarity triangles indicate nonzero C P violation as a generic feature of this class of mass models.
Majorana quasiparticles in semiconducting carbon nanotubes. Engineering effective p -wave superconductors hosting Majorana quasiparticles MQPs is nowadays of particular interest, also in view of the possible utilization of MQPs in fault-tolerant topological quantum computation. In quasi-one-dimensional systems, the parameter space for topological superconductivity is significantly reduced by the coupling between transverse modes. Together with the requirement of achieving the topological phase under experimentally feasible conditions, this strongly restricts in practice the choice of systems which can host MQPs.
Here, we demonstrate that semiconducting carbon nanotubes CNTs in proximity with ultrathin s -wave superconductors, e. By precise numerical tight-binding calculations in the real space, we show the emergence of localized zero-energy states at the CNT ends above a critical value of the applied magnetic field, of which we show the spatial evolution. Knowing the microscopic wave functions, we unequivocally demonstrate the Majorana nature of the localized states.
An effective four-band model in the k -space, with parameters determined from the numerical spectrum, is used to calculate the topological phase diagram and its phase boundaries in analytic form. Finally, the impact of symmetry breaking contributions, like disorder and an axial component of the magnetic field, is investigated. Classical probabilities for Majorana and Weyl spinors. The functional integral employs a lattice regularization for single Weyl or Majorana spinors.
We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions. Full Text Available We introduce a scheme for preparation, manipulation, and read out of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands.
Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. These pre-braiding experiments can be adapted to other manipulation and read out schemes as well. Search for Majorana fermions in topological superconductors. Pan, Wei [Sandia National Lab. The goal of this project is to search for Majorana fermions a new quantum particle in a topological superconductor a new quantum matter achieved in a topological insulator proximitized by an s-wave superconductor.
Majorana fermions MFs are electron-like particles that are their own anti-particles. MFs are shown to obey non-Abelian statistics and, thus, can be harnessed to make a fault-resistant topological quantum computer. With the arrival of topological insulators, novel schemes to create MFs have been proposed in hybrid systems by combining a topological insulator with a conventional superconductor. Majorana mass term, Dirac neutrinos and selective neutrino oscillations. In the case of three neutrino flavours no oscillation is allowed if the mass spectrum contains one Dirac and one nondegenerate Majorana massive neutrino.
The origin of these selection rules and their implications are discussed and the number of possible CP-violating phases in the lepton mixing matrix when Dirac and Majorana mass eigenstates coexist is given. It consists of two modular arrays of natural and 76Ge-enriched germanium detectors totalling Any neutrinoless double-beta decay search requires a thorough understanding of the background and the signal energy spectra. Data collection is monitored with a thorough regimen, instrumental background events are tagged for removal, and subsequent careful analysis of the collected data is performed to ensure that there are no deeper issues.
This talk will discuss the various techniques employed to ensure the integrity of the measured spectra. Majorana physics through the Cabibbo Haze. Motivated by SO 10 , where the charge two-thirds and neutral Dirac Yukawa matrices are related, we propose, using family symmetry, a special form for the seesaw Majorana matrix; it contains a squared correlated hierarchy, allowing it to mitigate the severe hierarchy of the quark sector.
Current Correlations in a Majorana Beam Splitter. We study current correlations in a T-junction composed of a grounded topological superconductor and of two normal-metal leads which are biased at a voltage V. We show that the existence of an isolated Majorana zero mode in the junction dictates a universal behavior for the cross correlation of the currents through the two normal-metal leads of the junction.
This behavior is robust in the presence of disorder and multiple transverse channels, and persists at finite temperatures. In contrast, an accidental low-energy Andreev bound state gives rise to non-universal behavior of the cross correlation. We employ numerical transport simulations to corroborate our conclusions. Lepton number violating processes and Majorana neutrinos. Some generic properties of lepton number violating processes and their relation to different entries of the Majorana neutrino mass matrix are discussed.
Present and near future experiments searching for these processes, except the neutrinoless double beta decay, are unable to probe light eV mass region and heavy hundred GeV mass region neutrinos. On the other hand, due to the effect of a resonant enhancement, some of lepton number violating decays can be very sensitive to the intermediate-mass neutrinos with typical masses in the hundred MeV region. These neutrinos may appear as admixtures of the three active and an arbitrary number of sterile neutrino species. The experimental constraints on these massive neutrino states are analyzed and their possible cosmological and astrophysical implications are discussed.
Electron teleportation and statistical transmutation in multiterminal Majorana islands. We study a topological superconductor island with spatially separated Majorana modes coupled to multiple normal-metal leads by single-electron tunneling in the Coulomb blockade regime. We show that low-temperature transport in such a Majorana island is carried by an emergent charge-e boson composed of a Majorana mode and an electronic excitation in leads. This transmutation from Fermi to Bose statistics has remarkable consequences.
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For noninteracting leads, the system flows to a non-Fermi-liquid fixed point, which is stable against tunnel couplings anisotropy or detuning away from the charge-degeneracy point. As a result, the system exhibits a universal conductance at zero temperature, which is a fraction of the conductance quantum, and low-temperature corrections with a universal power-law exponent. In addition, we consider Majorana islands connected to interacting one-dimensional leads, and find different stable fixed points near and far from the charge-degeneracy point. Majorana splitting from critical currents in Josephson junctions.
A semiconducting nanowire with strong Rashba spin-orbit coupling and coupled to a superconductor can be tuned by an external Zeeman field into a topological phase with Majorana zero modes. Here we theoretically investigate how this exotic topological superconductor phase manifests in Josephson junctions based on such proximitized nanowires. This includes signatures of the gap inversion at the topological transition and a unique oscillatory pattern that originates from Majorana interference.
Interestingly, this pattern can be modified by tuning the transmission across the junction, thus providing complementary evidence of Majoranas and their energy splittings beyond standard tunnel spectroscopy experiments, while offering further tunability by virtue of the Josephson effect. Quantized charge transport in chiral Majorana edge modes.
Majorana fermions can be realized as quasiparticles in topological superconductors, with potential applications in topological quantum computing. Recently, lattices of magnetic adatoms deposited on the surface of s -wave superconductors—Shiba lattices—have been proposed as a new platform for topological superconductivity. These systems possess the great advantage that they are accessible via scanning-probe techniques and thus enable the local manipulation and detection of Majorana modes.
Using a nonequilibrium Green's function technique we demonstrate that the topological Majorana edge modes of nanoscopic Shiba islands display universal electronic and transport properties. Most remarkably, these Majorana modes possess a quantized charge conductance that is proportional to the topological Chern number, C , and carry a supercurrent whose chirality reflects the sign of C.
These results establish nanoscopic Shiba islands as promising components in future topology-based devices. Majorana zero modes in superconductor-semiconductor heterostructures. Realizing topological superconductivity and Majorana zero modes in the laboratory is a major goal in condensed-matter physics. In this Review, we survey the current status of this rapidly developing field, focusing on proposals for the realization of topological superconductivity in semiconductor-superconductor heterostructures.
We examine materials science progress in growing InAs and InSb semiconductor nanowires and characterizing these systems. We then discuss the observation of robust signatures of Majorana zero modes in recent experiments, paying particular attention to zero-bias tunnelling conduction measurements and Coulomb blockade experiments.
We also outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana -based topological quantum computation. Present Status. Aguayo, E. Rephasing-invariant CP violating parameters with Majorana neutrinos. We analyze the dependence of the squared amplitudes on the rephasing-invariant CP-violating parameters of the lepton sector, involving Majorana neutrinos, for various lepton- conserving and lepton-violating processes.
We analyze the conditions under which the CP-violating effects in such processes vanish, in terms of the minimal set of rephasing invariants, giving special attention to the dependence on the extra CP-violating parameters that are due to the Majorana nature of the neutrinos. The Majorana Demonstrator MJD searches for neutrinoless double-beta decay of 76Ge using arrays of high-purity germanium detectors. If observed, this process would have implications for grand-unification and the predominance of matter over antimatter in the universe.
A problematic background in such large granular detector arrays is posed by alpha particles. In MJD, potential background events that are consistent with energy-degraded alphas originating on the passivated detector surface have been observed. We have studied these events by scanning the passivated surface of a P-type point contact detector like those used in MJD with a collimated alpha source.
We observe that surface alpha events exhibit high charge-trapping, with a significant fraction of the trapped charge being re-released slowly. This leads to both a reduced prompt signal and a measurable change in slope of the tail of a recorded pulse. In this contribution we discuss the characteristics of these events and the filter developed to identify the occurrence of this delayed charge recovery, allowing for the efficient rejection of passivated surface alpha events while retaining We also discuss the impact of this filter on the sensitivity of MJD.
This material is based upon work supported by the U. Full Text Available We study the properties of a quantum dot coupled to a topological superconductor and a normal lead and discuss the interplay between Kondo-and Majorana -induced couplings in quantum dots. The latter appears due to the presence of Majorana zero-energy modes localized, for example, at the ends of the one-dimensional superconductor.
We investigate the phase diagram of the system as a function of Kondo and Majorana interactions using a renormalization-group analysis, a slave-boson mean-field theory, and numerical simulations using the density-matrix renormalization-group method. We show that, in addition to the well-known Kondo fixed point, the system may flow to a new fixed point controlled by the Majorana -induced coupling, which is characterized by nontrivial correlations between a localized spin on the dot and the fermion parity of the topological superconductor and the normal lead.
We compute several measurable quantities, such as differential tunneling conductance and impurity-spin susceptibility, which highlight some peculiar features characteristic to the Majorana fixed point. Sensing Floquet- Majorana fermions via heat transfer. This rich phase diagram survives when the system is coupled to dissipative end reservoirs. Circumventing the obstacle of preparing and measuring quasienergy configurations endemic to Floquet- Majorana detection schemes, we show that stroboscopic heat transport and spin density are robust observables to detect both the dynamical phase transitions and Majorana modes in dissipative settings.
We find that the heat current provides very clear signatures of these Floquet topological phase transitions. In particular, we observe that the derivative of the heat current, with respect to a control parameter, changes sign at the boundaries separating topological phases with differing nonzero numbers of Floquet- Majorana modes.
We present a simple scheme to directly count the number of Floquet- Majorana modes in a phase from the Fourier transform of the local spin density profile. Our results are valid provided the anisotropies are not strong and can be easily implemented in quantum engineered systems. Majorana states in prismatic core-shell nanowires. We consider core-shell nanowires with conductive shell and insulating core and with polygonal cross section.
We investigate the implications of this geometry on Majorana states expected in the presence of proximity-induced superconductivity and an external magnetic field. A typical prismatic nanowire has a hexagonal profile, but square and triangular shapes can also be obtained. The low-energy states are localized at the corners of the cross section, i. The corner localization depends on the details of the shell geometry, i. We study systematically the low-energy spectrum of prismatic shells using numerical methods and derive the topological phase diagram as a function of magnetic field and chemical potential for triangular, square, and hexagonal geometries.
A strong corner localization enhances the stability of Majorana modes to various perturbations, including the orbital effect of the magnetic field, whereas a weaker localization favorizes orbital effects and reduces the critical magnetic field. The prismatic geometry allows the Majorana zero-energy modes to be accompanied by low-energy states, which we call pseudo Majorana , and which converge to real Majoranas in the limit of small shell thickness.
We include the Rashba spin-orbit coupling in a phenomenological manner, assuming a radial electric field across the shell. Topology and symmetry of surface Majorana arcs in cyclic superconductors. We study the topology and symmetry of surface Majorana arcs in superconductors with nonunitary "cyclic" pairing.
Cyclic p -wave pairing may be realized in a cubic or tetrahedral crystal, while it is a candidate for the interior P32 superfluids of neutron stars. The cyclic state is an admixture of full gap and nodal gap with eight Weyl points and the low-energy physics is governed by itinerant Majorana fermions. We here show the evolution of surface states from Majorana cone to Majorana arcs under rotation of surface orientation.
The Majorana cone is protected solely by an accidental spin rotation symmetry and fragile against spin-orbit coupling, while the arcs are attributed to two topological invariants: the first Chern number and one-dimensional winding number. Lastly, we discuss how topologically protected surface states inherent to the nonunitary cyclic pairing can be captured from surface probes in candidate compounds, such as U1 -xThxBe We examine tunneling conductance spectra for two competitive scenarios in U1 -xThxBe13 —the degenerate Eu scenario and the accidental scenario.
Optimal diabatic dynamics of Majorana -based quantum gates. In topological quantum computing, unitary operations on qubits are performed by adiabatic braiding of non-Abelian quasiparticles, such as Majorana zero modes, and are protected from local environmental perturbations. In the adiabatic regime, with timescales set by the inverse gap of the system, the errors can be made arbitrarily small by performing the process more slowly. To enhance the performance of quantum information processing with Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana -based qubits.
While we sacrifice complete topological protection, we impose constraints on the optimal protocol to take advantage of the nonlocal nature of topological information and increase the robustness of our gates. By using the Pontryagin's maximum principle, we show that robust equivalent gates to perfect adiabatic braiding can be implemented in finite times through optimal pulses. In our implementation, modifications to the device Hamiltonian are avoided.
While a noise-induced antiadiabatic behavior, where a slower process creates more diabatic excitations, prohibits indefinite enhancement of the robustness of the adiabatic scheme, our fast optimal protocols exhibit remarkable stability to noise and have the potential to significantly enhance the practical performance of Majorana -based information processing.
Analysis techniques for background rejection at the Majorana Demonstrator. The background rejection techniques to be applied to the data include cuts based on data reduction, pulse shape analysis, event coincidences, and time correlations. Model independent bounds on magnetic moments of Majorana neutrinos. We analyze the implications of neutrino masses for the magnitude of neutrino magnetic moments. For Dirac neutrinos, the bound is several orders of magnitude more stringent than present experimental limits. However, for Majorana neutrinos the magnetic moment contribution to the mass is Yukawa suppressed.
The discovery of a neutrino magnetic moment near present limits would thus signify that neutrinos are Majorana particles. The Kitaev honeycomb lattice is envisioned as an ideal host for Majorana fermions that are created out of the spin liquid background. Our inelastic neutron scattering measurements further corroborate two distinct characters of fractionalized excitations: an Y-like, dispersive, magnetic continuum at higher energies and a dispersionless excitation at low energies around the Brillouin zone center. Skip to main content Skip to table of contents. Advertisement Hide.
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