Crystal symmetry and pressure effects on the valence band structure of γ-InSe and ε-GaSe : Transport measurements and electronic structure calculations

This paper reports on Hall effect and resistivity measurements under high pressure up to 3--4 GPa in $p$-type $\ensuremath{\gamma}$-indium selenide (InSe) (doped with As, Cd, or Zn) and $\ensuremath{\epsilon}$-gallium selenide (GaSe) (doped with N or Sn). The pressure behavior of the hole concentration and mobility exhibits dramatic differences between the two layered compounds. While the hole concentration and mobility increase moderately and monotonously in $\ensuremath{\epsilon}$-GaSe, a large increase of the hole concentration near 0.8 GPa and a large continuous increase of the hole mobility, which doubled its ambient pressure value by 3.2 GPa, is observed in $\ensuremath{\gamma}$-InSe. Electronic structure calculations show that the different pressure behavior of hole transport parameters can be accounted for by the evolution of the valence-band maximum in each material under compression. While the shape of the valence band maximum is virtually pressure-insensitive in $\ensuremath{\epsilon}$-GaSe, it changes dramatically in $\ensuremath{\gamma}$-InSe, with the emergence of a ring-shaped subsidiary maximum that becomes the absolute valence-band maximum as pressure increases. These differences are shown to be a consequence of the presence or absence of a symmetry element (mirror plane perpendicular to the anisotropy axis) in the point group of each polytype (${D}_{3\mathrm{h}}$ for the $\ensuremath{\epsilon}$-polytype and ${C}_{3\mathrm{v}}$ for the $\ensuremath{\gamma}$-polytype), resulting in different selection rules that affect the $\stackrel{P\vec}{k}∙\stackrel{P\vec}{p}$ interaction between valence bands.