Dirac Tunneling

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows the tunneling through a barrier of height and width by a Dirac fermion of mass and energy . The upper two Argand plots show the weight of the reflected and transmitted waves (red: , green: , and blue: ). The lower plot shows the reflection coefficient (blue) and transmission coefficient (red). The gray area is where . The increase in the transmitted wave after tunneling is a consequence of the Klein paradox.

Contributed by: Niels Walet (March 2011)
Open content licensed under CC BY-NC-SA



This Demonstration implements the reflection from a barrier for a Dirac electron. For further details, see

[1] R.–K. Su, G. G. Siu, and X. Chou, "Barrier Penetration and the Klein Paradox," Journal of Physics A: Mathematical and General, 26, 1993 pp. 1001–1005.

[2] M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, "Chiral Tunnelling and the Klein Paradox in Graphene," Nature Physics, 2, 2006 pp. 620–625.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.