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Quantum methods of solid state physics program showing band structure od 2-dimentional carbon crystal - graphene. It's calculated using method of tight binding (TB).

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This program uses Tight Binding method - LCAO method taking into consiteration periodicity of the system. Bloch wave functions describe the electronic states in a periodic crystal lattice. Base function consists of two parts - Up localised on atoms and Bloch element. We create generalised eigenvalue problem and series of function of tightly bonded electrons. Considering the closest neighbouring atoms we get 3 positions R1, R2 and R3 and after that:

  1. We create a path from K point of symmetry to M point
  2. We fill Hamiltonian matrix
  3. Points gamma, K and M are given coordinates of reciprocal lattice.
  4. We take care of the units.

Results:

Band structure

K, M and Gamma points explained:

Band structure Image by: https://inspirehep.net/record/1297532/plots

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Quantum methods of solid state physics program showing band structure od 2-dimentional carbon crystal - graphene. It's calculated using method of tight binding (TB).

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