We study the scattering of edge states of 2D topological insulator in the uniform external magnetic field due to edge imperfections, common in realistic 2D topological insulator samples. The external magnetic field breaks time-reversal symmetry, opening the possibility of the scattering of otherwise topologically protected fermionic edge states. The scattering happens to be always an over-barrier event, irrespective of the shape of the edge deformation and magnitude of the magnetic field. We use the advanced Pokrovsky–Khalatnikov semiclassical approach, which allows us to obtain analytically both the main exponential and pre- exponential factors of the scattering amplitude for wide classes of analytic deformation profiles.

We study the effects of anisotropy on the magnetoresistance of Weyl semimetals (WSMs) in the ultraquantum regime. We utilize the fact that many Weyl semimetals are approximately axially anisotropic. We find that anisotropy manifests itself in the strong dependence of the magnetoresistance on the polar and azimuthal angles determining the orientation of the anisotropy axis with respect to the applied magnetic field and electric current. We also predict that the ratio of magnetoresistances in the geometries, where the magnetic field and anisotropy axes are aligned and where they are orthogonal, scales as $(v_\bot/v_\parallel)^2$ where $v_\bot$ and $v_\parallel$ are the corresponding Fermi velocities.

Physical properties of single-electron devices in the week Coulomb blockade regime are significantly dependent on non-perturbative effects. They arise as instanton solutions of equations of motion for the corresponding Ambegaokar-Eckern-Schoen action. In equilibrium those solutions are known as Korshunov instantons. In this paper we study non-equilibrium Ambegaokar-Eckern- Schoen action using Keldysh technique. We found instantons for the most general stationary out-of equilibrium state. We also found that action saddle-point value assumes a universal value irrespective of the stationary non-equilibrium state.