Anisotropy of the effective masses in semiconductors

Recently, I have received a referee report on my paper in which reviewer states the following: "... in all known direct band gap semiconductors the electron effective mass is isotropic or has a negligible anisotropy in a comparison with the hole effective mass which can have much more pronounced anisotropy ". Is this statement true? If it is so, why does the hole effective mass have much more significant anisotropy than the electron effective mass?

The anisotropy of the hole bands is due to the interaction of the various hole bands (light, heavy and spin orbit). The electron effective mass is isotropic because the band effectively does not interact with other bands.

Just to add to the fully correct statement by Dr Transport:

The angular momentum properties of the bands mostly originate from the states these bands originate from. For most materials with Zincblende structure (which includes the typical direct gap semiconductors such as GaAs and so on), the conduction band originates from s-type states, while the valence band originates from p-type states.

Therefore, there is only one conduction band, but three valence bands (heavy hole, light hole and split-off band). These bands may mix which introduces the anisotropy. Look for the Luttinger-Kohn model if you are interested in details.

If you want to provide a counterexample to the referee, then the currently heavily investigated perovskite-type materials have an inverted band structure. Here, the hole bands are s-type, while the conduction bands are p-type. The lowest energy conduction band is typically the split-off band, which does not interact that much with the other bands, so it is still rather isotropic, but here, the hole states usually also have very small anisotropy.