Tuesday, April 17, 2012

Seeing the positive charge of holes

When students first learn solid state physics the concept of holes and its utility is not easy to grasp. I find it really helpful to use the Solid state simulations program ziman very helpful to illustrate the difference between electrons and holes.
One can consider the motion of electrons in Bloch states for a band structure with the energy contours shown in green in the figure below. One can vary the external magnetic and electric field.

If one goes to preset 6 (which has zero electric field) one can start an electron on an electron or a hole Fermi surface. One sees that the motion in a magnetic field has the opposite circulation for electrons and holes, in both real and Bloch wave vector space.
Hence, the holes really do act like positively charged particles.


  1. That's pretty cool! I think physics classes especially could benefit from more visualization technology. Right now we rely on students to be able to imagine the correct pictures and make the correct logical leaps. A visual simulation instantly gets the correct picture across, much better than a string of words does.

  2. I've never thought about using a magnetic field to influence electron/hole motion in a solid before. Are the electrons attracted to collide with the edges?

    I'm reading Feynman Vol. II now. I love it how he derives the Aharonov-Bohm effect before introducing Faraday's law. :)