Welcome to Topological Insulator!

Notes on topological insulators.

Hint

This note is yet to be finished.

Contents

• Prerequisites
  • Time Reversal
  • Topology
  • Semiclassical Theory of Electron Transport
    • SdH Oscillation
    • Conductivity and Resistivity Tensor
  • Glossary
  • References
• Experimental Techniques
  • Quantum Oscillations
    • Laudau Quantization
      • Strong magnetic field
      • Weak magnetic field
    • Observation of Quantum Oscillation
      • Classical Theory of Electron Motion
      • Phenomena
  • ARPES
    • Conservation Laws
      • Conservation of Energy
      • Conservation of Momentum
    • Analyzing ARPES Data
    • Sensitivity to Surface Condition
  • Determination of Topological Insulators
    • Determination of 2D Topological Insulators
    • Determination of 3D Topological Insulators
    • CD-ARPES
  • Glossary
  • References
• Basic Theory of Topological Insulators
  • Berry Phase
  • QHE: Chern Number and Conductivity
    • Weak Magnetic Field
    • Strong Magnetic Field
      • Hall Conductance: TKNN Derivation
      • Hall Conductance: Kubo Derivation
      • Hall Conductance: Laughlin Argument
      • Hall Conductance: Wilson Loop Derivation
    • Example: A Two-Band Model
  • Pump: ℤ₂ Index and Polarization
    • Polarization and Time-Reversal Polarization
      • Spin Pump: ℤ₂ Index and Time-Reversal Polarization
    • ℤ₂ Index via Wilson Loop
  • Three-Dimensional Topological Insulators With Time-Reversal Invariance: ℤ₂ Index and Edge States
    • Three-Dimensional ℤ₂ Index
    • Inversion Symmetry
  • Remark: Why Does TRS Matter?
  • Topological Crystalline Insulators
    • Mirror Chern Number
  • Miscellaneous Effects
    • Spin-Orbit Coupling
      • Rashba Effect
      • Dresselhaus Effect
    • Localization
      • Weak Localization
      • Anderson Localization
  • Glossary
  • References
• Models
  • Index of Models (Diagonalizable)
  • Thouless Charge Pump (Rice-Mele Model)
  • Fu-Kane Spin Pump (Rice-Mele Model With Spin)
  • Su-Schrieffer-Heeger Model
  • QAHE (Haldane Model)
  • QSHE (Kane-Mele Model)
  • Bernevig-Hughes-Zhang Model
  • Miscellaneous
  • References
• Rice-Mele Model: Thouless Charge Pump
• Fu-Kane Spin Pump
• One-Dimensional Topological Insulator
• Kane-Mele Model: 2D TI
• Topological Materials
  • 2D Topological Insulators
    • CdTe/HgTe/CdTe Quantum Well
    • AlSb/InAs/GaSb/AlSb Quantum Well
    • Candidates of 2D Topological Materials
    • Remark: Why is Two-Dimensional More Preferable?
  • 3D Topological Insulators
    • Bi_1-xSb_x Alloy
    • Tetradymite
      • More Tetradymite Materials
      • BiQ Homologous Series
    • TlBiSe₂
    • GeBi₂Te₄
      • Ge-Based Homologous Series
    • Pb-Based Materials
      • Pb-Based Homologous Series
      • Natural Superlattice
    • BiTeCl
    • HgTe (Epitaxial)
    • Sn (Epitaxial)
    • Candidates of 3D Topological Materials
  • Topological Semimetals
    • Definition of Topological Semimetals
    • Weyl Semimetals
    • Candidates of Topological Semimetals
    • Heusler Compounds as Topological Semimetals
  • Topological Crystalline Insulator
    • SnTe
    • SnSe
  • Synthesization
    • Bulk Single Crystal
    • Thin Film
    • Nano-Ribbon and Nano-Plate
  • Bulk Insulation
  • Glossary
  • References
• Physical Properties of Topological Insulators
  • Helical Spin Polarization
  • Quasiparticle Interference
  • Resistivity
    • Dirac Particles
    • SdH Oscillation of Surface State
      • Fan Diagram
      • Temperature Dependency of Oscillation Frequencies
    • More Information from SdH Oscillation
    • Example: Two-Band Model
    • Weak Antilocalization
    • Topological Protection of Surface States
      • Aspects of Protection
      • Breaking of Protection
  • Aharonov-Bohm Effect in Nano-Ribbons
  • Magnetism
  • Quantum Anomalous Hall Effect
  • Topological Magnetoelectric Effect
  • Spintronics
    • Spin Transport in the Ballistic Transport Regime
    • Spin Transport in the Diffusive Transport Regime
  • Optics
  • References
• Computation: Topological Quantum Chemistry
• Topological Superconductors
  • Classification of Topological Superconductors
    • Candidates of Topological Superconductors
  • Majorana Fermions
  • Kitaev Model
    • Kitaev Model: Periodic Boundary Condition
    • Kitaev Model: Open Boundary Condition
  • Spinless P-Wave Chiral Superconductor
    • Topological Invariance of Spinless P-Wave Superconductor
  • Topological Superconductors in Hybrid Systems
• Applications
  • Thermoelectric Materials
    • Brief on Topological Thermoelectric Effects
    • Thermoelectric Topological Insulators
  • References

Maintenance

Badges

Badges are generated by badgen.