The Meissner effect in high-temperature hydrogen-rich superconductors under high pressure

In the last few years, the superconducting transition temperature, Tc, of hydrogen-rich compounds has increased dramatically, and is now approaching room temperature. However, the pressures at which these materials are stable exceed one million atmospheres and limit the number of available experimental probes - superconductivity has been primarily identified based on electrical transport measurements. Here, we report definitive evidence of the Meissner effect – a key feature of superconductivity – in H3S and LaH10. Furthermore, we have determined characteristic superconducting parameters: a lower critical field Hc1 of ∼1.9 and ∼1.0 T, and a London penetration depth λL of ∼13 and ∼21 nm in Im-3m-H3S and Fm-3m-LaH10, respectively. These compounds have low values of the Ginzburg-Landau parameter κ ∼7–14 and belong to the group of “moderate” type II superconductors.

Transmission coefficients of superconducting particles

Objectives. There is no general theory of superconductivity capable of fully describing this phenomenon, which imposes its own difficulties in the search for new superconducting materials, as well as in the study of their properties. In particular, the electrodynamics of a superconducting system is unexplored. With the aim of a possible further description of the electrodynamics of superconductors, the temperature dependences of the energy parameters of a Cooper pair in the potential field of Abrikosov vortex were analyzed.Methods. The basis for the obtained results of the work was the consideration of the transmission coefficient for a superconducting particle in the approximation of the Wentzel– Kramers–Brillouin method, as well as the relationship between the critical temperature and the London penetration depth and the coherence length based on the model of plasmon destruction of the superconducting state.Results. The dependences of the lifetime of a particle in a potential well, penetration depth, frequency of impacts of a particle against a potential barrier, blurring of the energy level, transmission coefficient, and potential and kinetic energy of a particle on temperature were obtained. The characteristic values of these parameters were obtained at absolute zero for various cuprate, organic, and other superconducting materials. The dependences of the critical electric potential on temperature, as well as the London penetration depth, coherence length, and electric potential on the transmission coefficient at different temperatures were obtained. The form of the dependences qualitatively corresponds to the experimental data.Conclusions. The results obtained can be used to construct a general theory of superconductivity, describe the electrodynamics of a superconducting state, and develop new superconductors with higher critical currents.

Superconductivity and nucleation from fractal anisotropy and product-like fractal measure

Superconductivity is analysed based on the product-like fractal measure approach with fractal dimension α introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media. Our study shows the emergence of a massless state at the boundary of the superconductor and the simultaneous occurrence of isothermal and adiabatic processes in the superconductor depending on the position of the electrons. Several physical quantities were found to be position-dependent comparable with those arising in heavy doping and p–n junction. At the boundary of the superconductor, a shrinkage of the magnetic field was observed, leading to a scenario equivalent to the Meissner–Ochsenfeld effect. An enhancement of the London penetration depth is revealed and such an improvement was observed in pnictides at the onset of commensurate spin-density-wave order inside the superconducting phase at zero temperature. The Bardeen–Cooper–Schrieffer theory was also analysed and the appearance of zero-energy states is detected. Nucleation of superconductivity in a bulk was also studied. The system acts as a quantum damped harmonic oscillator and our analysis showed that type-I superconductivity occurs when κ < 2 / ( 1 + α ) , whereas type II occurs for κ > 2 / ( 1 + α ) , where κ is the Ginzburg–Landau parameter. The transition at the passage from the ‘genuine’ to the ‘intermediate’ type-I estimates 0.767767 < α ≤ 1 .