Chains of magnetic atoms placed on the surface of an s-wave superconductor with large spin-orbit coupling provide a promising platform for the realization of topological superconducting states characterized by the presence of Majorana zero-energy mod
es. In this work we study the properties of the one-dimensional chain of Yu-Shiba-Rusinov states induced by magnetic impurities using a realistic model for the magnetic atoms that include the presence of multiple scattering channels. These channels are mixed by the spin-orbit coupling and, via the hybridization of the Yu-Shiba-Rusinov states at different sites of the chain, result in a multi-band structure for the chain. We obtain the topological phase diagram for such band structure. We identify the parameter regimes for which the different bands lead to a topological phase and show that the inclusion of higher bands can greatly enlarge the phase space for the realization of topological states.
We study the effect of strong spin-orbit coupling (SOC) on bound states induced by impurities in superconductors. The presence of spin-orbit coupling breaks the $mathbb{SU}(2)$-spin symmetry and causes the superconducting order parameter to have gene
rically both singlet (s-wave) and triplet (p-wave) components. We find that in the presence of SOC the spectrum of Yu-Shiba-Rusinov (YSR) states is qualitatively different in s-wave and p-wave superconductor, a fact that can be used to identify the superconducting pairing symmetry of the host system. We also predict that in the presence of SOC the spectrum of the impurity-induced bound states depends on the orientation of the magnetic moment $bf{S}$ of the impurity and, in particular, that by changing the orientation of $bf{S}$ the fermion-parity of the lowest energy bound state can be tuned. We then study the case of a dimer of magnetic impurities and show that in this case the YSR spectrum for a p-wave superconductor is qualitatively very different from the one for an s-wave superconductor even in the limit of vanishing SOC. Our predictions can be used to distinguish the symmetry of the order parameter and have implications for the Majorana proposals based on chains of magnetic atoms placed on the surface of superconductors with strong spin-orbit coupling.
The Hilbert function of standard graded algebras are well understood by Macaulays theorem and very little is known in the local case, even if we assume that the local ring is a complete intersection. An extension to the power series ring $R$ of the t
heory of Gr{o}bner bases (w.r.t. local degree orderings) enable us to characterize the Hilbert function of one dimensional quadratic complete intersections $A=R/I$, and we give a structure theorem of the minimal system of generators of $I$ in terms of the Hilbert function. We find several restrictions for the Hilbert function of $A$ in the case that $I$ is a complete intersection of type $(2,b). $ Conditions for the Cohen-Macaulyness of the associated graded ring of $A$ are given.
The inhomogenous real-space electronic structure of gapless and gapped disordered bilayer graphene is calculated in the presence of quenched charge impurities. For gapped bilayer graphene we find that for current experimental conditions the amplitude
of the fluctuations of the screened disorder potential is of the order of (or often larger than) the intrinsic gap $Delta$ induced by the application of a perpendicular electric field. We calculate the crossover chemical potential, $Delta_{rm cr}$, separating the insulating regime from a percolative regime in which less than half of the area of the bilayer graphene sample is insulating. We find that most of the current experiments are in the percolative regime with $Delta_{rm cr}<<Delta$. The huge suppression of $Delta_{rm cr}$ compared with $Delta$ provides a possible explanation for the large difference between the theoretical band gap $Delta$ and the experimentally extracted transport gap.
We review the physics of charged impurities in the vicinity of graphene. The long-range nature of Coulomb impurities affects both the nature of the ground state density profile as well as graphenes transport properties. We discuss the screening of a
single Coulomb impurity and the ensemble averaged density profile of graphene in the presence of many randomly distributed impurities. Finally, we discuss graphenes transport properties due to scattering off charged impurities both at low and high carrier density.
The ARGO-YBJ experiment is a full coverage EAS-array installed at the YangBaJing Cosmic Ray Laboratory (4300 m a.s.l., Tibet, P.R. China). We present the results on the angular resolution measured with different methods with the full central carpet.
The comparison of experimental results with MC simulations is discussed.
Measurements at 100 TeV and above are an important goal for the next generation of high energy gamma-ray astronomy experiments to solve the still open problem of the origin of galactic cosmic rays. The most natural experimental solution to detect ver
y low radiation fluxes is provided by the Extensive Air Shower (EAS) arrays. They benefit from a close to 90% duty cycle and a very large field of view (about 2 sr), but the sensitivity is limited by their angular resolution and their poor cosmic ray background discrimination. Above 10 TeV the standard technique for rejecting the hadronic background consists in looking for muon-poor showers. In this paper we discuss the capability of a large muon detector (A=2500 m2) operated with an EAS array at very high altitude (>4000 m a.s.l.) to detect gamma-ray fluxes around 100 TeV. Simulation-based estimates of energy ranges and sensitivities are presented.
