Topological Superconductivity induced by Ferromagnetic Metal Chains

Recent experiments have provided evidence that one-dimensional (1D) topological superconductivity can be realized experimentally by placing transition metal atoms that form a ferromagnetic chain on a superconducting substrate. We address some properties of this type of systems by using a Slater-Koster tight-binding model. We predict that topological superconductivity is nearly universal when ferromagnetic transition metal chains form straight lines on superconducting substrates and that it is possible for more complex chain structures. The proximity induced superconducting gap is $\sim \Delta E_{so} / J$ where $\Delta$ is the $s$-wave pair-potential on the chain, $E_{so}$ is the spin-orbit splitting energy induced in the normal chain state bands by hybridization with the superconducting substrate, and $J$ is the exchange-splitting of the ferromagnetic chain $d$-bands. Because of the topological character of the 1D superconducting state, Majorana end modes appear within the gaps of finite length chains. We find, in agreement with experiment, that when the chain and substrate orbitals are strongly hybridized, Majorana end modes are substantially reduced in amplitude when separated from the chain end by less than the coherence length defined by the $p$-wave superconducting gap. We conclude that Pb is a particularly favorable substrate material for ferromagnetic chain topological superconductivity because it provides both strong $s-$wave pairing and strong Rashba spin-orbit coupling, but that there is an opportunity to optimize properties by varying the atomic composition and structure of the chain. Finally, we note that in the absence of disorder a new chain magnetic symmetry, one that is also present in the crystalline topological insulators, can stabilize multiple Majorana modes at the end of a single chain.Comment: 19 pages, 15 figures; an analysis of Majorana decay length scale has been added in the revised versio

The influence of modification by superdispersed powders on the lead-tin-base bronze structure

The paper presents data on the influence of additives of the pre-treated aluminium oxide powder on the structure of cast lead-tin-based bronzes. Different quantities of the modifier, based on the superdispersed aluminum oxide powder, were added to the bronze melt. The studies have shown that addition of a small amount of aluminum oxide powder (0.07... 0.25 %) allows modifying the micro structure of the obtained castings. This modification includes grain refinement, reduction of the matrix dendrites size of tin solid solution in copper, as well as formation of spherical inclusions of the low-melting phase - lead. In this case, the addition of such modifier influences weakly the morphology and the quantity of solid eutectoid inclusions based on electron compound Cu[31] Sn[8]

Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor

Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero energy end states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains.Comment: 18 pages, 5 figures, and supplementary information. appears in Science (2014

One-dimensional Topological Edge States of Bismuth Bilayers

The hallmark of a time-reversal symmetry protected topologically insulating state of matter in two-dimensions (2D) is the existence of chiral edge modes propagating along the perimeter of the system. To date, evidence for such electronic modes has come from experiments on semiconducting heterostructures in the topological phase which showed approximately quantized values of the overall conductance as well as edge-dominated current flow. However, there have not been any spectroscopic measurements to demonstrate the one-dimensional (1D) nature of the edge modes. Among the first systems predicted to be a 2D topological insulator are bilayers of bismuth (Bi) and there have been recent experimental indications of possible topological boundary states at their edges. However, the experiments on such bilayers suffered from irregular structure of their edges or the coupling of the edge states to substrate's bulk states. Here we report scanning tunneling microscopy (STM) experiments which show that a subset of the predicted Bi-bilayers' edge states are decoupled from states of Bi substrate and provide direct spectroscopic evidence of their 1D nature. Moreover, by visualizing the quantum interference of edge mode quasi-particles in confined geometries, we demonstrate their remarkable coherent propagation along the edge with scattering properties that are consistent with strong suppression of backscattering as predicted for the propagating topological edge states.Comment: 15 pages, 5 figures, and supplementary materia

Influenza (H5N1) Viruses in Poultry, Russian Federation, 2005–2006

Migrating waterfowl may be the primary source of influenza (H5N1) in western Siberia and the European part of the Russian Federation

Measurement-induced entanglement and teleportation on a noisy quantum processor

Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors

Non-Abelian braiding of graph vertices in a superconducting processor

Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing