Far Infrared Magneto-Optical Activity in High Temperature Superconductors.

Infrared spectroscopy has been used in search for the energy gap since the discovery of high temperature superconductors (HTSC). In spite of extensive studies, it still remains a controversial topic. On the other hand, when a DC magnetic field is applied perpendicular to the a-b plane of a HTSC, several optical resonances with their excitation energies below the gap energy (in BCS picture) are expected to be observed. They are cyclotron resonance, quasi-particle excitation inside the vortex cores, and the vortex pinning resonance. In this dissertation, we report a detailed study of these optical resonances in the mixed state of high temperature superconducting thin films. Broad band Far infrared (20 cm^{-1} ~ 200cm ^{-1}) magneto-transmission experiments are done on YBa_2Cu_3 O_7 and Bi_2 Sr_2CaCu_2 O_8 thin films at 2 K under external magnetic fields up to 15 Tesla. Polarizing the incoming radiation into circular modes is an essential technique in this study: We measure the transmission of FIR radiation circularly polarized in one and then the other direction. We focus on the difference between these two measurements, which is called magneto -optical activity or chirality. Our transmission data show a clear magneto-optical activity over the whole range of frequencies. For w> 100cm^{ -1}, the optical activity is consistent with cyclotron resonance. The superconducting charge carriers are shown to be holes with effective mass of 2 ~ 3 times the bare electron mass. We observe the signature of vortex core excitation at w cong 65cm^{ -1} with chirality opposite to that of the cyclotron resonance. The vortex pinning resonance is observed at w cong 30cm^{ -1} and has the same chirality as the cyclotron resonance. We have extended the microscopic theory on vortex dynamics developed by T. Hsu in order to interpret the observed magneto-optical activity. In this theory, the response of the mixed state in a type II superconductor, based on a conventional s-wave BCS picture, is described using the field theoretical considerations. This theory starts from the observation that the order parameter near the core of a vortex is a self consistent quantity which determines and is determined by the quasi-particle wavefunction within the vortex core. Cyclotron resonance, vortex core excitations, and vortex pinning and damping are brought together into a single expression in this theory.