The behavior of the topological index (TI), characterizing the properties of superconducting phases of quasi-two-dimensional systems with nontrivial topology, is investigated depending on the temperature and system parameters. For this purpose, a method of calculating the TI, based on a self-consistent functional-integral theory, is proposed. The chirald + idsuperconducting phase of a quasi-two-dimensional model with effective attraction between the electrons located at the nearest sites of a triangular lattice is considered. It is shown that the structure of the energy dependence of the self-energy function, which occurs when taking into account thermal fluctuations, does not lead to a change in the topological properties of the system. It is found that taking into account thermal fluctuations with an increase in the effective attraction between electrons expands the temperature range in which the value of the TI is close to the integerC1≃-2.

The behavior of the topological index, characterizing the properties of superconducting phases of quasi-two-dimensional systems with nontrivial topology, is investigated depending on the temperature and parameters of the effective non-Hermitian Hamiltonian. For this purpose, a method of calculating the topological index, based on a self-consistent functional-integral theory, is proposed. The method makes it possible to take into account thermal fluctuations and study the behavior of the topological index as a function of temperature and Hamiltonian parameters. The chiral d+id superconducting phase of a quasi-two-dimensional model with effective attraction between the electrons located at the nearest sites of a triangular lattice is considered. It is shown that the characteristic features in the energy dependence of the self-energy part, which arise when thermal fluctuations are taken into account, have a structure that does not lead to a change in the topological properties of the system. It is found that thermal fluctuations, as well as an increase in effective attraction in this system, contribute to the expansion of the temperature region, in which the value of the topological index is close to the integer C1=-2.

A biased sampling algorithm for the restricted Boltzmann machine (RBM) is proposed, which allows generating configurations with a conserved quantity. To validate the method, a study of the short-range order in binary alloys with positive and negative exchange interactions is carried out. The network is trained on the data collected by Monte–Carlo simulations for a simple Ising-like binary alloy model and used to calculate the Warren–Cowley short-range order parameter and other thermodynamic properties. We demonstrate that the proposed method allows us not only to correctly reproduce the order parameters for the alloy concentration at which the network was trained, but can also predict them for any other concentrations.

The magnetic phase diagrams of the two-dimensional Hubbard model for isotropic and anisotropic triangular lattices are constructed within the Hartree--Fock and slave boson approximations. The triangular lattice specific non-collinear and spiral magnetic states, as well as phase separation between them, are shown to be realized in a wide range of model parameters along with collinear magnetic states (stripe antiferromagnetic and ferromagnetic). Phase transitions of the first and second order are found, and the boundaries of the phase separation regions are determined. A comparison of the two approximations, Hartree--Fock and slave boson, shows that electronic correlations suppress magnetic states, the region of paramagnetism being expand, for values U/t>~=5. At the same time, when the Fermi level is near the van Hove singularity, electron correlations do not change the diagrams qualitatively, which is consistent with the previously obtained result for square and cubic lattices. The results are compared with the data available in the literature for other methods and approaches. Keywords: Hubbard model, phase separation, spiral magnetic order, triangular lattice, metal-insulator transition

The synthesis and the structural and magnetic characteristics of ternary nonstoichiometric Fe 65 – x Al 35 – y M x , y (M y = Ga, B, Sn; M x = V, Mn; x = 3, 5, 10 at %) compounds are experimentally and theoretically studied. Quantum-mechanical calculations of the energy of formation and an electronic structure explain the characteristic features of the phase transformations that occur during the synthesis and describe the experimentally observed changes in the magnetic parameters for various impurity elements.

We investigate the structure of the energy dependence of the normal and anomalous self-energy components of the one-particle Green function in the superconducting state, which is calculated with account for charge carrier scattering by thermal fluctuations of electron–hole pairs. Analysis is performed using the self-consistent theory of continual integration based on the quasi-two-dimensional single-band model with attraction between electrons at neighboring sites. Asymptotic expressions for the self-energy components, which coincide in structure with analogous expressions of the phenomenological model of hybridization of electrons with hidden fermionic excitations, are obtained in the average t-matrix approximation. Analysis of the results shows that the energy dependences of both self-energy components have characteristic peaks that suppress each other in the total self-energy at low temperatures. Such a behavior is preserved in the range of anomalously low temperatures and disappears only in the quantum limit for T → 0, in which quantum fluctuations play the decisive role. With increasing temperature, the mutual suppression is replaced by mutual enhancement followed by mutual compensation in the range of temperatures close to the superconducting transition temperature.

The magnetic phase diagrams of the two-dimensional Hubbard model for isotropic and anisotropic triangular lattices are constructed within the Hartree-Fock and slave boson approximations. The triangular lattice specific non-collinear and spiral magnetic states, as well as phase separation between them, are shown to be realized in a wide range of model parameters along with collinear magnetic states (stripe antiferromagnetic and ferromagnetic). Phase transitions of the first and second order are found, and the boundaries of the phase separation regions are determined. A comparison of the two approximations, Hartree-Fock and slave boson, shows that electronic correlations suppress magnetic states, the region of paramagnetism being expand, for values U/t>5. At the same time, when the Fermi level is near the van Hove singularity, electron correlations do not change the diagrams qualitatively, which is consistent with the previously obtained result for square and cubic lattices. The results are compared with the data available in the literature for other methods and approaches.

The interplay between magnetic and superconducting states on a square lattice is studied using the extended Hubbard model, which takes into account the attraction of electrons located at nearest neighbor sites. Ferro-, antiferro-, and spiral magnetic states with all possible sets of spiral wave vectors, as well as singlet superconducting states with s-wave and d-wave pairing order parameters, are considered. Formation of a state with the intermediate s+id-symmetry and phase separation between different phases are allowed. The results of the Hartree-Fock and slave boson approximations are compared in order to study the role of correlation effects. Both macroscopic phase separation and microscopic coexistence of the superconducting and magnetic phases are found under certain model parameters.

The behavior of thermal fluctuations of a superconducting order parameter with extendedsand chirald+ idsymmetry is investigated. The study is carried out on a triangular lattice within the framework of the quasi-two-dimensional single-band model with attraction between electrons at neighboring sites. The method of consistent consideration of the order parameter fluctuations and the charge carrier scattering by fluctuations of coupled electron pairs, based on the theory of functional integration is used. The distribution functions of the phase fluctuation probabilities depending on temperature and charge carrier concentration are obtained. The temperature dependences of the amplitudes of the averaged superconducting order parameter are calculated. A phase diagram of superconducting states is constructed for the entire range of variation in the charge carrier concentration 0 <n< 2. Near the boundaries of this range, topologically trivial superconducting states with extendedssymmetry are realized, while a superconducting state with topologically nontrivial chirald+ idsymmetry is realized between them. The calculated anomalous self-energies are compared with the experimental ones obtained using machine learning techniques.

Generalization properties of the restricted Boltzmann machine (RBM) for two-dimensional Ising model are investigated. Both long-range and short-range order are examined: the first is studied for a spin lattice with ferromagnetic interaction, and the second is considered for a binary alloy on the square lattice. For each of these cases, algorithms are proposed that allow the once trained RBM to predict the order parameters for any temperature and alloy concentration.

We analyze the behavior of thermal fluctuations of the superconducting order parameter with extended s-wave and $${{d}_{{{{x}^{2}} - {{y}^{2}}}}}$$-wave symmetry. For this purpose, we develop a method of self-consistent consideration of the order parameter fluctuations and charge carrier scatterers by fluctuations of coupled electron pairs using the theory of functional integration. The study is performed based on the quasi-two-dimensional one-band model with attraction between electrons located at neighboring sites. We obtain the distribution functions of the phase fluctuation probabilities depending on temperature, charge carrier concentrations, and model parameters. It is shown that the phase of the order parameter in the superconducting region is coherent, and the density of states has a dip at the Fermi level. In approaching the incoherent region of the phase diagram, the dip in the density of states disappears simultaneously with the loss of phase coherence. At the same time, the order parameter amplitude averaged over fluctuations remains finite at any temperature and concentration of charge carriers. Our results show that the pseudogap state cannot be explained in the frames of this scenario.

A nanostructured Fe65Al30Sn5 alloy has been synthesized by mechanical alloying of elemental Fe, Al, and Sn powders in a planetary ball mill. The structure and phase composition of the as-milled sample and the samples after subsequent heat treatment at 400 °C, 500 °C, and 800 °C were investigated using X-ray diffraction, electron microscopy, 57Fe and 119mSn Mössbauer spectroscopy. We found that the as-milled sample is a nanocrystalline ternary bcc solid solution of the estimated composition Fe62Al32.6Sn5.4. The samples of Fe65Al30Sn5 after annealing are non-uniform materials that mainly comprise the ternary B2 ordered phase Fe65Al30Snx, xSn ≤ 1 at. pct. In addition to the dominant B2 ordered phase, we also identified chemically non-ordered regions, Sn and FeSn, FeSn2.

The competition between the singlet superconducting states with s- and d-wave symmetry of the order parameter is studied within a single-band model with nearest-neighbor attractive interaction. The ground state and finite-temperature phase diagrams are constructed for different ratios between the nearest- and next-nearest-neighbor electron transfer integrals. The mixed s+id pairing state is shown to be formed in the intermediate region between s- and d-waves. The temperature phase transitions between the pure and the mixed pairing state are found.

The possibility of synthesis of the ordered ternary Fe65Al35 – xМx and Fe65 – yAl35My alloys with x, y = 0, 3, 5, 10 at % and M = B, Ga, V, Mn is studied and conditions of the synthesis are reported. Nanocrystalline metastable disordered ternary alloys are used as the precursor materials for the ordered alloys, which are prepared by mechanical alloying from elemental components. The heat treatment of mechanically alloyed compositions allowed us to reach the single-phase state with the В2 superstructure for the compositions with Ga and V; the single-phase state with the D03 superstructure was reached for the compositions with B and Mn. ordered ternary Fe–Al-based alloys, mechanical synthesis, structure, hyperfine interactions

Results of structural, magnetic, and Mössbauer studies of quasi ordered alloys Fe 65 Al 35 − x M x ( M x = Ga, B; x = 0, 5 at %) are presented. The magnetic state of examined structurally–single-phase alloys at low temperatures is interpreted from the viewpoint of magnetic phase separation. An explanation is proposed for the observed behavior of magnetic characteristics of Fe 65 Al 35 and Fe 65 Al 30 Ga 5 in the framework of the model of two magnetic phases, a ferromagnetic-type one and a spin density wave. The boron-doped alloy Fe 65 Al 30 B 5 is shown to demonstrate behavior that is typical of materials with the ferromagnetic type of ordering.

Ground state magnetic phase diagrams of the square and simple cubic lattices are investigated for the narrow band Hubbard model within the slave-boson approach by Kotliar and Ruckenstein. The transitions between saturated (half-metallic) and non-saturated ferromagnetic phases as well as similar transition in antiferromagnetic (AFM) state are considered in the three-dimensional case. Two types of saturated antiferromagnetic state with different concentration dependences of sublattice magnetization are found in the two-dimensional case in the vicinity of half-filling: the state with a gap between AFM subbands and AFM state with large electron mass. The latter state is hidden by the phase separation in the finite-U case.

AbstractResults of structural, magnetic, and Mössbauer studies of quasi ordered alloys Fe_65Al_35 − x M_ x ( M _ x = Ga, B; x = 0, 5 at %) are presented. The magnetic state of examined structurally–single-phase alloys at low temperatures is interpreted from the viewpoint of magnetic phase separation. An explanation is proposed for the observed behavior of magnetic characteristics of Fe_65Al_35 and Fe_65Al_30Ga_5 in the framework of the model of two magnetic phases, a ferromagnetic-type one and a spin density wave. The boron-doped alloy Fe_65Al_30B_5 is shown to demonstrate behavior that is typical of materials with the ferromagnetic type of ordering.

The structure and the magnetic state of ordered Fe65Al35-xMx (Mx = Ga, B; x = 0; 5 at.%) alloys are investigated using X-ray diffraction, Mössbauer spectroscopy, and magnetic measurements. The behavior of the magnetic characteristics and Mössbauer spectra of the binary alloy Fe65Al35 and the ternary alloy with gallium addition Fe65Al30Ga5 is explained in terms of the phase separation into two magnetic phases: a ferromagnetic one and a spin density wave. It is shown that the addition of boron to the initial binary alloy Fe65Al35 results in the ferromagnetic behavior of the ternary alloy.