Quantum Aspects and Electrodynamics of High-Frequency Cyclotron Resonances in Bismuth

Abstract

We present a series of measurements on various aspects of cyclotron resonance in Bi at far-infrared laser frequencies (890.7, 964.3, 1539.5, and 2526.6 GHz). The experiments make use of a spectrometer where the sample forms one plate of a TEM-mode strip transmission line. We observe subharmonics of cyclotron resonance which appear split into a number of distinct resonance lines, each due to a particular transition between Landau levels of the nonparabolic conduction band of Bi. From the line positions for the binary-axis low-mass resonance we determine the band parameters $E_g=13.0\mathrm{}\pm 2$ meV and $m_{}^{*}{}_c{}^{}=(0.00170\mathrm{}\pm 0.00025)m_0$. The temperature dependence of the amplitudes of the resonance lines gives $E_F=29.7\mathrm{}\pm 0.5$ meV. We observe the amplitude decay of successive subharmonics of the resonance and show that the amplitude decreases with subharmonic number $n$ approximately as ${\left(\frac{R}{\delta }\right)}^{2n-2}$ for the binary-axis signal. In addition to cyclotron resonance, we observe and identify various impedance anomalies as due to cyclotron-wave propagation. Finally, we present some evidence for an energy-dependent relaxation time in Bi, from the observation that cyclotron-resonance linewidths are related to the energy separation of Landau level and Fermi energy.