Effective-mass anisotropy in GaAs-(Ga,Al)As two-dimensional hole systems: comparison of theory and very high-field cyclotron resonance experiments

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Abstract
Cyclotron resonance of two-dimensional holes in high-mobility GaAs-(Ga,Al)As heterojunctions with the growth directions (011), (111), (211), (311) and (100) has been measured at magnetic fields of around 35 T, corresponding to Landau level occupancies deep in the ultraquantum limit. A manipulation of the standard four-band Luttinger Hamiltonian has been used to show that the behaviour of the hole ground state is dominated by the leading field-dependent term in a power series expansion for the Landau level dispersion. The experimentally observed trend in measured effective mass with substrate orientation can therefore be qualitatively explained in terms of the variation of bulk hole mass with crystallographic direction.