Electronic and superconducting properties of a superlattice of quantum stripes at the atomic limit

The superconducting gap, the critical temperature and the isotope coefficient in a superlattice of metallic quan- tum stripes is calculated as a function of the electron number density. We show that it is possible to design a particu- lar artificial superlattice of quantum stripes that exhibits the curves of Tc and of the isotope coefficient as a function of the charge density as in cuprate superconductors. The shape of the superlattice is designed in order to tune the chem- ical potential near the bottom of the third subband for an ̊ −2 electron number density of ρ ∼ 5.810−2 A . The supercon- ducting critical temperature shows a resonant amplification as a function of electron number density ρ with a maximum at a critical value ρc . The isotope coefficient shows a sharp drop from a regime where α > 0.5 at ρ < ρc to a regime where α < 0.2 at ρ ≥ ρc . The underdoped and overdoped regime in cuprate superconductors is associated with a tran- sition from a quasi 1D behavior for ρ > ρc to quasi 2D behavior for ρ < ρc with opening of a pseudogap at ρ ∼ ρc .