Spin susceptibility in small Fermi energy systems: effects of nonmagnetic impurities

TL;DR

This paper investigates how non-magnetic impurities affect the spin susceptibility in small Fermi energy metals, revealing significant suppression when impurity scattering rivals the Fermi energy, with implications for understanding MgB₂'s nonadiabatic properties.

Contribution

It demonstrates the impact of impurity scattering on spin susceptibility in small Fermi energy systems, incorporating nonadiabatic electron-phonon interactions, and explains recent experimental findings in MgB₂.

Findings

Spin susceptibility decreases significantly when impurity scattering rate approaches Fermi energy.

Nonadiabatic electron-phonon effects are relevant in small Fermi energy metals.

MgB₂'s behavior under irradiation can be explained by small Fermi energy effects.

Abstract

In small Fermi energy metals, disorder can deeply modify superconducting state properties leading to a strong suppression of the critical temperature $T_c$. In this paper, we show that also normal state properties can be seriously influenced by disorder when the Fermi energy $E_{\rm F}$ is sufficiently small. We calculate the normal state spin susceptibility $\chi$ for a narrow band electron-phonon coupled metal as a function of the non-magnetic impurity scattering rate $\gamma_{\rm imp}$. We find that as soon as $\gamma_{\rm imp}$ is comparable to $E_{\rm F}$, $\chi$ is strongly reduced with respect to its value in the clean limit. The effects of the electron-phonon interaction including the nonadiabatic corrections are discussed. Our results strongly suggest that the recent finding on irradiated MgB$_2$ samples can be naturally explained in terms of small $E_{\rm F}$ values associated with the $\sigma$-bands of the boron plane, sustaining therefore the hypothesis that MgB$_2$ is a nonadiabatic metal.