Calculating the Energy Band Structure Using Sampling and Greens Function   Techniques
  In this paper, a new method based on Greens function theory and Fourier transform analysis has been proposed for calculating band structure with high accuracy and low processing time. This method utilizes sampling of potential energy in some points of crystals unit cell with Dirac delta functions, then through lattice Fourier transform gives us a simple and applicable formula for most of nanostructures. Sampling of potential in a crystal lattice of any kind contains accurate approximation of actual potential energy of atoms in the crystal. The step forward regarding the method concentrated on two novel ideas, Firstly, the potential was sampled and approximated by delta functions spread over the unit cell. Secondly, the principal equation of lattice is translated into reciprocal lattice and resulted in a huge reduction of calculations. By this method, it is possible to extract the band structure of any one, two or three dimensional crystalline structure. 
Milad Khoshnegar, Amir Hossein Hosseinia, Nima Arjmandi, Sina   Khorasani
cond-mat.mtrl-sci physics.comp-ph