Superconductivity in Repulsive Fermi-Systems at Low Density
Abstract. In the large variety of models such as 3D and 2D Fermi-gas model with hard-core repulsion, 3D and 2D Hubbard model, and the Shubin–Vonsovsky model, we demonstrate the possibility of triplet p-wave pairing at low electron density. We show that the critical temperature of the p-wave pairing can be strongly increased in a spin-polarized case or in a two-band situation already at low density and reach experimentally feasible values of (1–5) K. We also discuss briefly d-wave pairing and high-TC superconductivity with TC ∼ 100 K, which arises in the 2D t-J model in the range of parameters realistic for cuprates.
We demonstrate the instability of the normal state of purely repulsive fermionic systems towards the transition to the Kohn-Luttinger superconducting state. We construct the superconducting phase diagrams of these systems in the framework of the Hubbard and Shubin-Vonsovsky models on the square and hexagonal lattices. We show that an account for the long-range Coulomb interactions, as well as the Kohn- Luttinger renormalizations, lead to an increase in the critical superconducting temperatures in various materials, such as high-temperature superconductors, idealized monolayer, and bilayer of doped graphene. Additionally, we discuss the role of the structural disorder and the nonmagnetic impurities in superconducting properties of real graphene systems.
In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with TC of the order of 100 K) we should proceed to the t–Jmodel with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with TC of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.
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The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.
Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.