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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 ...
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 Rashba model in solids can be derived in the framework of the k·p perturbation theory [12] or from the point of view of a tight binding approximation. [13] However, the specifics of these methods are considered tedious and many prefer an intuitive toy model that gives qualitatively the same physics (quantitatively it gives a poor ...
Each model describes some types of solids very well, and others poorly. The nearly free electron model works well for metals, but poorly for non-metals. The tight binding model is extremely accurate for ionic insulators, such as metal halide salts (e.g. NaCl).
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 "unperturbed Hamiltonian" is H 0, which in fact equals the exact Hamiltonian at k = 0 (i.e., at the gamma point). The "perturbation" is the term H k ′ {\displaystyle H_{\mathbf {k} }'} . The analysis that results is called k·p perturbation theory, due to the term proportional to k·p .
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.