Is Chern number exactly an integer of half-integer?

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In summary, the question of whether the Chern number is exactly an integer or half-integer relates to the topological properties of certain quantum systems. Chern numbers, which arise in the study of topological phases of matter, can take on integer values associated with the quantized Hall effect. However, in specific contexts, such as systems with time-reversal symmetry, they may also yield half-integer values. The classification depends on factors like the symmetry of the system, the dimensionality, and the nature of the band structure, leading to a nuanced understanding of topological invariants in different physical scenarios.
  • #1
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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  • #2
What is a "Chem number"? Google just gives me the phone number of a company called "Chem Care".
 
  • #3
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.
 
  • #4
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?
 
  • #5
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?
 
  • #6
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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