The in-plane optical conductivity of Bi 2 Sr 2 CaCu 2 O 8+δ thin films with small carrier density (underdoped) up to large carrier density (overdoped) is analyzed with unprecedented accuracy. Integrating the conductivity up to increasingly higher energies points to the energy scale involved when the superfluid condensate builds up. In the underdoped sample, states extending up to 2 eV contribute to the superfluid. This anomalously large energy scale may be assigned to a change of in-plane kinetic energy at the superconducting transition, and is compatible with an electronic pairing mechanism. 74.25.Gz, 74.72.Hs Typeset using REVT E X

In conventional BCS superconductors, the electronic kinetic energy increases upon superfluid condensation (the change ∆E kin is positive). Here we show that in the high critical temperature superconductor Bi2Sr2CaCu2O 8+δ , ∆E kin crosses over from a fully compatible conventional BCS behavior (∆E kin > 0) to an unconventional behavior (∆E kin < 0) as the free carrier density decreases. If a single mechanism is responsible for superconductivity across the whole phase diagram of high critical temperature superconductors, this mechanism should allow for a smooth transition between such two regimes around optimal doping.One of the fundamental predictions of the BCS theory is that the kinetic energy of the charge carriers increases upon condensation in the superconducting state, while the interaction energy decreases and overcompensates the kinetic energy increase, resulting in a net energy gain. The value of this condensation energy is easily determined, for instance from the value of the thermodynamical critical field, but the respective changes in kinetic and interaction terms are not easily accessed. In fact, the change in kinetic energy in "conventional" BCS superconductors has never been determined experimentally. This change is of the order of (∆/E F ) 2 , where ∆ is the energy gap and E F the Fermi energy. It is exceedingly small for a typical low temperature superconductor, of the order of 10 −6 to 10 −8 . The situation is much more favorable in High Critical Temperature Superconductors (HCTS, cuprates), where the gap is larger and the Fermi energy smaller, so that the change in kinetic energy, if it is conform to the predictions of the BCS theory, should be of the order of 10 −3 to 10 −2 , a change that has become accessible experimentally [1,2,3]. However, the mechanism for HCTS is still under debate and the change in kinetic energy could well be different from that predicted by BCS, including in sign.It is of particular interest to investigate the case of overdoped high temperature superconductors. There is a general belief that in the overdoped range, the cuprates can be described in their normal state as Fermi liquids. Thus it is conceivable that in this regime, condensation is of the BCS kind. And if it is, according to the above considerations regarding orders of magnitude, the change in kinetic energy should be large enough to be measured, allowing a quantitative comparison between theory and experiment.Our analysis shows that the change in kinetic energy in overdoped Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) having T c = 63 K is indeed compatible with the predictions of the BCS theory, both in sign and in size. The latter result appears in the data in our previous papers, but was not explicitly mentioned [2,3]. This is in contrast with the change of kinetic energy in optimally doped, and definitely in underdoped Bi-2212, which has been found to be of the opposite sign [1,2,3]. We observe that going from the overdoped to the underdoped regime, the change in kinetic energy is actually progressive, going throug...

The ab-plane reflectance of Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi-2212) thin films was measured in the 30-25 000 cm(-1) range for one underdoped ( T(c) = 70 K), and one overdoped sample ( T(c) = 63 K) down to 10 K. We find similar behaviors in the temperature dependence of the normal-state infrared response of both samples. Above T(c), the effective spectral weight, obtained from the integrated conductivity, does not decrease when T decreases, so that no opening of an optical pseudogap is seen. We suggest that these are consequences of the pseudogap opening in the k = (0,pi) direction and of the in-plane infrared conductivity being mostly sensitive to the k = (pi,pi) direction.