Sum rules and energy scales in the high-temperature superconductor YBa2Cu3O6+x -: art. no. 024514

The Ferrell-Glover-Tinkham (FGT) sum rule has been applied to the temperature dependence of the in-plane optical conductivity of optimally doped YBa2Cu3O6.95 and underdoped YBa2Cu3O6.60. Within the accuracy of the experiment, the sum rule is obeyed in both materials. However, the energy scale omega(c) required to recover the full strength of the superfluid rho(s) in the two materials is dramatically different; omega(c)similar or equal to800 cm(-1) in the optimally doped system (close to twice the maximum of the superconducting gap 2Delta(0)), but omega(c)greater than or similar to5000 cm(-1) in the underdoped system. In both materials, the normal-state scattering rate close to the critical temperature is small, Gamma<2Delta(0), so that the materials are not in the dirty limit and the relevant energy scale for rho(s) in a BCS material should be twice the energy gap. The FGT sum rule in the optimally doped material suggests that the majority of the spectral weight of the condensate comes from energies below 2Delta(0), which is consistent with a BCS material in which the condensate originates from a Fermi-liquid normal state. In the underdoped material the larger energy scale may be a result of the non-Fermi-liquid nature of the normal state. The dramatically different energy scales suggest that the nature of the normal state creates specific conditions for observing the different aspects of what is presumably a central mechanism for superconductivity in these materials.