Figure 1

GaAs: Kohn-Sham conduction band energies along part of the $L\text{−}\Gamma \text{−}X$ direction in the Brillouin zone, showing the direct-to-indirect band gap transition under pressure. Left panel: ambient pressure. Right panel: at a theoretical pressure of $8\mathrm{GPa}$. In order to have the same scale, $\mid \mathbf{k}\mid$ is given in units of $2\pi ∕a$, where $a$ is the lattice parameter at equilibrium or at a pressure of $8\mathrm{GPa}$. The zero of energy is set at the top of the valence band. The mechanism for a virtual (real) transition is shown as a dot-dashed (dashed) line in the left (right) panel. The isoenergy surface mentioned in Sec. 3D is illustrated by the ellipse in the right panel.Reuse & Permissions

Figure 2

GaAs deformation potentials for transitions from the $\Gamma$ point to the $X$ valley. The abscissa evolves over one-quarter of the $\Gamma \text{−}X$ length. (a) Pressure dependence of the momentum ${\mathbf{q}}_{\mathit{\text{real}}}$ (in units of $2\pi ∕a_{\mathit{eq}}$) exchanged in the energy-conserving horizontal transitions from the $\Gamma$ point to the $X$ valley. These real transitions occur after the $\Gamma \text{−}X$ crossover pressure. (b) Deformation potential for real transitions as a function of ${\mathbf{q}}_{\mathit{\text{real}}}$. Filled circles: total deformation potential. Dashed (empty) circles: deformation potential for the LO (LA) scattering phonon. The $\mathbf{q}$ dispersion at ambient pressure of the virtual transition is shown for comparison (solid lines for $D_{\mathit{tot}}$, dashed line for $D_{\mathit{LO}}$, and dot-dashed line for $D_{\mathit{LA}}$). (c) Phonon frequencies for real transitions as a function of ${\mathbf{q}}_{\mathit{\text{real}}}$ (diamonds). The $\mathbf{q}$ dispersion of the phonon frequencies along $\Gamma \text{−}X$ at ambient pressure is reported for comparison (lines). Dashed diamonds (dashed line): frequency of the LO phonon. Empty diamonds (dot-dashed line): frequency of the LA phonon. (d) Same as (b) but for matrix elements of intervalley transition. The difference between (b) and (d) is due to the evolution of phonon frequencies reported in (c) [see Eq. (1)].Reuse & Permissions

Figure 3

GaAs, virtual transition (see text): theoretical pressure dependence (GPa) of the deformation potentials $\left(\mathrm{eV}{\mathrm{\AA }}^{-1}\right)$ $D_{\Gamma X_3}$ for the first CB (circles, left ordinate axis) and $D_{\Gamma X_1}$ for the second CB (squares, right ordinate axis).Reuse & Permissions