Unusual boundary effect on coherency of two-band superconductivity

We demonstrate that the healing of two-band superconductivity near the surface of the system is governed by length scales which are drastically different from correlation lengths. Similar to the one-band case, one of the characteristic lengths diverges at critical temperature $T_c$, while another one shows unusual behaviour having singularity at $T_{c+}<T_c$. By moving away from the boundary, these scales approach coherence lengths in the bulk state, where the divergence at $T_{c+}$ is removed by arbitrary weak interband coupling. Such a boundary-driven modification in coherency affects proximity phenomenon. We show that critical temperature of binary NS system can exhibit an inflection near $T_{c+}$ as two-band superconducting layer becomes thinner.