# Hamiltonian

Synopsys: Hamiltonian(n,Nc)

Hamiltonian is the NanoTCAD ViDES class, which allow the definition of a general Hamiltonian within the semi-empirical tight-binding model. As inputs, it requires the number of atoms n in the slice, and the number of slices Nc of the material to be considered. Nc must be at least larger than 4. For a complete understanding of such quantities, please refer to Tutorial 09.

The attributes of the classes are the following:
• Nc (int) the number of slices
• (int) the number of atoms within each slice
• x: (numpy array of length n*Nc) x coordinates of the atoms
• y: (numpy array of length n*Nc) y coordinates of the atoms
• z: (numpy array of length n*Nc) z coordinates of the atoms
• Phi: (numpy array of length n*Ncpotential of the atoms
• Eupper (double) the upper energy limit for which the NEGF is computed in the nanoribbon
• Elower (double) the lower energy limit for which the NEGF is computed in the nanoribbon
• dE (double) the energy step computed when solving the NEGF
• eta (double) the infinitesimal imaginary part used in the NEGF formalism
• mu1 (double) the Fermi level of the left reservoir
• mu2 (double) the Fermi level of the right reservoir
• Temp (double) the temperature of the nanoribbon
• E : (numpy array) array of the energies for which the transmission coefficient and the free charge is computed in the nanoribbon by means of the NEGF formalism
• T : (numpy array) array of the transmission coefficient computed in correspondence of the energies stored in the E array
• charge : (numpy array of length n*Nc) free charge computed in correspondence of each C atom of the nanoribbon.
• charge_T : (function) function which computes the free charge and the transmission coefficient in the energy interval specified by Eupper and Elower with an energy step equal to dE in correspondence of each C atoms of the nanoribbon. Such a computation is performed in the real space.
• H : (numpy matrix) the Hamiltonian stored in the VHF format.