We investigate single-particle ballistic scattering on a rectangular barrier in the nodal-line Weyl semimetals. Since the system under study has a crystallographic anisotropy, the scattering properties are dependent on mutual orientation of the crystalline axis and the barrier. To account for the anisotropy, we examine two different barrier orientations. It is demonstrated that, for certain angles of incidence, the incoming particle passes through the barrier with probability of unity. This is a manifestation of the Klein tunneling, a familiar phenomenon in the context of graphene and semimetals with Weyl points. However, the Klein tunneling in the Weyl-ring systems is observed when the angle of incidence differs from 90 • , unlike the cases of graphene and Weyl-point semimetals. The reflectionless transmission also occurs for the so-called 'magic angles'. The values of 'the magic angles' are determined by geometrical resonances between the barrier width and the de Broglie length of the scattered particle. In addition, we show that under certain conditions the wave function of the transmitted and reflected particles may be a superposition of two plane waves with unequal momenta. Such a feature is a consequence of the non-trivial structure of the iso-energy surfaces of the nodal-line semimetals.PACS numbers:

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Inelastic interactions of quantum systems with environment usually wash coherent effects out. In the case of Friedel oscillations the presence of disorder leads to a fast decay of the oscillation amplitude. Here we show both experimentally and theoretically that in the three-dimensional topological insulator Bi 2 Te 3 there is a nesting-induced splitting of coherent scattering vectors which follows a peculiar evolution in energy. The effect becomes experimentally observable when the lifetime of quasiparticles shortens, due to disorder. The amplitude of the splitting allows evaluating the lifetime of the electrons. A similar phenomenon should be observed in any system with a well-defined scattering vector regardless of its topological properties.Predicted a long ago, recently discovered three-dimensional topological insulators (TIs) [1][2][3][4][5][6][7] are characterized by conducting surface states with the linear dispersion, Dirac cones, evolving in the bulk gap. In real materials, the Dirac cones are often regular only close to their origin, the Dirac point (DP). Both theories and experiments showed that far from the Dirac point, the circular shape of the constant energy contour evolves into a hexagon and then to a snowflake with sharp tips extending along six crystallographic directions. [8][9][10] The warping is present in Bi 2 Se 3 , 11-13 Pb(Bi,Sb) 2 Te 4 14 and other TI materials. 10,15

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