High-pressure superconducting state in hydrogen

TL;DR

This study investigates the high-pressure superconducting properties of atomic hydrogen at 1-2.5 TPa, revealing very high critical temperatures and strong-coupling effects that challenge BCS theory predictions.

Contribution

The paper provides detailed thermodynamic parameters of superconducting hydrogen under extreme pressures using Eliashberg formalism, highlighting deviations from BCS theory.

Findings

Critical temperature ranges from 301.2 K to 437.3 K.

Electron effective mass increases significantly under pressure.

Energy gap ratio violates BCS predictions.

Abstract

The paper determines the thermodynamic parameters of the superconducting state in the metallic atomic hydrogen under the pressure at $1$ TPa, $1.5$ TPa, and $2.5$ TPa. The calculations were conducted in the framework of the Eliashberg formalism. It has been shown that the critical temperature is very high (in the range from $301.2$ K to $437.3$ K), as well as high are the values of the electron effective mass (from $3.43$ $m_{e}$ to $6.88$ $m_{e}$), where $m_{e}$ denotes the electron band mass. The ratio of the low-temperature energy gap to the critical temperature explicitly violates the predictions of the BCS theory: $2\Delta\left(0\right)/k_{B}T_{C}\in\left<4.84,5.85\right>$. Additionally, the free energy difference between the superconducting and normal state, the thermodynamic critical field, and the specific heat of the superconducting state have been determined. Due to the significant strong-coupling and retardation effects those quantities cannot be correctly described in the framework of the BCS theory.