Band Structure of a Quantum Wire with Rashba and Zeeman Interactions

The quantum wire is modeled via a lateral electrostatic confinement potential in the direction , leaving free electron propagation in the direction (which is the direction of the wire). The Rashba spin-orbit interaction that couples electron spin with its momentum arises due to lack of symmetry within the nanostructure and is induced by a macroscopic electric field directed along the direction. Zeeman interaction, which couples electron spin to applied magnetic field, is induced by a varying external magnetic field in three independent spatial directions , , and , where and are in-plane and is perpendicular to the nanostructure, as shown in the schematic. When the Rashba and Zeeman interactions are zero, the subbands are degenerate (shown for 10 subbands, being the ground state). The subbands undergo spin-splitting in the presence of either Rashba or Zeeman interaction.

Quantum wire schematic:

The quantum wire in this Demonstration is described by the Hamiltonian:

.

The dispersion relations for the quantum wire have the form:

or

.

Note that

and .

The parameter models the Rashba spin-orbit interaction strength, while , , and model the magnetic field strength in their respective directions.