Far-infrared magnetospectroscopy of the hole pocket in bismuth. I. Band-structure effects

Weak cyclotron, spin-flip, and combined resonances associated with the hole pocket of bismuth have been studied in magnetotransmission experiments at far-infrared frequencies in both the Voigt and Faraday configurations. The experiments were done on single-crystal samples at liquid-helium temperatures in magnetic fields up to 140 kG using far-infrared molecular-gas lasers (HCN, ${\mathrm{H}}_2$O, ${\mathrm{D}}_2$O). The anisotropy of the spectra was studied with emphasis on the case in which the magnetic field is oriented in the binary plane. The experimental data have been analyzed in terms of a one-band effective Hamiltonian derived by $\overrightarrow{P}·\overrightarrow{\pi }$ perturbation theory. Since the observed transitions are forbidden in the effective-mass approximation, the effective Hamiltonian was taken to fourth order in $\overrightarrow{P}$ and $\overrightarrow{\Pi }$. Higher-order terms can be neglected because the kinetic energy of the holes is small compared with the energy gap to the nearest band. Using Golin's calculations of the interband velocity matrix elements as a guide, the parameters of the effective Hamiltonian have been adjusted to give good account of the positions, linewidths, and intensities of the absorption lines. The resulting Hamiltonian is also consistent with the cyclotron masses and spin-splitting factors reported in the literature for the holes in bismuth. In the single-particle approximation the effective Hamiltonian does not account for the sharp fine structure that is observed on the absorption lines. Experiments show that these features are intrinsic effects in undeformed bismuth. They have been interpreted in terms of electron-electron interaction effects. The analysis of these effects will be published separately.