1. Topological Insulators Effects of spin on transport of electrons in solids

2. Most figures from:

3. SPIN Mott insulators Rashba effect Superconductivity Quantum information and computation

4. Topological insulator Exhibits insulating behaviour in the bulk but has conducting edge or surface states So far the only models exploit spin-orbit interactions is generally related to introducing a time- reversal-symmetry breaking interaction, as is the case for SO. Existence established in some systems from ARPES experiments

5. Rashba effect Spin-orbit coupling-like potential 

6. SO in graphene

7. Cases A gap is produced For the gap is Quantized Hall conductivity: BUT! It will vanish for

8.  Gapless edge states At the edges opposite spins travel opposite directions. (Kane et al) At low energy

9. Use like wires

10. Observation Graphene SO effects very small, hard to observe Bi 1-x Sb x Observed! Surface states instead of edge states Using ARPES

12. Promises Topological states robust to perturbation  Stable qubits for Quantum Computation Dissipation-less spin current transport  good for Spintronics  new SuperConductivity-like effects to be observed, I presume. Not literally.