Shape Resonances in superconducting gaps in a 2DEG at oxide- oxide interface

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 a superconducting 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 obtain shape resonances in the superconducting gaps, characterisc gaps to Tc ratios and the BCS-BEC crossover in the upper subband for different pairing strength in the shallow Fermi surface, pointing toward the best configurations for enhanced superconductivity in 2DEG.