[Wannier] Hermiticity of Berry potential matrix

[Lun Yue]

Dear all,

I am writing a real-time propagation code that requires high accuracy of 
the the Berry connection matrix A_{nm}(k) = i <u_n|d_k u_m> in the 
Hamiltonian gauge, which is e.g. given in WYSV2006 Eq.(25) and depends 
on A in the Wannier gauge. However, in the calculation of the Berry 
connection matrix in the Wannier gauge (get_oper.F90), it is mentioned 
that this quantity is not Hermitian and Hermiticity is explicitly forced:

/"//Since Eq.(44) WYSV06 does not preserve the Hermiticity of the Berry 
potential matrix, take Hermitean part (whether this makes a difference 
or not for e.g. the AHC, depends on which expression is used to evaluate 
the Berry curvature.//See comments in berry_wanint.F90)"/

I believe that this step introduces some small error, which is reflected 
in my final results. I also cannot find the mentioned file 
berry_wanint.F90. I am wondering if there are some ways to solve this 
problem, i.e. by making the Berry connection matrix naturally Hermitian? 
Any help or references is appreciated.

Best regards,

Lun Yue

Louisiana State University

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