No abstract

A 6-dimensional grand unified theory with the compact space having the topology of a real projective plane, i.e., a 2-sphere with opposite points identified, is considered. The space is locally flat except for two conical singularities where the curvature is concentrated. One supersymmetry is preserved in the effective 4d theory. The unified gauge symmetry, for example SU(5) , is broken only by the non-trivial global topology. In contrast to the Hosotani mechanism, no adjoint Wilson-line modulus associated with this breaking appears. Since, locally, SU(5) remains a good symmetry everywhere, no UV-sensitive threshold corrections arise and SU(5)-violating local operators are forbidden. Doublettriplet splitting can be addressed in the context of a 6d N = 2 super Yang-Mills theory with gauge group SU(6). If this symmetry is first broken to SU(5) at a fixed point and then further reduced to the standard model group in the above non-local way, the two light Higgs doublets of the MSSM are predicted by the group-theoretical and geometrical structure of the model.

We study the Josephson effect in clean heterojunctions that consist of superconductors connected through two metallic ferromagnets with insulating interfaces. We solve the scattering problem based on the Bogoliubov-de Gennes equation for any relative orientation of in-plane magnetizations, arbitrary transparency of interfaces, and mismatch of Fermi wave vectors. Both spin singlet and triplet superconducting correlations are taken into account, and the Josephson current is calculated as a function of the ferromagnetic layers thicknesses and of the angle α between their magnetizations. We find that the critical Josephson current Ic is a monotonic function of α when the junction is far enough from 0 − π transitions. This holds when ferromagnets are relatively weak. For stronger ferromagnets, variation of α induces switching between 0 and π states and Ic(α) is non-monotonic function, displaying characteristic dips at the transitions. However, the non-monotonicity is the effect of a weaker influence of the exchange potential in the case of non-parallel magnetizations. No substantial impact of spin-triplet superconducting correlations on the Josephson current has been found in the clean limit. Experimental control of the critical current and 0−π transitions by varying the angle between magnetizations is suggested.

In (S/F) hybrids the suppression of superconductivity by the exchange field h(ex) of the ferromagnet can be partially lifted when different directions of h(ex) are sampled simultaneously by the Cooper pair. In F/S/F trilayers where the magnetization directions of the F layers can be controlled separately, this leads to the so-called spin switch. Here we show that domain walls in a single F layer yield a similar effect. We study the transport properties of Ni(0.80)Fe(0.20)/Nb bilayers structured in strips of different sizes. For large samples a clear enhancement of superconductivity takes place in the resistive transition, in the very narrow field range (order of 0.5 mT) where the magnetization of the Py layer switches and many domains are present. This effect is absent in microstructured samples.

There was an error in the sign of the vector product of M and H eff in the Landau-Lifshitz-Gilbert equation, Eq. (6) in the original Letter, which effectively corresponds to the sign change of gyromagnetic ratio γ. Therefore the presented results correspond simply to the inverted direction of the spin precession. This does not affect the qualitative conclusions of the Letter but leads to some sign changes in the formulas.Equation (9) should readEquation (11) should readExpression (12) should readwith Ω AE ¼ ðω AE 1Þ 2 þ α 2 ω 2 . m z -1 -0.5 0 0.5 1 0.7 0.8 0.9 1 1.1 Γ=ω=0.5, α=0.6, r=1 (b) m z -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 Γ=ω=1, α=0.1, r=1 (c) m z -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 Γ=ω=1, α=0.05, r=5 (d) t m z (t) 0 0.5 1 1.5 2 2.5 3 -1 0 1 Γ=5π, ω=5 α=0.1, r=0.1 (a) analytic numeric m y m x m y FIG. 2. Results of numerical analysis of the magnetic moment dynamics of the φ 0 -junction. (a) Reversal of m z from analytical expression Eq. (15) (dashed curve) and numerical one (normal curve). The other curves are related to the M trajectory: (b) in strong damping case (c) and (d) in the strong coupling regime revealing incomplete and complete magnetic moment reversal, respectively. PHYSICAL REVIEW LETTERS 123, 169901(E) (2019) 0031-9007=19=123(16)=169901(2) 169901-1