Pressure-dependence of electron-phonon coupling and the superconducting phase in hcp Fe - a linear response study

TL;DR

This study investigates how pressure affects electron-phonon interactions and superconductivity in hcp Fe, finding that conventional mechanisms alone cannot fully explain the observed superconducting phase and its pressure dependence.

Contribution

The paper provides a detailed linear response analysis of electron-phonon coupling in hcp Fe under pressure, highlighting the limitations of phonon-mediated pairing in explaining superconductivity.

Findings

Electron-phonon coupling accounts for superconductivity in hcp Fe.

Pressure dependence of transition temperature is not fully explained by calculations.

Magnetic fluctuations and impurities influence superconducting properties but do not match observed pressure range.

Abstract

A recent experiment by Shimizu et al. has provided evidence of a superconducting phase in hcp Fe under pressure. To study the pressure-dependence of this superconducting phase we have calculated the phonon frequencies and the electron-phonon coupling in hcp Fe as a function of the lattice parameter, using the linear response (LR) scheme and the full potential linear muffin-tin orbital (FP-LMTO) method. Calculated phonon spectra and the Eliashberg functions $\alpha^2 F$ indicate that conventional s-wave electron-phonon coupling can definitely account for the appearance of the superconducting phase in hcp Fe. However, the observed change in the transition temperature with increasing pressure is far too rapid compared with the calculated results. For comparison with the linear response results, we have computed the electron-phonon coupling also by using the rigid muffin-tin (RMT) approximation. From both the LR and the RMT results it appears that electron-phonon interaction alone cannot explain the small range of volume over which superconductivity is observed. It is shown that ferromagnetic/antiferromagnetic spin fluctuations as well as scattering from magnetic impurities (spin-ordered clusters) can account for the observed values of the transition temperatures but cannot substantially improve the agreeemnt between the calculated and observed presure/volume range of the superconducting phase. A simplified treatment of p-wave pairing leads to extremely small ($\leq 10^{-2}$ K) transition temperatures. Thus our calculations seem to rule out both $s$- and $p$- wave superconductivity in hcp Fe.