1. It has long been recognized that the superconductors are intrinsically nonlinear. The investigation of their nonlinear behaviour might shed light into the mechanism of high- temperature superconductivity. Do the carriers of superconductivity (Cooper pairs) survive above the macroscopic critical temperature T c ? If they do, what is the mechanism that prolongs their lifetime in underdoped cuprates? Is the nonlinear behaviour above T c inductive or resistive in nature? Nonlinear measurements in optimally- and under- doped cuprates might provide the answers. Intrinsic Microwave Nonlinearities in High-Temperature Superconductors Steven M. Anlage, University of Maryland, NSF/DMR - 0201261 Measurement and numerical fit of third-order nonlinear response for underdoped YBCO (YBa 2 Cu 3 O 6.63 ): above the macroscopic critical temperature T c =61.0 K. The sample preserves a feature of the superconducting state: the intrinsic nonlinear behavior. Measurements of the nonlinear response above T c can be used to estimate the lifetime of the Cooper pairs (~ 10 -11 s in this case)

2. Intrinsic Microwave Nonlinearities in High-Temperature Superconductors Steven M. Anlage, University of Maryland, NSF/DMR - 0201261 Traditionally the microwave nonlinear behaviour has been investigated by using resonator techniques: the sample is placed in a macroscopic microwave field and the nonlinear response originating from the entire volume of the sample is measured. The local technique, employed at the University of Maryland has major advantages: it eliminates all the extrinsic nonlinear effects associated with the edges and corners of the sample. A microscopic microwave field is excited in close proximity of the sample surface and the nonlinear response of a small volume of the sample is studied as a function of temperature, input power and orientation of the excitation microwave field. Measurements of YBCO thin films reveal that in underdoped samples the nonlinear effects are significant even when the macroscopic superconductivity is suppressed by temperature (for T>Tc). The tail of the peak centred on Tc (see Fig. 1) has been interpreted as a resistive contribution due to the survival of the Cooper pairs above Tc. The lifetime of Cooper pairs above Tc has been estimated from measurements. In optimally doped YBCO this resistive contribution is hardly observable which suggests that in underdoped YBCO an unknown mechanism prolongs the lifetime of Cooper pairs.

3. Education: Two graduate students (Sheng-Chiang Lee and Dragos I. Mircea) contributed to this project. Currently, Sheng- Chiang is a postdoc at the University of Florida and Dragos is graduate student in the Center for Superconductivity Research, at the University of Maryland. In order to extend our collaborations with industry, Dragos has spent the summer of 2005 at Seagate Technologies in Pittsburgh, PA as a summer intern. We plan to utilize advanced technologies from the magnetic recording industry to improve the sensitivity of our experiments. Societal Impact: The high-temperature superconductors (HTS) are successfully implemented in microwave filters for wireless communications. However, their nonlinear behaviour limits the operating power of the microwave resonators that are based on HTS superconducting technologies. A deeper understanding of the microwave nonlinear response of HTS is required in order to improve the properties of the superconducting materials used in microwave filters. Our intern student at Seagate is also transferring technology and know-how from our lab to industry to enable higher-density magnetic recording technologies. Intrinsic Microwave Nonlinearities in High-Temperature Superconductors Steven M. Anlage, University of Maryland, NSF/DMR - 0201261

4. It has been recognized since the discovery of high-temperature superconductivity that these materials have high potential for microwave passive devices (resonators and filters). Currently, about 5000 high-temperature superconducting microwave filters for the wireless industry are deployed in the USA. The Nonlinear Microwave Microscope, developed with the support of NSF – GOALI, can be used in order to assess the viability of different superconducting films for the needs of the industry. Additionally, the Nonlinear Microwave Microscope has been utilized to investigate the nature of the intrinsic nonlinear response and the time reversal symmetry breaking in high-temperature superconductors. Intrinsic Microwave Nonlinearities in High-Temperature Superconductors Steven M. Anlage, University of Maryland, NSF/DMR - 0201261