Electron distribution using tight binding band structure?

[radyab1297]

Hi everyone,

I am just wondering how to calculate electron distribution using tight binding band structure for a system like graphene or any other solid.
So the goal is to get |\psi(r)|^2 which \psi is the band state and it is the linear combination of Bloch sum:
\psi={\sum_n,R}{c_nk}exp(ik.R){\phi(r-r_nR)}

c_nk is the eigenvector of the tight binding band structure that we already have them. n is the the orbital position in R unit cell and \phi is \pi orbital.

Thank you for your help in advance.

 

[eljose79]

Hello,

Calculating the electron distribution using tight binding band structure for a system like graphene or any other solid involves a few steps. First, we need to obtain the tight binding band structure for the system, which can be done through various methods such as density functional theory (DFT) calculations or empirical tight binding models. Once we have the tight binding band structure, we can then use the Bloch sum to calculate the electron distribution.

The Bloch sum is a linear combination of the wave functions of the individual atoms in the unit cell, which are multiplied by a phase factor determined by the wave vector (k) and the lattice vector (R). This gives us the wave function (\psi) for a particular band state, which is a function of both position (r) and the band index (n).

To calculate the electron distribution, we need to square the magnitude of the wave function (\psi) and sum over all the occupied band states. This will give us the electron density at each point in the system.

In the case of graphene, the wave function (\psi) is a combination of the \pi orbitals of the carbon atoms in the unit cell. The coefficients (c_nk) in the Bloch sum are the eigenvectors of the tight binding band structure, which can be obtained from DFT calculations or other methods.

I hope this helps. Let me know if you have any further questions.