Topological glass transition in entangled flux state

Abstract

We predict a glass transition in the recently discovered flux-fluid state of high-${\mathit{T}}_{\mathit{c}}$ superconductors due to topological entanglements. Two possible relaxation mechanisms are considered---single-flux-line motion with relaxation time ${\mathrm{\ensuremath{\tau}}}_{1}$\ensuremath{\sim}exp{exp[(\ensuremath{\Lambda}/d${)}^{2}$]}, and collective motion of many flux lines with relaxation time ${\mathrm{\ensuremath{\tau}}}_{\mathrm{col}\mathrm{\ensuremath{\sim}}}$exp[(\ensuremath{\Lambda}/d${)}^{6}$], where \ensuremath{\Lambda} is the magnitude of transverse fluctuations of flux lines and d is the intervortex spacing. This extremely slow relaxation enables the system of entangled flux lines to support supercurrents in the presence of only a few strong pinning centers.