berry curvature calcualtion

[Yiming Pan]

Hello developers,

In one of my projects I wanted to calculate berry curvature for each occupied states on a very dense k points mesh,so I naturally think of using wannier interpolation approach implemented in wanniertools. However, after I read the codes in berrycurvature.f90, there are something I didn’t understand and here are my questions.

• I could well understand the calculation in subroutine berry_curvature_singlek_EF which seems to be a direct interpretation of Eq(30) in PRB 74, 1995118. However,for the subroutine  berry_curvature_singlek_EF_old, I couldn’t understand why you did the unitary transformation for DHDk and DHDkdag(between line 90 and 96) given that matrices v have been transformed to Hamiltonian gauge from line 52 to 58, although in the main program berry_curvature_singlek_EF_old is not used.
• According to the Eq(27)  PRB 74, 1995118, there are another three terms contributing to the berry curvature but they are not considered in your code. Is it because that their contributions are minor? How will the results be influenced if they are neglected according to your tests?

As I am new to wanniertools and computational physics, I would be grateful if you could answer these questions.

[Brook]

Hi Yiming,

1. Yes, you are right. It’s not necessary to rotate it. However, the rotation will not give you wrong results if we care about the trace of the matrix. That’s why I abandoned it.
2. It’s because those terms are small. It’s discussed in the reference you mentioned. Those terms measures the entanglement between the Wannier bands and the DFT bands close to the  chemical potential you care about. Since WannierTools is based on tight binding model. So we assume the tight binding model is completed.

Best,

QuanSheng

[Yiming Pan]

Hi Quansheng,

Thank you so much for your reply.  If we are interested in the sum of berry curvature in occupied states(for example,to calculate the anomalous hall conductivity) it is only the trace of the matrix that we care about. But I’m interested in the berry curvature of each state around the fermi level . So I should do my calculations in Hamiltonian gauge, using the subroutine berry_curvature_singlek_EF  ,perhaps with some modification.

Best

[Author]

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