  In multiband superconductivity, the case where the single electron hopping
between different Fermi surface spots of different symmetry is forbidden by
selection rules is recently attracting a large interest. The focus is addressed
to superconductivity made of multiple condensates with different symmetry where
the chemical potential crosses a 2.5 Lifshitz transition. This can now be
investigated experimentally by fine-tuning of the chemical potential in the
range of tens meV around a band edge using gate voltage control. We discuss
here the case of the two-dimensional electron gas (2DEG), at the interface
between two insulating oxides confined within a slab of 5 nanometers thickness,
where the electronic structure is made of subbands generated by quantum size
effects. We focus on the case of the BCS-BEC transition in the upper subband
for different pairing strength in the shallow Fermi surface.
