Far-infrared magnetospectroscopy of the hole pocket in bismuth. II. Electron-electron interaction effects

Fine structure observed on the cyclotron, spin-flip, and combined resonance absorption lines reported in the previous paper are interpreted in terms of electron-electron interaction effects. The experiments are first interpreted qualitatively in terms of the Landau-Silin theory of Fermi liquids modified to account for the nonellipsoidal constant-energy surfaces for the carriers in the hole pocket in bismuth. This analysis is suggestive of electron-electron interaction effects in the absorption line shapes but it is not conclusive because the condition for the theory (ωEF) is not well satisfied in the experiments. A microscopic theory of these effects is then developed using the generalized random-phase approximation which is justified because rₛ0.1 in bismuth. The resulting physical picture for the interpretation of the experiments closely resembles that of the excitonic effects on the absorption edges in semiconductors. The final-state interaction of the electron-hole pairs produced in the optical absorption permits the formation of quasibound collective or excitonic states of lower energy than an uncorrelated pair. The excitonic states for this case are novel in that they are associated with parallel (or nearly parallel) bands and, like the Cooper pair, momentum-space restrictions at the Fermi level enter into their description. An equation is derived which can be thought of as the Schr\"odinger equation in the momentum-space representation for these excitonic states. The corresponding excitonic states are found to be the microscopic equivalent to the Fermi-liquid modes of an interacting charged Fermi gas in an applied magnetic field. The frequency-dependent conductivity tensor including electron-electron interaction effects is also calculated within the random-phase approximation. From this theory numerical calculations of the line shapes are performed for comparison with the experiments on cyclotron, spin-flip, and combined resonance. A Yukawa potential is used to represent the screened Coulomb interaction between the particles in bismuth. The calculations are successful in accounting for the fine-structure features observed in the experiments with reasonable parameters in the model interaction potential. It is concluded that there is a possibility that the interpretation in terms of the excitonic picture with a screened Coulomb interaction is the correct one.