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Band calculations for the hole doped La$_2$CuO$_4$ system show thatartificial periodicities of Ba dopants can give the material differentproperties than from a uniform distribution of dopants. A periodicity withinthe planes make static pseudogaps which could be tuned to raise thedensity-of-states (DOS) at $E_F$ and the superconducting $T_C$.  A periodic doping dependence perpendicular to the CuO planes can increase thematrix element for spin fluctuations.

Mechanisms for higher $T_C$ in copper oxide superconductors; Ideas from band calculations