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Parafermionic zero modes are a novel set of excitations displaying non-Abelian statistics somewhat richer than that of Majorana modes. These modes are predicted to occur when nearby fractional quantum Hall edge states are gapped by an interposed superconductor. Despite substantial experimental progress, we argue that the necessary crossed Andreev reflection in this arrangement is a challenging milestone to reach. We propose a superconducting quantum dot array structure on a fractional quantum Hall edge that can lead to parafermionic zero modes from coherent superconducting forward scattering on a quantum Hall edge. Such coherent forward scattering has already been demonstrated in recent experiments. We show that for a spin-singlet superconductor interacting with loops of spin unpolarized 2/3 fractional quantum edge, even an array size of order 10 should allow one to systematically tune into a parafermionic degeneracy.

We study charge transport through a floating mesoscopic superconductor coupled to counterpropagating fractional quantum Hall edges at filling fraction $\ensuremath{\nu}=2/3$. We consider a superconducting island with finite charging energy and investigate its effect on transport through the device. We calculate conductance through such a system as a function of temperature and gate voltage applied to the superconducting island. We show that transport is strongly affected by the presence of parafermionic zero modes, leading at zero temperature to a zero-bias conductance quantized in units of $\ensuremath{\nu}{e}^{2}/h$ independent of the applied gate voltage.

Eu and Mn doped NaMgF3 nanoparticles have been made using a reverse micro-emulsion method. All nanoparticles show Mn2+, Eu2+, or Eu3+ photoluminescence (PL) and radioluminescence (RL) as well as PL from an unidentified defect that does not display RL. The Mn2+ sample contains PL emissions from distorted and undistorted Mn2+ sites but the RL is dominated by the undistorted Mn2+ site. The PL lifetime is lowest for the highest Eu concentration. This may be due to energy transfer from Eu3+ sites in the core to Eu3+ sites near the surface followed by non-radiative decay. However, the possibility that Eu3+ substitution leads to more non-radiative decay sites in the core cannot be excluded. The internal quantum efficiency at 270 K is highest for the NaMgF3:1% Eu nanoparticles (76%). The RL is independent of dose after an initial ∼10 kGy irradiation.

BaMgF 4 nanoparticles doped with Ce 3+ , Eu 3+ , Mn 2+ , and Nd 3+ have been successfully synthesized using a reverse microemulsion method. They form nanorods that aggregate into “moustache” shaped clusters. All doped samples show photoluminescence where the Ce 3+ and Eu 3+ photoluminescence spectra are consistent with substitution onto different crystal sites, while only a single site was found for the Mn 2+ doped sample. Mn 2+ was successfully sensitized by Ce 3+ in BaMgF 4 :Mn 2+ :Ce 3+ nanoparticles. The Ce 3+ PL lifetimes are strongly wavelength dependent, which could be due to different Ce 3+ sites with different PL lifetimes as well as energy transfer between Ce 3+ sites. Transparent thick polymer films containing nanoparticles have been made. The appearance of photoluminescence in rare earth and transition metal doped BaMgF 4 nanoparticles and the ability to make transparent thick films means that the BaMgF 4 nanoparticles have a range of potential applications that include optical amplification.

Photoluminescence (PL), PL lifetime, and radioluminescence (RL) measurements were made on LaF3 nanoparticles doped with Eu3+ or Sm3+. The radiative lifetimes decreased with increasing rare earth concentrations, which can be attributed to energy transfer to the surface of the nanoparticles followed by non-radiative recombination. The RL signal increases with increasing concentration for Eu3+ concentrations up to 20% Eu3+ but it saturates and disappears for >10% Sm3+. A dose-independent RL was observed up to 10 kGy during continual X-ray irradiation for Eu3+ and Sm3+ doped nanoparticles, which is advantageous for real time dosimetry applications (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we report the results from characterization and optical measurements on samarium doped KMgF3 nanoparticles. Photoluminescence (PL) is observed that can be attributed to Sm2+ and Sm3+. The Sm2+ temperature dependent PL lifetime data can be interpreted in terms of back transfer from the 5D0 level to the lowest 5d level followed by non-radiative decay from the 5d level.

We show that the $\nu=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a function of the relevant length scales, in spite of the presence of gapless excitations, including gapless fermions. These results are compatible with charge conservation, but do not require it. We discuss generalizations to other integer and fractional quantum Hall states, and classify possible mechanisms for appearance of Majorana zero modes at domain walls., Comment: Published version, 12 pages, 3 figures. Fourth author added

In this study, we examine effective field theories of superconducting phases with topological order, making a connection to proposed realizations of exotic topological phases (including those hosting Ising and Fibonacci anyons) in superconductor-quantum Hall heterostructures. Our effective field theories for the non-Abelian superconducting states are non-Abelian Chern-Simons theories in which the condensation of vortices carrying non-Abelian gauge flux leads to the associated Abelian quantum Hall states. This Chern-Simons-Higgs condensation process is dual to the emergence of superconducting non-Abelian topological phases in coupled chain constructions. In such transitions, the chiral central charge of the system generally changes, so they fall outside the description of bosonic condensation transitions put forth by Bais and Slingerland [F. A. Bais and J. K. Slingerland, Phys. Rev. B 79, 045316 (2009)] (though the two approaches agree when the described transitions coincide). Our condensation process may be generalized to Chern-Simons theories based on arbitrary Lie groups, always describing a transition from a Lie algebra to its Cartan subalgebra. We include several instructive examples of such transitions.

The molecular structure of (Ph3SnO2C)3C6H3 reveals distorted tetrahedral C3O geometries for each tin atom. No intermolecular Sn...O associations occur between the molecules so that the trinuclear molecule may be considered monomeric. An increase in coordination number at tin is indicated by 119Sn NMR measurements conducted in d6-DMSO solution and this has been confirmed by a structure analysis of (DMSO·Ph3SnO2C)3C6H3·2 DMSO. In this structure, the tin atom geometries are distorted trigonal bipyramidal, existing within trans-C3O2 donor sets. Thus, while is it possible for the tin atoms to increase their coordination numbers in (Ph3SnO2C)3C6H3, molecular aggregation to form polymeric arrays is precluded, most likely due to steric constraints.

Heterostructures formed by quantum Hall systems and superconductors have recently been shown to support widely coveted Majorana fermion zero-modes and still more exotic `parafermionic' generalizations. Here we establish that probing such zero-modes using quantum Hall edge states yields non-local transport signatures that pave the way towards a variety of novel circuit elements. In particular, we demonstrate quite generally that at low energies the zero-modes convert chirally moving quasiparticles into oppositely charged quasiholes propagating in the same direction---that is, they swap the sign of the chiral edge currents. One may then construct new and potentially useful circuit elements using this `perfect Andreev conversion' process, including superconducting current and voltage mirrors as well as transistors for fractional charge currents. Characterization of these circuit elements should provide striking evidence of the zero-mode physics., Comment: 7 pages, 5 figures, v2: references added

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z_3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that---unlike Ising anyons---allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a two-fold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types yet depending on non-universal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements., Comment: 37 pages. v2 fixed typos and clarified some issue

Under appropriate external conditions a semiconductor nanowire in proximity to an $s$-wave superconductor can be in a topological superconducting (TS) phase. This phase supports localized zero-energy Majorana fermions at the ends of the wire. However, the non-Abelian exchange statistics of Majorana fermions is difficult to verify because of the one-dimensional topology of such wires. In this paper we propose a scheme to transport Majorana fermions between the ends of different wires using tunneling, which is shown to be controllable by gate voltages. Such tunneling-generated hops of Majorana fermions can be used to exchange the Majorana fermions. The exchange process thus obtained is described by a non-Abelian braid operator that is uniquely determined by the well-controlled microscopic tunneling parameters.

Heterostructures of spin-orbit coupled materials with s-wave superconductors are thought to be capable of supporting zero-energy Majorana bound states. Such excitations are known to obey non-Abelian statistics in two dimensions, and are thus relevant to topological quantum computation (TQC). In a one-dimensional system, Majorana states are localized to phase boundaries. In order to bypass the constraints of one-dimension, a wire network may be created, allowing the exchange of Majoranas by way of junctions in the network. Alicea et al. have proposed such a network as a platform for TQC, showing that the Majorana bound states obey non-Abelian exchange statistics even in quasi-one-dimensional systems. Here we show that the particular realization of non- Abelian statistics produced in a Majorana wire network is highly dependent on the local properties of individual wire junctions. For a simply connected network, the possible realizations can be characterized by the chirality of individual junctions. There is in general no requirement for junction chiralities to remain consistent across a wire network. We show how the chiralities of different junctions may be compared experimentally and discuss the implications for TQC in Majorana wire networks., Comment: 8 pages, 4 figures, some additional discussion. Updated version for journal submission

Recent proposals using heterostructures of superconducting and either topologically insulating or semiconducting layers have been put forth as possible platforms for topological quantum computation. These systems are predicted to contain Ising anyons and share the feature of having only neutral edge excitations. In this note, we show that these proposals can be combined with the recently proposed "sack geometry" for implementation of a phase gate in order to conduct robust universal quantum computation. In addition, we propose a general method for adjusting edge tunneling rates in such systems, which is necessary for the control of interferometric devices. The error rate for the phase gate in neutral Ising systems is parametrically smaller than for a similar geometry in which the edge modes carry charge: it goes as $T^3$ rather than $T$ at low temperatures. At zero temperature, the phase variance becomes constant at long times rather than carrying a logarithmic divergence., 5 pages, 1 figure

The motion of a vortex domain wall in a ferromagnetic strip of submicron width under the influence of an external magnetic field exhibits three distinct dynamical regimes. In a viscous regime at low fields the wall moves rigidly with a velocity proportional to the field. Above a critical field the viscous motion breaks down giving way to oscillations accompanied by a slow drift of the wall. At still higher fields the drift velocity starts rising with the field again but with a much lower mobility dv/dH than in the viscous regime. To describe the dynamics of the wall we use the method of collective coordinates that focuses on soft modes of the system. By retaining two soft modes, parametrized by the coordinates of the vortex core, we obtain a simple description of the wall dynamics at low and intermediate applied fields that describes both the viscous and oscillatory regimes below and above the breakdown. The calculated dynamics agrees well with micromagnetic simulations at low and intermediate values of the driving field. In higher fields, additional modes become soft and the two-mode approximation is no longer sufficient. We explain some of the significant features of vortex domain wall motion in high fields through the inclusion of additional modes associated with the half-antivortices on the strip edge., Minor revisions as suggested by referee

We express dynamics of domain walls in ferromagnetic nanowires in terms of collective coordinates generalizing Thiele's steady-state results. For weak external perturbations the dynamics is dominated by a few soft modes. The general approach is illustrated on the example of a vortex wall relevant to recent experiments with flat nanowires. A two-mode approximation gives a quantitatively accurate description of both the steady viscous motion of the wall in weak magnetic fields and its oscillatory behavior in moderately high fields above the Walker breakdown., Comment: 4 pages, update to published version

We discuss a new type of topological defect in XY systems for which the O (2) symmetry is broken in the presence of a boundary. Of particular interest is the appearance of such defects in nanomagnets with a planar geometry. They are manifested as kinks of magnetization along the edge and can be viewed as halfvortices with winding numbers ±1/2. We argue that the halfvortices play a role in flat nanomagnetics equally important to that of ordinary bulk vortices. We show that domain walls found in experiments and numerical simulations in strips and rings are composite objects containing two or more elementary defects. We also discuss a closely related system: the two-dimensional smectic liquid crystal films with planar boundary condition.

We examine the T=0 phase diagram of a thin ferromagnetic film with a strong out-of-plane anisotropy in the vicinity of the reorientation phase transition (with Co on Pt as an example). The phase diagram in the anisotropy-applied field plane is universal in the limit where the film thickness is the shortest length scale. It contains uniform fully magnetized and canted phases, as well as periodically nonuniform states: a weakly modulated spin-density wave and strongly modulated stripes. We determine the boundaries of metastability of these phases and point out the existence of a critical point at which the difference between the SDW and stripes vanishes. Out-of-plane magnetization curves exhibit a variety of hysteresis loops caused by the coexistence of one or more phases. Additionally, we study the effect of a system edge on the orientation of stripes. We compare our results with recent experiments., Comment: added references and clarified derivations in response to referee comments

Magnetostatic interactions between vortices in closely spaced planar structures are important for applications including vortex-based magnonic crystals and spin torque oscillator networks. Analytical theories that include magnetostatic interaction effects have been proposed but have not yet been rigorously tested. Here, we compare micromagnetic simulations of the dynamics of magnetic vortices confined in three disks in an equilateral triangle configuration to analytical theories that include coupling. Micromagnetic simulations show that the magnetostatic coupling between the disks leads to splitting of the gyrotropic resonance into three modes and that the frequency splitting increases with decreasing separation. The temporal profiles of the magnetization depend on the vortex polarities and chiralities; however, the frequencies depend only on the polarity combinations and will fall into one of two categories: all polarities equal or one polarity opposite to the others, where the latter leads to a larger frequency splitting. Although the magnitude of the splitting observed in the simulations is larger than what is expected based on purely dipolar interactions, a simple analytical model that assumes dipole-dipole coupling captures the functional form of the frequency splitting and the motion patterns just as well as more complex models.

We report unexpected phenomena during magnetization reversal in ultrathin Co films and $\mathrm{Co}/\mathrm{Pt}$ multilayers with perpendicular anisotropy. Using magneto-optical Kerr microscopy and magnetic force microscopy we have observed asymmetrical nucleation centers where the reversal begins for one direction of the field only and is characterized by an acute asymmetry of domain-wall mobility. We have also observed magnetic domains with a continuously varying average magnetization, which can be explained in terms of the coexistence of three magnetic phases: up, down, and striped.

Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1/2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaux. In particular, anisotropic interactions generically open a gap in the region between the plateaux, but we show that this gap closes upon entering fractional plateaux. All of these conclusions, based on analytical arguments, are supported by extensive Density Matrix Renormalization Group calculations., Comment: 15 pages, 15 figures. minor changes in text

In the title compound, C45H40N4O5, the cyclohexane entity on the (3-cyano-2,5-dihydrofuran-2-ylidene)propanedinitrile group, which replaces the usual dimethyl substituents, has not perturbed the delocalization geometry significantly. Weak intermolecular interactions, viz. C—H...N(cyano), C—H...O(ether), C—H...π and π–π [between the aromatic rings with the shortest centroid–centroid distance of 3.603 (3) Å], consolidate the crystal packing, which exhibits voids of 57 Å3.