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Section Navigation

  • Disorder
    • Anderson Localization
  • Dynamics
    • Bloch Oscillations and the Wannier-Stark Ladder
  • Flat Bands
    • Flat-Band Lattices: Kagome and Lieb
  • Magnetic Field
    • Hofstadter’s Butterfly
    • Landau Levels: Square Lattice vs. Graphene
    • Aharonov-Bohm Ring: A Magnetic Field on a Lattice
  • Non-Hermitian lattices
    • PT Symmetry, Exceptional Points, and a Selectively Amplified Edge Mode
  • Strain
    • Strain as a Gauge Field: Pseudo-Landau Levels in Graphene
  • Tight-Binding
    • Graphene: Real-Space Flake and Reciprocal-Space Bands
    • The Square Lattice: Bloch’s Theorem in its Simplest Form
    • Visualizing a Model: tbkit.plot.Plot
  • Topology
    • Edge States on Ribbons
    • The Haldane Model: Berry Curvature and a Topological Phase Transition
    • A Topological Flat Band on the Kagome Lattice
    • The SSH Model: Bulk-Boundary Correspondence
    • The Thouless Quantum Pump (Rice-Mele Model)
  • Examples
  • Magnetic Field

Magnetic Field#

The Peierls substitution on a lattice: an Aharonov-Bohm ring’s flux-periodic spectrum, and the self-similar, fractal Hofstadter butterfly swept continuously in flux.

Hofstadter’s Butterfly

Hofstadter's Butterfly

Landau Levels: Square Lattice vs. Graphene

Landau Levels: Square Lattice vs. Graphene

Aharonov-Bohm Ring: A Magnetic Field on a Lattice

Aharonov-Bohm Ring: A Magnetic Field on a Lattice

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Flat-Band Lattices: Kagome and Lieb

next

Hofstadter’s Butterfly
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