Chapter 2: Theory of spin-orbit effects in semiconductors

The theory of spin–orbit effects in semiconductors and the origins of spin–orbit coupling and the way it affects the band structure of semiconductors are discussed along with the Pauli Hamiltonian by expanding the Dirac equation to clarify the origins of the spin–orbit coupling in the electronics structure of semiconductors. The chapter reviews the basics of the k·p approximation, the effective mass or envelope function approximation, the effective reduced 2-band Hamiltonian of the conduction electrons obtained from the 8-band Kane model, and the effective 2-d Hamiltonians that follow along with the basic mechanisms for anomalous and spin Hall transport derived from a semiclassical point of view. The application of these concepts to the 2d-graphene and 2d-Rashba system is described as an illustration and a connection is made to the microscopic approach of the Kubo diagrammatic formalism where the equivalence between the two approaches is shown most clearly