Flux bunching in type-II superconductors

We show that a type-II superconductor at low flux densities ($B\ll H_{c1\mathrm{}}$) is globally unstable to formation of a two-phase state with some regions containing flux, and others containing no flux. The basic source of the instability is the dependence of the vortex energy on the matter density, which leads to an effective attractive interaction between vortices. The instability of a uniform array of vortices discovered by P. H. Roberts is shown to signal the tendency of the system to separate into these two phases. The phase separation is expected to occur only at very low flux densities in laboratory superconductors; however, we estimate that the proton superconductor in neutron stars may be in the two-phase state.