Tight-Binding#

The generic real-space and reciprocal-space machinery: the square lattice, whose single band is simple enough to check by hand, as the smallest complete illustration of Bloch’s theorem; Brillouin zones and the standard high-symmetry paths of the 2D and 3D Bravais lattices; Monkhorst-Pack k-point grids; a graphene flake diagonalized directly and its Bloch band structure along a k-path, including Wallace’s 1947 linear (Dirac) dispersion near the K point; the physics behind the 2004 isolation of graphene – flakes, edge states, and the Berry phase of pi of its Dirac cones; the zigzag edge states of graphene ribbons and the 3m + 2 rule of armchair ribbons; surface Green’s functions by Lopez Sancho decimation; and tbkit.plot.Plot’s lattice, spectrum, density-of-states, and eigenstate-intensity plots; parametrized Hamiltonians, whose value functions let a flux or dimerization sweep re-evaluate the hoppings instead of rebuilding the model; periodic boundaries in real space, tori and cylinders whose spectra match the Bloch bands on a k-mesh; and the analysis of a band structure: Fermi surfaces and their Lifshitz transitions, bands projected on sublattices or spins and spin textures, and the tetrahedron method for the density of states.