Superconductivity in two-band systems with a small concentration of carriers

Superconductors with two characteristic features of high-temperature superconducting materials, i.e., a small concentration of charge carriers and overlapping energy bands on the Fermi surface, are considered. At T=0, the order parameters _n and the chemical potential for the Bose condensate of local pairs (<0) is determined in the mean field approximation. The equation for the bound state energy _b is obtained and the relationship _b=2 is established. An application of the path integral method to the two-band model is developed and on this basis, the transition from the Fermi to the Bose pattern of elementary excitations in the presence of a two-particle bound state in the system is demonstrated. The expression for the temperature of Bose condensation T_k is obtained and the contribution of the residual boson interactions is estimated for systems with different dimensions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 1, pp. 137–151, October, 1996.     

Superconductivity based on a model with three overlapping energy bands and a nonphonon mechanism

A study is made of the thermodynamic properties of a three-band superconductor with an electron (or hole) mechanism of superconductivity. Interband carrier interaction is considered as the main reason for the occurrence of superconducting pairs. Expressions are obtained for the order parameters _n (T) (n=1, 2, 3), the specific heatC _S, and the thermodynamic critical fieldH _c in the region of low temperatures and also the temperatureT _c of the superconducting transition, the jump in the specific heat (C _S–C_N) at the pointT=T _c; and 2 _n (0)/T _c . It is shown that a characteristic feature in the behavior ofT _c, (C _S–C_N), and _n (0) as functions of the carrier concentrationn is the presence of a smeared step. It is also shown that (C _S–C_N)/C _N1.43 and that this ratio depends strongly on the relationship between the densities of the electron states of the considered bands.Institute of Applied Physics, Moldavian Republic Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 3, pp. 483–499, June, 1992.     

Investigation of 5D point symmetry groups with an invariant 3D plane and immobile point on it

To reveal the structure of 5D point symmetry groups with an invariant 3D plane and immobile point on it, we review in detail the catalog of 1208 3D point groups of ten rosette P-symmetries at P ? G ₂₀, which interpret (accurate to the structure) the aforementioned symmetry groups of the 5D Euclidean space of the category G ₅₃₀, where the numbers in the index 530 indicate successively the dimension of space and the dimensions of invariant subspaces in this space.     

Incommensurable state of a spin density wave and superconductivity in quasi-two-dimensional systems with an anisotropic energy spectrum

We investigate phase transitions in quasi-two-dimensional systems with an anisotropic energy spectrum and a deviation from the half-filling of the energy band (μ ≠ 0). We demonstrate the possibility of the transition of an insulator into a half-metallic state when the nesting condition is violated because the parameter μ ≠ 0 and of taking the umklapp processes into account. We obtain the basic equations for the parameters of the superconducting (Δ) and magnetic (M) orders and determine the conditions for the emergence of superconductivity on the background of a spin-density-wave state and also for the coexistence of superconductivity and magnetism. We show that the transition of a magnetic system into a superconducting state as the parameter μ increases can be a first-order phase transition at low temperatures. We also obtain an expression for the heat capacity jump C _S -C _N at T = T _c , which depends on M and μ and differs essentially from the case of the Bardeen-Cooper-Schrieffer theory. We also consider the transformations related to the density of electron states of the relevant anisotropic system, which can undergo essential changes under pressure or doping.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Magnetism and superconductivity in a quasi-2D anisotropic system doped with charge carriers

The theory of multiband superconducting systems with variable density of charge carriers is analyzed. The possibility of emergence of nonphonon high-temperature superconductivity due to the predominance of electron–electron interband interactions over intraband interactions, as well as due to the fact that the thermodynamic and magnetic properties of multiband systems in the superconducting phase differ qualitatively from those of single-band systems, is indicated. Phase transitions in a quasi-2D anisotropic medium upon a change in the carrier concentration, i.e., a transition from the commensurate to the incommensurate state of the spin density wave, are analyzed. Such a transition is observed when the Umklapp processes in the lattice structure are taken into account. These processes facilitate a deviation of wavevector Q of the spin density wave from 2k_F, as well as a displacement of the bandgap relative to the Fermi surface. This leads to the generation of free charge carriers and the possibility of superconductivity. It is shown that superconductivity accompanies the magnetism. The conditions for the coexistence of these two phenomena are determined.     

Complete derivation of space groups of magnetic symmetry of crystals by numerical construction

The solution is given to the problem regarding the derivation of the so-called space groups of magnetic symmetry with crystallographic angles of rotation of the spin vector, which was formulated as far back as the early 1970s. The crystallographic P-symmetries that should be used in the generalization with the three-dimensional space Fedorov groups G ₃ are revealed. The space groups G ₃ are generalized with each of these P-symmetries.     

The influence of thermal processing on the relative mobility of edge and screw dislocations in NaCl crystals

The effect of thermal processing on the mobility of dislocations is investigated in NaCl crystals doped with impurities of various types—high-solubility impurities (Ca²⁺) and low-solubility impurities (Pb²⁺). The results obtained after aging and thermal processing indicate that the type of impurity and its state (e.g., level of aggregation) in the crystal have a strong effect on the relative mobility of edge and screw dislocations, and also on the parameters of double transverse slip. Fiz. Tverd. Tela (St. Petersburg) 41, 1041–1043 (June 1999)