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

• Published in: Physica Status Solidi. B: Basic Solid State Physics 2015-04, Vol.252 (4), p.730-742
• Main Authors: Moskalenko, S. A., Podlesny, I. V., Dumanov, E. V., Liberman, M. A., Novikov, B. V.
• Format: Article
• Language: English
• Subjects: Crystal lattices; Dispersions; Electric fields; Energy levels; heavy holes; Landau quantization; Mathematical analysis; nonparabolicity; Pauli equation; Quantization; Rashba spin-orbit coupling; Spin-orbit interactions; Splitting; Two dimensional; Zeeman splitting
• ISSN: 0370-1972; 1521-3951; 1521-3951
• DOI: 10.1002/pssb.201451296

The origin of the g‐factor of two‐dimensional (2D) electrons and holes moving in the periodic crystal lattice potential with 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 pairs of the Landau quantization levels due to the spinor‐type wave functions. The energy levels depend on the amplitudes of the magnetic and electric fields, on the g‐factor gh, and on the parameter of nonparabolicity C. The dependences of two energy levels in any pair on the Zeeman parameter Zh=ghmh/4m0, where mh is the hole effective mass, are nonmonotonous and without intersections. The smallest distance between them at C=0 takes place at the value Zh=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.