We study the correlations between two neutrons in borromian nuclei 11Li and 6He by using a three-body model with a density-dependent contact two-body interaction. It is shown that the two neutrons show a compact bound feature at the nuclear surface due to the mixing of single particle states of different parity. We study the Coulomb breakup cross sections of 11Li and 6He using the same three-body model. We show that the concentration of the B(E1) strength near the threshold can be well reproduced with this model as a typical nature of the halo nuclei. The energy distributions of two emitted neutrons from dipole excitations are also studied using the correlated wave functions of dipole excitations.