Making High T$_c$ Higher: A Theoretical Proposal

There is considerable evidence that the highest $T_c$ obtainable in a copper-oxide plane is limitted by the competition between two effects: On the one hand, as the concentration of doped-holes, $x$, is increased, the pairing scale, which is related to the properties of a doped Mott insulator, decreases. On the otherhand, the superfluid density, which controls the stiffness of the system to phase fluctuations, vanishes as $x \to 0$, and increases with increasing $x$. Optimal $T_c$ is obtained at a crossover from a phase ordering dominated regime at small $x$ to a pairing dominated regime at large $x$. If this description is valid, then higher $T_c$'s can be obtained in an array of coupled planes with different doped hole concentrations, such that a high pairing scale is derived from the underdoped planes and a large phase stiffness from the optimally or overdoped ones.