Is Chern number exactly an integer of half-integer?

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SUMMARY

The discussion centers on the calculation of the Chern number, particularly in systems where non-integer values such as 0.9 or 1.93 are obtained. It is established that Chern numbers should generally be integers, but non-integer values can arise in metallic systems lacking a gapped band structure at the Fermi level. The use of a tight-binding Hamiltonian, Kubo formula, and MATLAB programming language is highlighted as the method for calculation. Participants suggest that adjustments in numerical methods may yield better results.

PREREQUISITES
  • Tight-binding Hamiltonian
  • Kubo formula
  • MATLAB programming language
  • Understanding of band structure in condensed matter physics
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  • Research integer Chern numbers in gapped band structures
  • Explore numerical methods for calculating Chern numbers in MATLAB
  • Study the implications of non-integer Chern numbers in metallic systems
  • Review the paper referenced: DOI: 10.1103/PhysRevB.106.205416
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Physicists, researchers in condensed matter physics, and anyone involved in topological insulator studies or Chern number calculations.

Mohammad-gl
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I'm trying to calculate the Chern number for a specific system. When I calculate the Chern number, it's not an integer, for example, I have 0.9 for it. Is it the wrong result or can I consider it as 1?
I'm trying to calculate the Chern number for a specific system. When I calculate the Chern number, it's not an integer, for example, I have 0.9 for it. Is it the wrong result or can I consider it as 1?
 
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What is a "Chem number"? Google just gives me the phone number of a company called "Chem Care".
 
What is the system you are considering? In general, yes, it should be an integer.

You could have non-integer Chern numbers, for example, in a metallic system, because you do not have a gapped band structure at the Fermi level (Chern number non well defined in the conventional sense). But there are workarounds to still define an integer Chern number.

What methods are you using to calculate it? If it's just numerics you might adjust your code to get better results.
 
I'm usi
dRic2 said:
What is the system you are considering? In general, yes, it should be an integer.

You could have non-integer Chern numbers, for example, in a metallic system, because you do not have a gapped band structure at the Fermi level (Chern number non well defined in the conventional sense). But there are workarounds to still define an integer Chern number.

What methods are you using to calculate it? If it's just numerics you might adjust your code to get better results.
I'm using tight-binding Hamiltonian, Kubo formula and MATLAB programming language. Is it ok if I calculate Chern number 1.93 or 0.7?
 
Mohammad-gl said:
I'm usi

I'm using tight-binding Hamiltonian, Kubo formula and MATLAB programming language. Is it ok if I calculate Chern number 1.93 or 0.7?
Are you following a specific reference?
 
I'm using this paper.
DOI: 10.1103/PhysRevB.106.205416

Can you help me with Matlab codes? If you can I will send you the code maybe I made a mistake in coding.
 

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