9478

Band Structure of a Quantum Wire with Rashba and Zeeman Interactions

This Demonstration investigates the band structure and dispersion relations ( versus plots) of a quantum wire nanostructure in the presence of Rashba spin-orbit and Zeeman interactions.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+