Rashba Hamiltonian

We also assume that k lo E and, therefore, the Rashba Hamiltonian can be treated locally as uniform field that describes the random SO coupling in the semiclassical approximation as ... 

In quantum wires formed in a two-dimensional electron gas (2DEG) by lateral confinement the Rashba spin-orbit interaction is not reduced to a pure ID Hamiltonian H[s = asopxaz. As was shown in Ref. [4] the presence of an inplane confinement potential qualitatively modifies the energy spectrum of the ID electrons so that a dispersion asymmetry appears. As a result the chiral symmetry is broken in quantum wires with Rashba coupling. Although the effect was shown [4] not to be numerically large, the breakdown of symmetry leads to qualitatively novel predictions. 

Figure 1.13 Valence band structure of ZnO near the F point. The open circles represent the calculation results using the ASA-LMTO method including spin-orbit coupling. The solid lines are fits to the Rashba-Sheka-Pikus effective Hamiltonian. (After Ref [60].)...

LaShell et ul. [109] observed for this state an energy splitting that is proportional to the wave vector. In contrast to the case of Cu(lll) (Figure 3.2.2.24c), the Fermi surface was here found to consist of two concentric circles around the normal emission direction. Based on the Rashba term in the Hamiltonian, describing the spin-orbit interaction in propagating electronic states. 

---