History

“It was found that the wave functions […] in a periodic potential have exactly the form of a modulated plane wave.” – F. Bloch, 1928

A chronology of the breakthroughs behind Tight-Binding theory, from Bloch’s 1928 theorem to the Weyl semimetals, Floquet and non-Hermitian lattices of the 2010s, in one chapter per theme. Every stop has a pointer to the corresponding tbkit functionality and a short, runnable, numerically-verified example in examples/ – nothing here is asserted without also being checked in code.

• Breakthroughs in Building and Solving Models – Bloch’s theorem, Slater-Koster and k·p models, Wannier functions, and solvers for very large lattices.

• Breakthroughs in Fields, Strain and Disorder – magnetic fields (Peierls substitution, Landau levels, Hofstadter’s butterfly), strain, and disorder.

• Breakthroughs in Band Topology – Chern, Z2, mirror and spin Chern numbers, Berry phases, the Bott index, Weyl points, and higher-order phases.

• Breakthroughs in Response and Transport – Hall-type responses, Landauer transport between leads, and linear and nonlinear optics.

• Breakthroughs in Flat Bands and Interactions – flat bands from geometry and from a moiré twist, the Hubbard model, and superconductivity.

• Breakthroughs in Driven and Open Systems – wavepacket dynamics, Floquet lattices, and non-Hermitian bands with exceptional points.