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In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site.
Here we give a simple derivation of the Peierls substitution, which is based on The Feynman Lectures (Vol. III, Chapter 21). [3] This derivation postulates that magnetic fields are incorporated in the tight-binding model by adding a phase to the hopping terms and show that it is consistent with the continuum Hamiltonian.
The Hubbard model is based on the tight-binding approximation from solid-state physics, which describes particles moving in a periodic potential, typically referred to as a lattice. For real materials, each lattice site might correspond with an ionic core, and the particles would be the valence electrons of these ions.
In recent physics literature, a large majority of the electronic structures and band plots are calculated using density-functional theory (DFT), which is not a model but rather a theory, i.e., a microscopic first-principles theory of condensed matter physics that tries to cope with the electron-electron many-body problem via the introduction of ...
Tight-binding methods, e.g. a large family of methods known as DFTB, [24] are sometimes classified as semiempirical methods as well. More recent examples include the semiempirical quantum mechanical methods GFNn-xTB (n=0,1,2), which are particularly suited for the geometry, vibrational frequencies, and non-covalent interactions of large molecules.
In solid-state physics, the k·p perturbation theory is an approximated semi-empirical approach for calculating the band structure (particularly effective mass) and optical properties of crystalline solids. [1] [2] [3] It is pronounced "k dot p", and is also called the k·p method.
In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. [1] It was devised by Wu-Pei Su, John Robert Schrieffer, and Alan J. Heeger in 1979, to describe the increase of electrical conductivity of polyacetylene polymer chain when doped, based on the existence of solitonic defects.
It is a tight binding code (both orthogonal and non-orthogonal), allowing for multipole charges and electron spin. It also contains Density Functional Theory programs: these were restored to enable clear benchmarking to tight binding simulations, but can be used in their own right.