Tight Binding Hamiltonian and Potential (U)

[Arya_]

Hi All,

Greetings !

Here is what I wish to know. Specifying a tight binding hamiltonian requires values of potential (U). Consider a 3d solid. If I have potential profile in x direction (U1, U2, U3...so on) can I directly plug in these U values into the tight binding hamiltonian or do I need to do some transformation (like change of space etc) before I can plug in 'potential values vs X' into Hamiltonian.

Thanks,
-Arya

 

[Douasing]

Yes,I think you can directly plug in these V(x) values into the tight binding hamiltonian.Because potential function meets the superposition principle.

 

[DrDu]

The tight binding hamiltonian is an empirical effective hamiltonian which is parametrized in such a way as to give correct energies for the lowest eigenstates of the hamiltonian. Excited atomic states also make a contribution, also to the potential. So there is no 1 to 1 correspondence between some potential in the full hamiltonian and the U's appearing in the tight binding approximation.