Differential conductance of a ballistic quantum wire in the presence of Rashba spin-orbit and Zeeman interactions : a thesis presented in partial fulfilment of the requirements for the degree of Master of Philosophy in Theoretical Condensed Matter Physics at Massey University
This thesis calculates the theoretical differential conductance of a ballistic quantum wire semiconductor nanostructure in the presence of Rashba spin-orbit and Zeeman interactions. In semiconductor heterostructures the Rashba spin-orbit interaction arises due to structure inversion asymmetry and couples the spin of the electron to its orbital momentum. In our work Zeeman interaction is induced by application of external magnetic fields in directions transverse, parallel, and perpendicular to the wire axis. Differential conductance is defined as the rate of change of current with respect to a voltage which is applied between two contacts, one on the left (source) and the other on the right (drain) side of the nanostructure. The dispersion relations of the wire are obtained and from these differential conductance is calculated. Differential conductance is presented for zero and strong spin-orbit interaction situations and for magnetic fields applied in the various directions. The wire is studied under two specific regimes, namely normal and full Rashba mediated by the Rashba spin-orbit Hamiltonian. In the normal Rashba regime the wire is modelled without Rashba intersubband coupling while the full Rashba model includes this coupling. Spin-orbit interaction and the direction of applied magnetic field significantly modifies dispersions and have drastic effects on the differential conductance profile. The application of magnetic field in directions parallel (and perpendicular) to the wire in the normal regime in the strong Rashba limit results in the formation of energy gaps. The presence of these gaps drastically reduces conductance. These gaps are suppressed in the full Rashba model of the wire in the strong Rashba limit and therefore reduction in conductance is not observed in the parallel and perpendicular field directions. In the normal Rashba regime in the strong Rashba limit conductance is enhanced for a greater range of source-drian bias voltages at low fields, especially for fields applied in the parallel (and perpendicular) directions. Whereas, in the full Rashba regime in the strong Rashba limit conductance is enhanced up to mid range fields and voltages for all field directions. In both Rashba regimes in the strong Rashba limit the overall conductance is reduced at low fields and voltages for all field directions. Hence, it is concluded that weak Zeeman and weak spin-orbit effects at low bias voltages favours electron transmission in ballistic quantum wires.