Tight-binding model

A method for calculating electronic energy bands by combining atomic orbitals localized around lattice sites. It treats electrons as mostly bound to atoms, with hopping between neighboring sites.

Bloch theorem: A symmetry principle stating that eigenstates in a periodic potential are plane waves modulated by lattice-periodic functions. It converts the lattice-periodic tight-binding Hamiltonian into momentum-space bands.
Atomic orbital: A quantum-mechanical wavefunction describing an electron's state around an atomic nucleus. Atomic orbitals supply the localized basis functions combined in the model.
Graphene: A single layer of carbon atoms arranged in a two-dimensional honeycomb lattice. Nearest-neighbor carbon-orbital hopping reproduces graphene's characteristic Dirac bands.
Nearly free electron model: A model of electrons moving through a weak periodic potential, treated as perturbed free particles. It starts from delocalized plane waves, opposite to tight binding's localized-orbital basis.
John Clarke Slater: An American theoretical physicist whose work shaped quantum theory, atomic structure, and solid-state physics. His methods for atomic orbitals and crystal bands helped establish the framework's foundations.
Hopping parameter: A Hamiltonian matrix element that quantifies an electron's transfer between localized orbitals on different sites. Its magnitude and sign determine how strongly neighboring orbitals spread into bands.
Lattice (group): A discrete set of points generated by integer combinations of primitive translation vectors. Lattice sites identify where the model places its localized orbitals.
Kagome lattice: A two-dimensional lattice of corner-sharing triangles with a characteristic pattern of sites and bonds. Tight-binding models on it produce flat bands and geometrically frustrated dispersions.
Free electron model: A model in which electrons move without a periodic potential or interactions. It omits the lattice and orbital structure that generate tight-binding bands.
George Frederick Koster: An American physicist known for work on electronic band structures and solid-state theory. His collaboration with Slater produced influential orbital-based band calculations.

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