Magnetic Field#
The Peierls substitution on a lattice: gauge-invariant flux through the plaquettes, an Aharonov-Bohm ring’s flux-periodic spectrum, Landau levels of the square lattice and of graphene, Zak’s magnetic translations and the magnetic supercell at rational flux, and the self-similar, fractal Hofstadter butterfly swept continuously in flux, and the orbital magnetization of a Chern insulator, checked against the Streda formula on a flake.
Zak’s Magnetic Translation Group: the Magnetic Supercell at Rational Flux
Zak's Magnetic Translation Group: the Magnetic Supercell at Rational Flux
The Peierls Substitution: Flux Through the Plaquettes, in Any Gauge
The Peierls Substitution: Flux Through the Plaquettes, in Any Gauge