The Majorana spin in magnetic atomic chain systems

In this paper, we establish that Majorana zero modes emerging from a topological band structure of a chain of magnetic atoms embedded in a superconductor can be distinguished from trivial localized zero energy states that may accidentally form in this system using spin resolved measurements. To demonstrate this key Majorana diagnostics, we study the spin composition of magnetic impurity induced in-gap Shiba states in a superconductor using a quantum impurity model (at the mean-field level). By examining the spin and spectral densities in the context of the Bogoliubov-de Gennes (BdG) particle-hole symmetry, we derive a sum rule that relates the spin densities of localized Shiba states with those in the normal state without superconductivity. Extending our investigations to ferromagnetic chain of magnetic impurities, we identify key features of the spin properties of the extended Shiba state bands, as well as those associated with a localized Majorana end mode when the effect of spin-orbit interaction is included. We then formulate a phenomenological theory for the measurement of the local spin densities with spin-polarized scanning tunneling microscopy (STM) techniques. By combining the calculated spin densities and the measurement theory, we show that spin-polarized STM measurements can reveal a sharp contrast in spin polarization between an accidentally-zero-energy trivial Shiba state and a Majorana zero mode in a topological superconducting phase in atomic chains. We further confirm our results with numerical simulations that address generic parameter settings.Comment: 22 pages, 12 figures (references updated

Observation of a Majorana zero mode in a topologically protected edge channel

Superconducting proximity pairing in helical edge modes, such as those of topological insulators (TI), is predicted to provide a unique platform for realizing Majorana zero modes (MZMs). We use scanning tunneling microscopy measurements to probe the influence of proximity induced superconductivity and magnetism on the helical hinge states of Bi(111) films, grown on a superconducting Nb substrate and decorated with magnetic Fe clusters. Consistent with model calculations, our measurements reveal the emergence of a localized MZM at the interface between the superconducting helical edge channel and the Fe clusters with strong magnetization component along the edge. Our experiments also resolve the MZM spin signature that distinguishes it from trivial in-gap states that may accidently occur at zero energy in a superconductor

Exploring the fate, transport and risk of Perfluorooctane Sulfonate (PFOS) in a coastal region of China using a multimedia model

Perfluorooctane Sulfonate (PFOS) and related substances have been widely applied in both industrial processes and domestic products in China. Exploring the environmental fate and transport of PFOS using modeling methods provides an important link between emission and multimedia diffusion which forms a vital part in the human health risk assessment and chemical management for these substances. In this study, the gridded fugacity based BETR model was modified to make it more suitable to model transfer processes of PFOS in a coastal region, including changes to PFOS partition coefficients to reflect the influence of water salinity on its sorption behavior. The fate and transport of PFOS in the Bohai coastal region of China were simulated under steady state with the modified version of the model. Spatially distributed emissions of PFOS and related substances in 2010 were estimated and used in these simulations. Four different emission scenarios were investigated, in which a range of half-lives for PFOS related substances were considered. Concentrations of PFOS in air, vegetation, soil, fresh water, fresh water sediment and coastal water were derived from the model under the steady-state assumption. The median modeled PFOS concentrations in fresh water, fresh water sediment and soil were 7.20ng/L, 0.39ng/g and 0.21ng/g, respectively, under Emission Scenario 2 (which assumed all PFOS related substances immediately degrade to PFOS) for the whole region, while the maximum concentrations were 47.10ng/L, 4.98ng/g and 2.49ng/g, respectively. Measured concentration data for PFOS in the Bohai coastal region around the year of 2010 were collected from the literature. The reliability of the model results was evaluated by comparing the range of modeled concentrations with the measured data, which generally matched well for the main compartments. Fate and transfer fluxes were derived from the model based on the calculated inventory within the compartments, transfer fluxes between compartments and advection fluxes between sub-regions. It showed that soil and costal water were likely to be the most important sinks of PFOS in the Bohai costal region, in which more than 90% of PFOS was stored. Flows of fresh water were the driving force for spatial transport of PFOS in this region. Influences of the seasonal change of fresh water fluxes on the model results were also analyzed. When only seasonal changes of the fresh water flow rates were considered, concentrations of PFOS in winter and spring were predicted to be higher than that under annual average conditions, while the concentrations in summer and autumn were lower. For PFOS fluxes entering the sea, opposite conclusions were drawn compared to the concentrations. Environmental risks from the presence of PFOS in fresh water were assessed for this region through comparison with available water quality criteria values. The predicted concentrations of PFOS in the Bohai coastal region provided by the model were lower than the water quality criteria published by the United States Environmental Protection Agency and Chinese researchers, while the concentrations in more than 80% of the sampling locations exceeded the European Union Water Framework Directive Environmental Quality Standards values. Seasonal variations of flow rate might cause a significant increase in environmental risks

Stabilizing fluctuating spin-triplet superconductivity in graphene via induced spin-orbit coupling

A recent experiment showed that proximity induced Ising spin-orbit coupling enhances the spin-triplet superconductivity in Bernal bilayer graphene. Here, we show that, due to the nearly perfect spin rotation symmetry of graphene, the fluctuations of the spin orientation of the triplet order parameter suppress the superconducting transition to nearly zero temperature. Our analysis shows that both Ising spin-orbit coupling and in-plane magnetic field can eliminate these low-lying fluctuations and can greatly enhance the transition temperature, consistent with the recent experiment. Our model also suggests the possible existence of a phase at small anisotropy and magnetic field which exhibits quasi-long-range ordered spin-singlet charge 4e superconductivity, even while the triplet 2e superconducting order only exhibits short-ranged correlations. Finally, we discuss relevant experimental signatures.Comment: 6 pages, 2 figures + 8 pages, 1 figure supplementa

Thermodynamics of free and bound magnons in graphene

Symmetry-broken electronic phases support neutral collective excitations. For example, monolayer graphene in the quantum Hall regime hosts a nearly ideal ferromagnetic phase at filling factor $\nu=1$ that spontaneously breaks spin rotation symmetry. This ferromagnet has been shown to support spin-wave excitations known as magnons which can be generated and detected electrically. While long-distance magnon propagation has been demonstrated via transport measurements, important thermodynamic properties of such magnon populations--including the magnon chemical potential and density--have thus far proven out of reach of experiments. Here, we present local measurements of the electron compressibility under the influence of magnons, which reveal a reduction of the $\nu=1$ gap by up to 20%. Combining these measurements with estimates of the temperature, our analysis reveals that the injected magnons bind to electrons and holes to form skyrmions, and it enables extraction of the free magnon density, magnon chemical potential, and average skyrmion spin. Our methods furnish a novel means of probing the thermodynamic properties of charge-neutral excitations that is applicable to other symmetry-broken electronic phases