Topological glass transition in entangled flux state

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 ${\mathrm{\tau }}_1$∼exp{exp[(Λ/d${)}^2$]}, and collective motion of many flux lines with relaxation time ${\mathrm{\tau }}_{\mathrm{col}\mathrm{\sim }}$exp[(Λ/d${)}^6$], where Λ 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.