Vortex patterns and sheets in segregated two component Bose–Einstein condensates

We study minimizers of a Gross–Pitaevskii energy describing a two-component Bose–Einstein condensate set into rotation. We consider the case of segregation of the components in the Thomas–Fermi regime, where a small parameter ε conveys a singular perturbation. We estimate the energy as a term due to a perimeter minimization and a term due to rotation. In particular, we prove a new estimate concerning the error of a Modica Mortola type energy away from the interface. For large rotations, we show that the interface between the components gets long, which is a first indication towards vortex sheets.