  Quantum confinement of the perpendicular motion of electrons in
single-crystalline metallic superconducting nanofilms splits the conduction
band into a series of single-electron subbands. A distinctive feature of such a
nanoscale multi-band superconductor is that the energetic position of each
subband can vary significantly with changing nanofilm thickness, substrate
material, protection cover and other details of the fabrication process. It can
occur that the bottom of one of the available subbands is situated in the
vicinity of the Fermi level. We demonstrate that the character of the
superconducting pairing in such a subband changes dramatically and exhibits a
clear molecule-like trend, which is very similar to the well-known crossover
from the Bardeen-Cooper-Schrieffer regime to Bose-Einstein condensation
(BCS-BEC) observed in trapped ultracold fermions. For Pb nanofilms with
thickness of 4 and 5 monolayers (ML) this will lead to a spectacular scenario:
up to half of all the Cooper pairs nearly collapse, shrinking in the lateral
size (parallel to the nanofilm) down to a few nanometers. As a result, the
superconducting condensate will be a coherent mixture of almost molecule-like
fermionic pairs with ordinary, extended Cooper pairs.
