E. A. Mazur

Critical temperature of metallic hydrogen at a pressure of 500 GPa

The Eliashberg theory generalized for electron–phonon systems with a variable electron density of states is used to study Tc in the I41/AMD phase of metallic hydrogen under compression taking into account the frequency behavior of the renormalization of the mass of the electron and the chemical potential. The phonon contribution to the anomalous electron Green’s function is considered. Pairing is taken into account within the entire electron band rather than in a narrow region near the Fermi surface. The frequency and temperature dependences of the complex renormalization of the mass Re Z(ω), as well as the density of states N(ω) renormalized by the electron–phonon coupling and the spectral function of the electron–phonon coupling, which are obtained in calculations, are used to calculate the anomalous electron Green’s function. The frequency dependence of the real and imaginary parts of the order parameter in the I41/AMD phase is obtained. The solution of the system of Eliashberg equations gives the value Tc = 217 K in the I41/AMD phase of hydrogen at a pressure of 500 GPa.

Reasons for high-temperature superconductivity in the electron–phonon system of hydrogen sulfide

We have calculated the electron and phonon spectra, as well as the densities of the electron and phonon states, of the stable orthorhombic structure of hydrogen sulfide SH2 in the pressure interval 100–180 GPa. It is found that at a pressure of 175 GPa, a set of parallel planes of hydrogen atoms is formed due to a structural modification of the unit cell under pressure with complete accumulation of all hydrogen atoms in these planes. As a result, the electronic properties of the system become quasi-two-dimensional. We have also analyzed the collective synphase and antiphase vibrations of hydrogen atoms in these planes, leading to the occurrence of two high-energy peaks in the phonon density of states.

High Tc in cuprates as a universal property of the electron–phonon system

The Eliashberg theory, which is generalized due to peculiar properties of the finite-width electron band for electron–phonon (EP) systems with a variable electron density of states (DOS), as well as with allowance for the electron–hole nonequivalence of the frequency behavior of the chemical potential renormalization depending on the doping level and electron correlations in the vertex function, is used to study Tc in cuprates. The phonon contribution to the nodal anomalous electron Green’s function (GF) is considered. Pairing within the total width of the electron band, and not only in a narrow layer at the Fermi surface, is taken into account. The calculated frequency and temperature dependences, as well as the dependence on the doping level of the complex renormalization ReZ, ImZ of the mass, complex renormalization Reχ(ω), Imχ(ω) of the chemical potential, and DOS N(ε) renormalized due to the EP interaction are used to calculate the electron nodal anomalous GF. It is found that the effect of suppressing the high-frequency contribution to the Eliashberg equations derived anew for the EP system with a finite width of the electron band is a decisive factor for the manifestation of the effect of high-temperature superconductivity (HTSC). It is shown that in the vicinity of the optimal hole-type doping level in cuprates, the high value of Tc is reproduced by the spectral function of the electron–phonon interaction, which is obtained from tunneling experiments. Upon an increase in the doping level, leading to an increase in the degree of electron–hole nonequivalence, the new logarithmic term appearing in the equations for Tc has a tendency to increase Tc, while intensification of damping of charge carriers (especially suppression of the cutoff factor) leads to a decrease in Tc.

Effect of temperature on phonon contribution to Green function of high-temperature superconducting cuprates

The phonon contribution to the nodal electron Green function in cuprates is considered. It is shown that the temperature dependence of the real part of the self-energy component of the Green function for cuprates with a hole doping level close to optimal is described by the electron-phonon interaction in the framework of the extended Eliashberg model.

Normal state of metallic hydrogen sulfide

A generalized theory of the normal properties of metals in the case of electron–phonon (EP) systems with a nonconstant density of electron states has been used to study the normal state of the SH3 and SH2 phases of hydrogen sulfide at different pressures. The frequency dependence of the real Re Σ (ω) and imaginary ImΣ (ω) parts of the self-energy Σ (ω) part (SEP) of the Green’s function of the electron Σ (ω), real part Re Z (ω), and imaginary part Im Z (ω) of the complex renormalization of the mass of the electron; the real part Re χ (ω) and the imaginary part Imχ (ω) of the complex renormalization of the chemical potential; and the density of electron states N (ε) renormalized by strong electron–phonon interaction have been calculated. Calculations have been carried out for the stable orthorhombic structure (space group Im3̄m) of the hydrogen sulfide SH3 for three values of the pressure P = 170, 180, and 225 GPa; and for an SH2 structure with a symmetry of I4/mmm (D4h1̄7) for three values of pressure P = 150, 180, and 225 GP at temperature T = 200 K.

Critical temperature of metallic hydrogen sulfide at 225-GPa pressure

The Eliashberg theory generalized for electron—phonon systems with a nonconstant density of electron states and with allowance made for the frequency behavior of the electron mass and chemical potential renormalizations is used to study Tc in the SH3 phase of hydrogen sulfide under pressure. The phonon contribution to the anomalous electron Green’s function is considered. The pairing within the total width of the electron band and not only in a narrow layer near the Fermi surface is taken into account. The frequency and temperature dependences of the complex mass renormalization ReZ(ω), the density of states N(ε) renormalized by the electron—phonon interactions, and the electron—phonon spectral function obtained computationally are used to calculate the anomalous electron Green’s function. A generalized Eliashberg equation with a variable density of electron states has been solved. The frequency dependence of the real and imaginary parts of the order parameter in the SH3 phase has been obtained. The value of Tc ≈ 177 K in the SH3 phase of hydrogen sulfide at pressure P = 225 GPa has been determined by solving the system of Eliashberg equations.

Metallic hydrogen with a strong electron–phonon coupling at a pressure of 300–500 GPa

Atomic metallic hydrogen, which has a lattice with the FDDD unit cell symmetry, has been shown to be a stable phase at a hydrostatic pressure of 350–500 GPa. The found structure has a phonon spectrum which is stable with respect to decay. The structural, electronic, phonon, etc., characteristics of normal metallic phases of hydrogen at a pressure of 350–500 GPa have been ab initio calculated.

Reconstruction of the conduction band in metallic hydrogen sulfide

The theory of the normal properties of a metal generalized to the case of particular properties of an electron band with a finite width for electron–phonon systems with a varying electron density of states has been used to study the normal state of the SH3 phase of hydrogen sulfide at a pressure of 225 GPa and a temperature of 200 K. The frequency dependences of the real, ReΣ(ω), and imaginary, ImΣ(ω), parts of the selfenergy part of the Green’s function of the electron Σ(ω), as well as the electron density of states N(ε) of the Im–3m stable orthorhombic structure of SH3 hydrogen sulfide at a pressure of P = 225 GPa, which is renormalized by the strong electron–phonon coupling, have been calculated. It has been established that a part of the electron conduction band of the SH3 phase of hydrogen sulfide adjacent to the Fermi level undergoes renormalization-induced reconstruction in the form of a number of energy pockets with the widths equal to fractions of the characteristic phonon energies of the system.

Metal hydrogen sulfide superconducting temperature

Abstract Éliashberg theory is generalized to the electronphonon (EP) systems with the not constant density of electronic states. The phonon contribution to the anomalous electron Green’s function (GF) is considered. The generalized Éliashberg equations with the variable density of electronic states are resolved for the hydrogen sulphide SH3 phase under pressure. The dependence of both the real and the imaginary part of the order parameter on the frequency in the SH3 phase is obtained. The Tc = 177 K value in the hydrogen sulfide SH3 phase at the pressure P = 225 GPa has been defined. The results of the solution of the Eliashberg equations for the Im-3m (170 GPa), Im-3m (200 GPa) and R3m (120 GPa) phases are presented. A peak value Tc = 241 K of the superconducting transition temperature has been predicted.

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(ε) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.