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The model gives good qualitative results in many cases and can be combined with other models that give better results where the tight-binding model fails. Though the tight-binding model is a one-electron model, the model also provides a basis for more advanced calculations like the calculation of surface states and application to various kinds ...
As with any 1D model, with two sites per cell, there will be two bands in the dispersion relation (usually called optical and acoustic bands). If the bands do not touch, there is a band gap. If the gap lies at the Fermi level, then the system is considered to be an insulator. The tight binding Hamiltonian in a chain with N sites can be written ...
The Aubry–André model describes a one-dimensional lattice with hopping between nearest-neighbor sites and periodically varying onsite energies. It is a tight-binding (single-band) model with no interactions. The full Hamiltonian can be written as
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 introduces short-range interactions between electrons to the tight-binding model, which only includes kinetic energy (a "hopping" term) and interactions with the atoms of the lattice (an "atomic" potential). When the interaction between electrons is strong, the behavior of the Hubbard model can be qualitatively different from ...
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.
The tight binding Hamiltonian in of a Kitaev chain considers a one dimensional lattice with N site and spinless particles at zero temperature, subjected to nearest neighbour hoping interactions, given in second quantization formalism as [4]
The kicked rotator, also spelled as kicked rotor, is a paradigmatic model for both Hamiltonian chaos (the study of chaos in Hamiltonian systems) and quantum chaos. It describes a free rotating stick (with moment of inertia I {\displaystyle I} ) in an inhomogeneous "gravitation like" field that is periodically switched on in short pulses.