GTFindStateNumbers

GTFindStateNumbers[eigenvalues,emin,emax]
findes the number of states in the list eigenvalues lying in the energy interval [emin,emax].

DetailsDetails

  • Usually the size of tight-binding Hamiltonians in k-space is small and it is not difficult to inspect the results of a calculation. If a tight-binding Hamiltonian is created in matrix form in real space, it can become huge and it might be complicated to inspect the properties of a certain eigenvalue of the problem.
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

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The density of stes of GaAs is used as an example. The DOS is first calcuated in k-space. The Hamiltonian for the calculation is already prepared. The Hamiltonian is prepared with a sp^3s^* basis.

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The density of states in k-space can be calculated now.

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The Hamiltonian in real space has the dimension 709x709. The corresponding cluster consists of 709 Ga and 709 As atoms. This real space Hamiltonian is also already prepared:

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The density of states can be calculated.

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The comparison of both DOS calculations shows, that due to the surface of the cluster surface states appear in the band gap in the real space calculation.

GTFindStateNumbers can be used to finde the numbers of eigenstates in an energy interval.

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