For the first time, magnetoresistive properties of the single crystal of HgSe with a low electron concentration were studied in wide range of temperature and magnetic field. Some fundamental parameters of spectrum and scattering of electrons were experimentally determined.Two important features of magnetic transport were foundstrong transverse magnetoresistance (МR) and negative longitudinal MR, which can indicate the existence of the topological phase of the Weyl semimetal (WSM) in HgSe. Taking this hypothesis into account we suggest a modified band diagram of the mercury selenide at low electron energies. The obtained results are essential for the deeper understanding of both physics of gapless semiconductors and WSMspromising materials for various applications in electronics, spintronics, computer and laser technologies. Weyl and Dirac semimetals have recently attracted great attention as materials that possess strong spin-orbit coupling (SOC) and relativistic electron spectrum. Such materials can be considered to be three-dimensional analogues of graphene. For an WSM phase to exist there should be breaking of either inversion symmetry, as in monophosphides and monoarsenides of tantalum and niobium TaP [1,2], TaAs [3], NbP [4], NbAs [5], or time reversal symmetry, as in the ferromagnetic spinel HgCr2Se4 [6]. The breaking of inversion symmetry also occurs in mercury selenidegapless semiconductor that crystallizes into a zinc-blende structure and has inverted electron spectrum in the center of the Brillouin zone. The zinc-blende structure consists of two mutually interpenetrating face-centered cubic lattices with a tetrahedral coordination of atoms. HgSe belongs to the space symmetry group F43m with the lattice constant а = 6.074Å and coordination number Z = 4. The band order is inverted because of relativistic effects including SOC [7]. Mercury selenide with low electron concentration can become relevant material in the topological condensed matter physics. In this regard, it should be noted that in HgSe under no annealing condition could the electron concentration be reduced below ~ 10 16 cm -3 at 4.2K [7]. Smallness of the electron concentration is essential to reveal the Weyl nodesfeatures of an energy spectrum of topological nature. The Weyl nodes (or magnetic monopoles) are band touching points in the momentum space, which always come in pairs of opposite chirality [8]. Near

The temperature dependences of the resistivity, Hall coefficient, and magnetic susceptibility of iron-vanadium-aluminum alloys have been investigated. It has been established that the alloy Fe1.9V1.1Al exhibits semiconductor behavior for the method used to obtain uniform alloys. It is shown that at temperatures below 30K the semiconductor alloy possesses the characteristic low-temperature scale of the dependences observed, which could be responsible for the appearance of a narrow pseudogap in the electron density of states. A simple theoretical description of the effects of a pseudogap is proposed. A consistent fit of the theoretical to the experimental relations made it possible to determine the effective width of the pseudogap (∼1MeV) and its relative depth (∼102).

An investigation has been carried out of the quantum oscillations of the magnetic susceptibility of an isotropic metal at constant pressure and at low temperatures in strong magnetic fields, when the amplitude of the density of electron states is of the order of the classical value. It is shown that quantum magnetostriction gives rise to a dependence of susceptibility on the ratio of the contributions to the moduli of elasticity due to electrons and to the lattice. The shape of susceptibility oscillations depends substantially on the Fermi-liquid interaction parameters. Conditions are discussed under which the thermodynamic stability at the oscillation peaks may be broken. The low-temperature oscillations of the derivative of volume with respect to the magnetic field are also considered. It is shown that at points of magnetic instability, jumps in volume are possible.