Semimetals with certain crystal symmetries may possess unusual electronic structure topology, distinct from that of the conventional Weyl and Dirac semimetals. Characteristic property of these materials is the existence of band-touching points with multiple (higher than two-fold) degeneracy and nonzero Chern number. CoSi is a representative of this group of materials exhibiting the so-called 'new fermions'. We report on an ab initio calculation of the electronic structure of CoSi using density functional methods, taking into account the spin-orbit interactions. The linearized [Formula: see text] Hamiltonian, describing the anisotropic electronic structure of CoSi near the Γ point is derived. The topological features of band-touching nodes with four- and six-fold degeneracy located at the Γ and R points in the first Brillouin zone are analysed using the linearized Hamiltonians and first principle calculations. In particular, we show, using the non-Abelian Berry curvature, that these band-touching points carry topological charges of [Formula: see text], which change signs at certain values of parameters of the Hamiltonians. We describe the resulting Fermi arc surface states and their spin texture. We also discuss the influence of many body [Formula: see text] corrections on the electronic band structure and the topological properties of CoSi.

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Many efficient thermoelectric materials belong to the class of topological insulators. Therefore, in recent years considerable efforts have been made to elucidate the influence of nontrivial electronic topology on the thermoelectric properties of thermoelectrics. This review describes the basic transport properties of helical surface states of topological insulators. Their effect on the thermoelectric efficiency of materials is discussed. The main attention is paid to (Bi,Sb)2(Te,Se)3 alloys, which combine the properties of the best thermoelectrics and a model topological insulator.

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Cobalt monosilicide and its solid solutions with Fe or Ni crystallize in B20 cubic noncentrosymmetric structure. These compounds have long been known as promising thermoelectric materials. Recently it was revealed, that they also have unconventional electronic topology. This renewed interest to the investigation of their transport properties. In order to improve theoretical description of thermoelectric transport in these compounds, we take into account electron scattering beyond commonly used constant relaxation time approximation.Using first principle calculations, we investigate the scattering of charge carriers by phonons and point defects. The dependence of the scattering rate on the energy correlates with that for the total density of states. This implies that in this material not only the intraband, but also the interband scattering is important, especially for bands with low density of states. The Seebeck coefficient and the electrical resistivity of CoSi and of dilute solid solutions Co 1−x M x Si (M=Fe or Ni, x < 0.1) are calculated as a function of temperature and the alloy composition. We show that the account of strong energy dependence of relaxation time is important for the description of experimentally observed rapid increase of the resistivity and qualitative change of its temperature dependence with the substitution of cobalt for iron, as well as for the description of the magnitude of the Seebeck coefficient, its temperature and composition dependence.