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Landau quantization, Rashba spin-orbit coupling and Zeeman splitting of two-dimensional heavy holes

The origin of the g-factor of the two-dimensional (2D) electrons and holes moving in the periodic crystal lattice potential with the perpendicular magnetic and electric fields is discussed. The Pauli equation describing the Landau quantization accompanied by the Rashba spin-orbit coupling (RSOC) and Zeeman splitting (ZS) for 2D heavy holes with nonparabolic dispersion law is solved exactly. The solutions have the form of the pairs of the Landau quantization levels due to the spinor-type wave functions. The energy levels depend on amplitudes of the magnetic and electric fields, on the g-factor {g-h}, and on the parameter of nonparabolicity C. The dependences of two energy levels in any pair on the Zeeman parameter {Z_h}={g_h}{m_h}/4{m_0}, where {m_h} is the hole effective mass, are nonmonotonous and without intersections. The smallest distance between them at C=0 takes place at the value {Z_h}=n/2, where n is the order of the chirality terms determined by the RSOC and is the same for any quantum number of the Landau quantization.