Topological Insulators

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Topological Insulators

• Effects of spin on transport of electrons in
  solids

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• Most figures from

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SPIN

• Mott insulators
• Rashba effect
• Superconductivity
• Quantum information and computation

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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

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Rashba effect

• Spin-orbit coupling-like potential
• ?

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SO in graphene
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Cases

• A gap is produced
• For the gap is
• Quantized Hall conductivity
• BUT! It will vanish for

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? Gapless edge states

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

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Use like wires
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Observation

• Graphene
• SO effects very small, hard to observe
• Bi1-xSbx
• Observed! Surface states instead of edge states
• Using ARPES

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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.

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