Study of electron-phonon interaction and magneto-optical anomalies in two-dimensionally confined systems

Abstract

This paper presents a study of the nature of electron-optical phonon coupling in two-dimensionally confined systems (e.g., inversion or accumulation layers in metal-oxide semiconductors, heterojunctions, and superlattices of polar semiconductors) and shows that magneto-optical anomalies in two dimensions provide a powerful tool for their investigation. Several models of electron-optical phonon coupling are studied. These include coupling with (i) three-dimensional optical phonon with fixed $k_z$, the wave vector normal to the two-dimensional plane of confinement, (ii) three-dimensional optical phonons with arbitrary $k_z$ due to the loss of wave-vector selection rules in finite structures, (iii) interface optical-phonon modes, and (iv) purely two-dimensional optical-phonon modes. Where appropriate, zone-folding effects are explicitly taken into account. Resonant magneto-optical absorption studies are shown to be a means of unambiguously probing the electron-phonon coupling in these novel materials. Within the framework of the Fröhlich model and including only the resonant self-energy diagram in the theory, it is shown that at resonance the relevant cyclotron peak splits into a doublet. The resonance effect is found to be much sharper in two dimensions compared to the bulk case, a consequence of the lack of $k_z$ continuum of electronic energy. For a given magnetic field of strength $B$, the resonant splitting is proportional to $B^{\frac{3}{4}}$ for two-dimensionally confined carriers, in contrast to the $B^{\frac{1}{2}}$ behavior in the bulk. The proportionality factor depends on the specific phonon mechanism considered. The spectral weights of the split peaks are evaluated. Allowing, phenomenologically, finite width of the resonant Landau levels, as well as for the Landau level from which optical transition originates, the expressions for optical absorption and Raman scattering are obtained. The significance of electron-light vertex correction is investigated and shown to be important under certain conditions. The possibility of a resonant splitting in two dimensions in direct intersubband transition without any magnetic field is also investigated.