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We report on the strong anisotropy of the inter-band process of impact ionization in direct-gap cubic semiconductors with either weak or strong spin-orbit coupling at low effective temperatures of electron distribution $T$, and the crossover to isotropic behavior with increasing $T$. Such anisotropy is related to specific mechanism of the impact ionization involving coupling of the electron and heavy hole states $\it via$ remote bands, which is vanishing for some high-symmetry propagation directions of an initial electron, namely $\mathrm{[100]}$ and $\mathrm{[111]}$. At room temperature impact ionization rate in narrow-gap semiconductors $\mathrm{InSb}$, $\mathrm{InAs}$, $\mathrm{GaSb}$ and $\mathrm{In}_{0.53}\mathrm{Ga}_{0.47}\mathrm{As}$ is isotropic while in middle-gap $\mathrm{InP}$, $\mathrm{GaAs}$ and $\mathrm{CdTe}$ both terms are comparable. We propose simple and justified analytic generalization of Keldysh formula for the impact ionization rate valid for direct-gap semiconductors with $E_g$ up to $\mathrm{1.5}~\mathrm{eV}$, which is suitable for incorporation into modelling software., Comment: 8 pages, 5 figures

The evolution of the polycrystalline pattern of electron paramagnetic resonance (EPR) spectra of intrinsic and induced paramagnetic centers in an ensemble of submicrometer diamond particles on diminishing average particle size is considered. Recent experimental data unambiguously demonstrate consistent reduction and then zeroing of typical hyperfine pattern from P1 centers on approaching a certain particle size and below it. These changes are accompanied by appearance and strengthening of new structureless signals. In small particles the electron wave function of a surface paramagnetic center is delocalized over the whole nanoparticle. In result the electron spin "experiences" the average field of all surrounding nuclei, which is zero. At the same time, the paramagnetic centers localized in the bulk of a nanoparticle are also cut off the hyperfine interaction due to the electron spin diffusion. Thus, upon the nanodiamond particle size decreases the hyperfine related features of the polycrystalline EPR spectrum become weaker and the spectrum appear to be structureless.

Microscopic theory of the nonradiative energy transfer in a system of III-V semiconductor quantum dots is elaborated in our work. The energy transfer both due to direct Coulomb and due to exchange interactions between two quantum dots (energy donor and acceptor) is considered. An analysis of energy transfer process is performed in the frame of the Kane model that provides the most adequate description of the real energy spectra and wave functions of III-V semiconductors. The density-matrix method is applied, which enabled us to analyze the energy transfer rate both in the weak-interaction approximation and in the strong-interaction approximation. For the first time the detailed analytical calculations of the exchange energy transfer rate for the quantum dot system are performed. The analytical expressions for contributions to the transfer rate are derived. The numerical calculations showed that at nearly contact distances between two quantum dots the rate of the energy transfer due to the direct Coulomb interaction as well as by exchange interaction can reach the saturation. At the small distances, these two contributions can be of the same order and can have the same value in the saturation range. It is revealed that the exchange interaction should be taken into consideration in qualitative describing the energy transfer at small distances between the quantum dot donor and the quantum dot acceptor., Comment: 58 pages 7 figures

We present quantum-mechanical theory of impact ionization in semiconductors with the direct band gap in \$\Gamma\$-point. It is shown that energy dependence of the impact ionization rate \$\mathcal{W}(E)\$ near a threshold \$E_{th}\$ is given by superposition of the two terms, one of which is strongly anisotropic and quadratic in \$E-E_{th}\$, while another one is isotropic and cubic in \$E-E_{th}\$. Explicit form of the coefficients in such representation is derived in the framework of the 14-band \${\bf k\cdot p}\$ model, and we claim the room temperature domination of the cubic contribution for most of the direct-gap materials with \$E_g\$ up to 1.5 eV., Comment: 9 pages (in Russian), 3 figures, JETP Letters vol. 105, iss. 9 (2017)

A microscopic calculation of the conductivity in the integer quantum Hall effect (IQHE) regime is carried out. The problem of precision of quantization is analyzed for samples of finite size. It is demonstrated that the precision of quantization shows a power-law dependence on the sample size. A new scaling parameter describing a dependence of this kind is introduced. It is also demonstrated that the precision of quantization linearly depends on the ratio between the amplitude of the chaotic potential and the cyclotron energy. The results obtained are compared with the magnetotransport measurements in mesoscopic samples., Comment: 5 pages, 4 figures