Quantum Hall effect in a p-type heterojunction with a lateral surface superlattice -: art. no. 165301

The quantization of the Hall conductance in a p-type heterojunction with a lateral surface superlattice is investigated. The topological properties of the four-component hole wave function are studied both in r and k spaces. A method of calculation of the Hall conductance in a two-dimensional hole gas described by the Luttinger Hamiltonian and affected by a lateral periodic potential is proposed, based on an investigation of the four-component wave-function singularities in k space. The effects of spin-orbit interaction, spin splitting in a magnetic field, and the asymmetric heterojunction potential are included. Deviations from the quantization rules for electron magnetic subbands of the Hofstadter "butterfly" are found, and the explanation of this effect is proposed. For the case of a strong periodic potential the mixing of magnetic subbands is taken into account, and the exchange of the Chern numbers between magnetic subbands is discussed.