The quantum wire is modeled via a lateral electrostatic confinement potential in the
, 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
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.
models the Rashba spin-orbit interaction strength, while
model the magnetic field strength in their respective directions.