It is known that carriers in the surface states of topological insulator have their spin locked at a right angle to their momentum (called spin-momentum locking). Now, I cannot visualize this that how the spins are locked to their momentum at right angles. Can anyone explain this in simple terms? I am also sharing a document. Can anyone also explain by seeing this document (explain figure 1d in this document)?
http://www.physics.upenn.edu/~kane/pubs/p69.pdf
The mentioned effect is not specific to topological insulators. It results from strong spin orbit coupling in surface states. See the following paper
http://prl.aps.org/abstract/PRL/v77/i16/p3419_1
for its first (I think) observation (by photoelectron spectroscopy) at the Au(111) surface.
How does it work? You may recall from atomic physics that the magnitude of spin orbit coupling may be expressed using the gradient of the electrostatic potential. This is, why it is larger for core electrons and electrons of heavy (high atomic number) elements. The mathematical expression for spin orbit coupling energy actually involves the vector product of velocity (or momentum) and the potential gradient.
For surface states of crystalline matter we have two observations. (i) linear momentum is a good quantum number, the momentum vector of surface Bloch states lies in the surface. (ii) the potential gradient points along the surface normal.
Their vrctor product is a vector in the surface, perpendicular to the momentum vector. This is, why the spin direction of minimum energy is locked to momentum the way you describe it in your question.
This type of spin orbit coupling at surfaces is also called Rashba coupling.
Electronic life at surfaces may be more complicated, though - see e.g.
http://prl.aps.org/abstract/PRL/v108/i18/e186801
Now, while Rashba coupling is not restricted to topological insulators, it is an essential ingredient to their physical properties.
- Badges
- Science topic
- Similar topics
- Filing