The gap amplification at a "shape resonance" in a superlattice of quantum stripes: a mechanism for high Tc

The amplification of the superconducting critical temperature Tc from the low temperature range in homogeneous 2D planes (Tc<23 K) to the high temperature range (23 K<Tc<150 K) in an artificial heterostructure of quantum stripes is calculated. The high Tc is obtained by tuning the chemical potential near the bottom of the nth subband at a "shape resonance", in a range, whithin the energy cutoff for the pairing interaction. The resonance for the gap at the nth "shape resonance" is studied for a free electron gas in the BCS approximation as a function of the stripe width L, and of the number of electrons {\rho} per unit surface. An amplification factor for coupling 0.1<{\lambda}<0.3 is obtained at the third shape resonance raising the critical temperature in the high Tc range.