Electron localization effects on the low-temperature high-field magnetoresistivity of three-dimensional amorphous superconductors

Abstract

The electrical resistivity $\ensuremath{\rho}$ of three-dimensional amorphous superconducting films $a$-${\mathrm{Mo}}_{3}\mathrm{Si}$ and $a$-${\mathrm{Nb}}_{3}\mathrm{Ge}$ is measured in magnetic fields ${\ensuremath{\mu}}_{0}H$ up to 30 T. At low temperatures and at magnetic fields above the upper critical field ${H}_{c2}$, $\ensuremath{\rho}$ is temperature independent and decreases as a function of magnetic field. This field dependence is consistent with localization theory in the high-field limit $[{\ensuremath{\mu}}_{0}H\ensuremath{\gg}\ensuremath{\Elzxh}{/(4\mathrm{eL}}_{\ensuremath{\varphi}}^{2})$, where ${L}_{\ensuremath{\varphi}}$ is the phase-coherence length]. Above the superconducting transition temperature ${T}_{c},$ the temperature dependence of the conductivity is consistent with inelastic scattering processes which are destructive to the phase coherence for electron localization, thereby allowing estimates for ${L}_{\ensuremath{\varphi}}(T)$. The Hall effect data on $a$-${\mathrm{Mo}}_{3}\mathrm{Si}$, in conjunction with the resistivity data, allow the determination of the carrier concentration and mean free path. The upper critical field is comparable to (in $a$-${\mathrm{Mo}}_{3}\mathrm{Si})$ and significantly larger than (in $a$-${\mathrm{Nb}}_{3}\mathrm{Ge})$ the Clogston-Chandrasekhar paramagnetic limit. This phenomenon is discussed in the context of electron localization.