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      Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor

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          Abstract

          Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. While elementary particles of the Majorana type were not identified yet, quasi-particles with Majorana like properties, born from interacting electrons in the solid, were predicted to exist. Here, we present thorough experimental studies, backed by numerical simulations, of a system composed of an aluminum superconductor in proximity to an indium arsenide nanowire, with the latter possessing strong spin-orbit coupling. An induced 1d topological superconductor - supporting Majorana fermions at both ends - is expected to form. We concentrate on the characteristics of a distinct zero bias conductance peak (ZBP), and its splitting in energy, both appearing only with a small magnetic field applied along the wire. The ZBP was found to be robustly tied to the Fermi energy over a wide range of system parameters. While not providing a definite proof of a Majorana state, the presented data and the simulations support strongly its existence.

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          Fault-tolerant quantum computation by anyons

          A. Kitaev (1997)
          A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.
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            Anyons in an exactly solved model and beyond

            A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static \(\mathbb{Z}_{2}\) gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number \(\nu\). The Abelian and non-Abelian phases of the original model correspond to \(\nu=0\) and \(\nu=\pm 1\), respectively. The anyonic properties of excitation depend on \(\nu\bmod 16\), whereas \(\nu\) itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
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              Controlled polytypic and twin-plane superlattices in iii-v nanowires.

              Semiconductor nanowires show promise for use in nanoelectronics, fundamental electron transport studies, quantum optics and biological sensing. Such applications require a high degree of nanowire growth control, right down to the atomic level. However, many binary semiconductor nanowires exhibit a high density of randomly distributed twin defects and stacking faults, which results in an uncontrolled, or polytypic, crystal structure. Here, we demonstrate full control of the crystal structure of InAs nanowires by varying nanowire diameter and growth temperature. By selectively tuning the crystal structure, we fabricate highly reproducible polytypic and twin-plane superlattices within single nanowires. In addition to reducing defect densities, this level of control could lead to bandgap engineering and novel electronic behaviour.
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                Author and article information

                Journal
                31 May 2012
                2012-07-28
                Article
                10.1038/nphys2479
                1205.7073
                e5ae46e2-2401-4e3a-87e8-ddf59c0980e2

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Nature Physics 8, 887-895 (2012)
                cond-mat.mes-hall

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