USE OF KRAMERS-KRONIG RELATIONS TO EXTRACT THE CONDUCTIVITY OF HIGH-TC SUPERCONDUCTORS FROM OPTICAL-DATA

In principle the conductivity of the cuprate superconductors can be obtained from reflectivity measurements using the Kramers-Kronig-transform technique. However, at low temperatures and for frequencies below approximately 300 cm-1 the reflectivities of materials such as YBa2Cu3O7 are close to unity. Uncertainty in the precise signal level corresponding to unity reflectivity and a lack of knowledge of the reflectivity below the lowest measured frequency cause this method to become unreliable. To address this problem we have used a bolometric technique and a resonant technique to obtain accurate submillimeter and microwave data for the residual losses in epitaxial thin films of YBa2Cu3O7 at low temperatures. The Kramers-Kronig analysis of our data is in good agreement with results from fitting our data to simple weakly coupled grain and two-fluid models for the a-b plane conductivity. However, below 450 cm-1 it is in disagreement with some published results of other workers obtained from Kramers-Kronig analysis of reflectivity data. To understand this discrepancy we analyze how the conductivity determined by the Kramers-Kronig-transform technique depends on some commonly used low-frequency extrapolations of reflectivity data,