The Hamiltonian for a particle subject to spin-orbit interaction is more complicated than that of a free particle, containing terms corresponding to the electric dipole and Thomas precession processes. For a thin quantum wire in the x-y plane, a non-zero electric field perpendicular to the plane of the wire gives rise to yet another process of spin-orbit interaction called the Rashba spin-orbit interaction. The contribution of this Rashba mechanism is dictated by a parameter α which is proportional to the perpendicular electric field. Additionally, a strong potential well within the x-y plane may be associated with an electric field, which is not negligible compared to the field that causes the α -interaction. In this case of planar, as well as perpendicular confinement, there is one more contribution to the Hamiltonian and the spin-orbit interaction, this time corresponding to the parameter β , which is dictated by the width and potential depth of the nanowire. Typical values of β are about one tenth of α .1 Our goal was to write a program that would compute the eigenenergies of an electron in the nanowire.
Brennan, Ryan FCRH '11; Ahmed, Sheehan FCRH '11; Balassis, Antonios; and Fessatidis, Vassilios
"Energy of Electrons in a Nanowire Subject to Spin-orbit Interaction,"
The Fordham Undergraduate Research Journal: Vol. 1
, Article 9.
Available at: https://research.library.fordham.edu/furj/vol1/iss1/9