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We study Andreev bound states in the presence of a magnetic moment in a ferromagnetic topological insulator in superconductor/magnetic topological insulator/superconductor Josephson junctions. We analytically find zero energy states for out-of-plane and in-plane directions of the magnetic moment. In the case of the out-of-plane magnetic moment, the energy is independent of the scattering angle. If both magnetic and nonmagnetic scattering mechanisms are considered, the zero energy state requires the scattering angle to the electrode to be zero as in the case of Majorana fermions. In the presence of an in-plane magnetic moment, the energy band always exhibits a nonvanishing gap if the magnetic moment has a nonzero component, i.e., there are no zero energy states. Here we assume that the electrons tunnel in the direction. If the magnetic moment is aligned with the tunneling direction, the zero energy states always exist and are independent of the scattering angle. Contrary to the Majorana fermion case, the phase shift between two superconductor electrodes is not. This phase difference depends on the system parameters such as the Fermi velocity, the barrier potential magnitude, the exchange coupling between localized and delocalized electrons, and the component of the magnetic moment. We find an anomalous Josepheson current when the magnetic moment has a component in the direction, where the current is nonzero despite. This is due to the violation of time reversal and chiral symmetries in the Josepheson junction. This leads to the observation of the Josephson Diode effect as well. For large scattering magnitudes, we find that the transmission coefficient approaches one at larger barrier magnitudes. This is the main reason why in superconductor/magnetic topological insulator/superconductor Josephson junctions critical current is much higher than in superconductor/normal metal/superconductor junctions. This effect is similar in origin to Klein Tunneling for relativistic Dirac electrons. In the case of nonmagnetic and out-of-plane magnetic scatterings, the current vanishes when the barrier amplitudes are approximately equal and large. This effect cannot be explained by the relativistic nature of the Dirac equation and is specific to the model. We also study temperature dependencies for in- and out-of-plane magnetic moments. We find that current at high temperatures is significantly smaller than at low temperatures. The current approaches a constant value at low temperatures, at approximately. This value depends on the other system parameters. The existence of new zero energy states in magnetic topological insulators in superconductor/magnetic topological insulator/superconductor Josephson junctions opens new opportunities in quantum computing because of the presence of the additional symmetry with respect to the scattering angle. 

Abstract We study magnetotransport in conical helimagnet crystals using the nonequilibriun Boltzmann equation approach. Spin dependent magnetoresistance exhibits dramatic properties for high and low electron concentrations at different temperatures. For spin up electrons we find negative magnetoresistance despite only considering a single carrier type. For spin down electrons we observe giant magnetoresistance due to depletion of spin down electrons with an applied magnetic field. For spin up carriers, the magnetoresistance is negative, due to the increase in charge carriers with a magnetic field. In addition, we investigate the spin dependent Hall effect. If a magnetic field reaches some critical value for spin down electrons, giant Hall resistance occurs, i.e. Hall current vanishes. This effect is explained by the absence of spin down carriers. For spin up carriers, the Hall constant dramatically decreases with field, due to the increase in spin up electron density. Because of the giant spin dependent magnetoresistance and Hall resistivity, conical helimagnets could be useful in spin switching devices. 

Abstract We study helical structures in spin-spiral single crystals. In the continuum approach for the helicity potential energy the simple electronic band splits into two non-parabolic bands. For low exchange integrals, the lower band is described by a surface with a saddle shape in the direction of the helicity axis. Using the Boltzmann equation with the relaxation due to acoustic phonons, we discover the dependence of the current on the angle between the electric field and helicity axis leading to the both parallel and perpendicular to the electric field components in the electroconductivity. The latter can be interpreted as a planar Hall effect. In addition, we find that the transition rates depend on an electron spin allowing the transition between the bands. The electric conductivities exhibit nonlinear behaviors with respect to chemical potential µ . We explain this effect as the interference of the band anisotropy, spin conservation, and interband transitions. The proposed theory with the spherical model in the effective mass approximation for conduction electrons can elucidate nonlinear dependencies that can be identified in experiments. We find the excellent agreement between the theoretical and experimental data for parallel resistivity depending on temperature at the phase transition from helical to ferromagnetic state in a M n P single crystal. In addition, we predict that the perpendicular resistivity abruptly drops to zero in the ferromagnetic phase.