# Tight binding s-orbital for 2D binary compound

• Braggplane
In summary, the speaker is new to the forum and needs help with a question regarding a 2D binary compound AB in a rocksalt structure. They are asked to consider a single s-orbital on each atom and nearest neighbor hopping integrals between pairs of atomic types, neglecting overlap. They need to write a system of equations in the tight binding approximation, in terms of the hopping integrals and lattice constant. The speaker is preparing for an exam and has a question about specifying a primitive cell for the rocksalt structure, but later figures it out with the help of a physicist. The primitive cell will contain 1 atom of A and 1 atom of B, and the atomic orbitals can be expressed in terms of Bloch

#### Braggplane

Hi guys! I'm new to the forum, i hope you can help me with this trouble! it really is important =D

i have a 2D binary compound AB (made of one of the 100 family of planes of a rocksalt structure) and i am asked to "consider a single s-orbital on each atom (atomic energies Ea,Eb) and nearest neighbor hopping integrals between pairs of each of the atomic types (AA,BB,AB), neglecting overlap. Write the system of equations that one should solve in the tight binding approssimation, in terms of the hopping integrals (AA,BB,AB) and a (lattice constant)."

i have to discss that problem with my professor for the exam so please help me :S

Do you have any concrete question? Can you specify a primitive cell for the rocksalt structure?

DrDu said:
Do you have any concrete question? Can you specify a primitive cell for the rocksalt structure?

You can specify a triangular lattice with a one atom basis or a square lattice with a basis it makes no difference but i don't know how to to write the system of equations, because i know how to apply tight binding on elemental solids, it's a trouble with a binary compound

Your primitive cell will contain 1 atom of A and one of B. You can express your atomic orbitals in terms of Bloch functions. If you do this, you should get a 2x2 matrix eigenvalue equation for each wavevector k.

DrDu said:
Your primitive cell will contain 1 atom of A and one of B. You can express your atomic orbitals in terms of Bloch functions. If you do this, you should get a 2x2 matrix eigenvalue equation for each wavevector k.
Thanks DrDu, i was now with a phisicist and we figured out indeed this way! (i am an engineer XD)