Tight binding s-orbital for 2D binary compound

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Discussion Overview

The discussion revolves around the tight binding approximation applied to a 2D binary compound AB, specifically focusing on the formulation of equations involving s-orbitals and hopping integrals in a rocksalt structure. Participants explore the setup of the problem, including the definition of the primitive cell and the representation of atomic orbitals.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks assistance in formulating the system of equations for a 2D binary compound AB using the tight binding approximation, mentioning specific parameters like atomic energies and hopping integrals.
  • Several participants inquire about the specification of a primitive cell for the rocksalt structure, suggesting that it can be represented as either a triangular or square lattice.
  • A participant notes that the primitive cell should contain one atom of A and one of B, and suggests expressing atomic orbitals in terms of Bloch functions to derive a 2x2 matrix eigenvalue equation for each wavevector k.
  • Another participant confirms that they were able to understand the approach after discussing it with a physicist, indicating a collaborative effort in resolving the problem.

Areas of Agreement / Disagreement

Participants generally agree on the need to define the primitive cell and the use of Bloch functions, but there is no consensus on the specific formulation of the system of equations, as some participants express uncertainty regarding the tight binding application to binary compounds.

Contextual Notes

Limitations include the lack of clarity on how to write the system of equations specifically for the binary compound, as well as potential dependencies on the chosen lattice structure and assumptions about overlap.

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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
 
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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)
 

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