IR Hall Angle Measurements On Single Crystal Bi-2212 (BSCCO)

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## Abstract

The far-infrared complex ac- Hall angle was studied in thin optimally doped single crystal Bi-2212 as a continuous function of temperature in both the normal and superconducting states. The temperature was varied from 25 to 300 K at a discrete set of frequencies in the range of 25 to 175 cm^-1.

Much of this dissertation focuses on the design and construction of an instrument that is capable of measuring the FIR ac-Hall angle in BSCCO as a continuous function of temperature with high sensitivity. The heterodyne system is capable of measuring the real and imaginary part of the Hall angle to an accuracy of ~ 0.1 mrad over a temperature range of 20 to 320 K, and a frequency range of 20 to 240 cm^-1.

The normal state properties are measured from Tc up to room temperature at four discrete frequencies, demonstrating clear non-Drude frequency dependence. Furthermore, a recently proposed square- Lorentzian model does not reasonably describe the present data, although previous relatively noisy FIR Hall angle measurements which the model appeared to describe are consistent with the present measurements.

Specifically, the real part of the inverse Hall angle obeys a temperature power law, T^a, where a = 1.65 +/- 0.1 which is consistent with the dc- value of 1.75 +/- 0.05. The values show a decrease with increasing frequency, clearly displaying non-Drude behavior.

For the three frequencies below 90 cm^-1, the Hall frequency is a constant in temperature and frequency to within 20% from Tc up to room temperature. The Hall frequency is 0.38 +/- 0.03 cm^-1/T which corresponds to an effective mass of 2.5 +/- 0.21 m_e in reasonable agreement with the values found in FIR optical measurements (3.0 +/- 0.4), ARPES dispersion results along the (pi,pi) nodal direction (2.9 m_e), and near-IR ac- Hall measurements (2.8 m_e) where m_e is the bare electron mass.

The salient features of the superconducting state are qualitatively consistent with a simple model of the conductivity which contains a quasi-particle cyclotron resonance, a zero frequency (London) superfluid resonance, and a finite frequency chiral oscillator at ~ 35 cm^-1. The high frequency (175 cm^-1) data is consistent with one collective mode cyclotron resonance. A frequency dependent feature in the imaginary part of the Hall angle is observed 10 K above Tc, suggestive of precursive superconducting state behavior.