Topological Insulators
Effects of spin on transport of electrons in solids

Most figures from:
SPIN
Mott insulators
 Rashba effect
 Superconductivity
 Quantum information and
computation

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 timereversal-symmetry breaking interaction, as
is the case for SO.
 Existence established in some systems
from ARPES experiments

Rashba effect
Spin-orbit coupling-like potential


H 
k
2
2m

  k



z
2

k

2m


  ( k y  ik x )


 ( k y  ik x ) 

2
k


2m

SO in graphene
Cases

A gap is produced
For
the gap is
 Quantized Hall conductivity:


BUT! It will vanish for
 Gapless edge states

At the edges opposite spins travel opposite
directions. (Kane et al)

At low energy
Use like wires
Observation
Graphene
SO effects very small, hard to observe
 Bi1-xSbx
Observed! Surface states instead of edge states
 Using ARPES

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.