Topological InsulatorsTopological InsulatorsEffects of spin on transport of electrons in solids

Most figures from:

SPINSPINMott insulatorsRashba effectSuperconductivityQuantum information and computation

Topological insulatorTopological insulatorExhibits 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

Rashba effectRashba effectSpin-orbit coupling-like potential

mkikk

ikkmk

kmkH

xy

xy

z

2)(

)(2

2 2

2

2

SO in grapheneSO in graphene

CasesCasesA gap is produced

For the gap is Quantized Hall conductivity:

BUT! It will vanish for

Gapless edge statesGapless edge states

At the edges opposite spins travel opposite directions. (Kane et al)

At low energy

Use like wiresUse like wires

Observation Observation Graphene

SO effects very small, hard to observeBi1-xSbx Observed! Surface states instead of

edge statesUsing ARPES

Promises Promises Topological states robust to

perturbationStable qubits for Quantum

ComputationDissipation-less spin current transportgood for Spintronics

new SuperConductivity-like effects to be observed, I presume. Not literally.