Group Theoretical Analysis of Phonon Assisted Optical Transition in GaSe

Abstract

The selection rules for the indirect optical transition in ε- and γ-GaSe are investigated group-theoretically by using the band structure of β-GaSe calculated by Schlüter. Without taking into account the spin-orbit interaction, the indirect transition is allowed only for the light with polarization vector E parallel to the crystal c-axis (E⁄⁄c) in ε-GaSe as in β-GaSe, but it is allowed both for E⁄⁄c and for E⊥c in γ-GaSe. The irreducible representations of the phonon mode associated with the transitions are M₁⁺(A_g) in β, M₁(A_g) in ε and M₁(A′) in γ. The M₁(A′) mode of γ-GaSe is compatible with M₁(A_g) and M₃(B_g) of ε-GaSe, and with M₁⁺(A_g), M₃⁺(B_2g), M₂⁻(B_3u) and M₄⁻(B_1u) of β-GaSe. So, the number of phohons associated with the indirect optical transition in GaSe is affected by the mixture of these modifications.