Sergey A. Vyrko

We consider n ‐type gallium nitride crystals heavily doped with hydrogen‐like donors (silicon or germanium atoms) and weakly to moderately compensated by hydrogen‐like acceptors (magnesium atoms). Donor and acceptor concentrations correspond to the metallic side of the insulator–metal concentration phase transition (Mott transition). The shift of the conduction band (CB) electron mobility edge into the bandgap, caused by electrostatic fluctuations in the interaction energy between electrons and impurity ions, is taken into account. Within the relaxation time approximation for electron quasi‐momentum, the dependences of stationary (DC) electrical resistivity and drift mobility on the concentration of CB electrons in n ‐GaN crystals are calculated. Each act of elastic Coulomb scattering of a CB electron by a donor or acceptor ion is assumed to occur within a spherical volume of the crystal matrix associated with a single ion. Electron scattering on phonons is considered according to Matthiessen's rule. The calculation results, obtained using the proposed formulas without fitting parameters, quantitatively agree with experimental data over a wide range of CB electron concentrations. From analysis of experimental data, a new approximation formula for drift mobility at room temperature is obtained. The results using the new approximation and the proposed theoretical formula are consistent.

Context Existence of bistability for carbon nanobracelets (cyclic molecules with alternating polycyclic regions and double carbon chains) is predicted using calculations based on density functional theory (DFT). It was found that two stable states have the same topological structure of covalent bonds, but different symmetries, with the total energy of the low-symmetry state lower by 1.0 and 0.8 eV than the energy of the high-symmetry state for the nanobracelets consisting of 4 and 5 monomers, respectively. On the basis of the calculated structural characteristics and electronic properties, we propose that the bistability of the carbon nanobracelets is related to the competition between the electron structure energy and the energy of interaction between the adjacent chains. Methods Structure optimization of carbon nanobracelets was performed using spin-polarized all-electron DFT calculations with the PBE functional implemented in the Priroda code. Due to chain flexibility, a multi-step procedure was employed. The initial coordinates, derived from molecular mechanics and hand-made designs, were refined via PM3 (MOPAC2016) to generate starting points for high- and low-symmetry states. The final optimization was performed in the Priroda code without symmetry restrictions. Energies included zero-point corrections. Extended triple-n Gaussian basis sets, with kinetically balanced small components, were employed. Molecular symmetry was determined using WebMO algorithms. Positive vibrational frequencies confirmed true energy minima. The GFN-xTB method with van der Waals correction D4 was used to verify DFT-PBE calculations. To investigate the stability of the local minima, we performed ab initio molecular dynamics simulations. The molecular electrostatic potential was visualized using Jmol.

The influence of the clustering degree of electron spin magnetic moments from crystalline defects on the low-temperature magnetic susceptibility of materials is theoretically studied. The susceptibility of two diamond samples containing only identical spin radicals (uncompensated electron spins of radiation defects) with a concentration of 10 ¹⁹ cm ⁻³ is calculated. The first sample contains only isolated spin radicals. The second sample contains the same spin radicals grouped into identical spherical clusters—ferrons (clusters). With an average sample concentration of 10 ¹⁹ cm ⁻³ , the local concentration of spin radicals inside each ferron is assumed to be at the limiting value of 10 ²⁰ cm ⁻³ . As the number of spin radicals in each ferron increased from 10 to 350, the diameters of the ferrons increased from 6 to 19 nm, respectively. The low-temperature magnetic susceptibility of both samples is calculated based on the Brillouin function. It is shown that as the number of spin radicals in each ferron increases, the superparamagnetic behavior of the second sample is enhanced. At helium temperatures, in the limit of zero external magnetic field induction, the magnetic susceptibility of the second sample, in which the spin radicals are grouped into ferrons, is much greater than the susceptibility of the first sample, which contains only isolated spin radicals. This finding is supported by experimental measurements of low-temperature magnetic susceptibility in natural type IIa diamond samples irradiated with reactor neutrons.

Twisted graphene layers exhibit extremely low friction for relative sliding. Nevertheless, previous studies suggest that the area contribution to friction for commensurate moiré systems is finite and might restrict macroscopic superlubricity for large layer overlaps. In this paper, we investigate the potential energy surface (PES) for relative displacement of the layers forming moiré patterns (2,1) and (3,1) by accurate density functional theory calculations using the vdW-DF3 functional. The amplitudes of PES corrugations on the order of 0.4 and 0.03 $μ$eV per atom of one layer, respectively, are obtained. The account of structural relaxation doubles this value for the (2,1) pattern, while causing only minimal changes for the (3,1) pattern. We show that different from aligned graphene layers, for moiré patterns, PES minima and maxima can switch their positions upon changing the interlayer distance. The PES shape is closely described by the first spatial Fourier harmonics both with and without account of structural relaxation. A barrier for relative rotation of the layers to an incommensurate state that can make superlubricity robust is estimated based on the approximated PES. We also derive a set of measurable physical properties related to interlayer interaction including shear mode frequency, shear modulus and static friction force. Furthermore, we predict that it should be possible to observe domain walls separating commensurate domains, each comprising a large number of moiré pattern unit cells, and provide estimates of their characteristics.

The effect of structure relaxation on the potential energy surface (PES) of interlayer interaction of twisted graphene bilayer is studied for a set of commensurate moiré systems using the registry-dependent empirical potential of Kolmogorov and Crespi. It is found that the influence of structure relaxation on the amplitude of PES corrugations (determining static friction) depends on the unit cell size (or related twist angle) of the moiré system. For moiré systems with the smallest unit cells, the amplitudes of PES corrugations calculated with and without account of structure relaxation are approximately the same. However, for large unit cell sizes, the structure relaxation can lead to an increase of PES corrugations by orders of magnitude. This means that structure relaxation can provide the main contribution into the static friction of a superlubric system under certain conditions (such as the contact size and twist angle). Moreover, the change of the PES type because of structure relaxation from a trigonal lattice of maxima to a trigonal lattice of minima is observed for the systems with the moiré patterns (5,1) and (5,3). Based on the results obtained, possible crossovers between static friction modes taking place upon changing the twist angle in a macroscopic superlubric system consisting of identical layers are discussed. Additionally it is shown that the PES for relaxed structures can still be approximated by the first Fourier harmonics compatible with symmetries of twisted layers analogously to the PES for rigid layers.