[Wannier] How to calculate current operator

[Saeed Bahramy]

Dear Wannier90 developers and users,

I'm trying to calculate the current operator Jx using Wannier90 code.  
By definition, I consider Jx to be the first derivative of H(k) with  
respect to kx. Having the real space Wannier hamiltonian H(R), then It  
should be possible to calculate Jx analytically by,

Jx(k)=SUM_R[ i Rx H(R) exp(ik.R)]

were SUM_R indicates the summation over all real space R-vectors. My  
procedure to calculate Jx is as follows,

1) I read the components of R-vectors (irvec) and H(R) from the  
Wannier90 output file seedname_hr.dat.

2) I build the R-vector as R=irvec(1,j)*A1+irvec(2,j)*A2+irvec(3,j)A3.  
Here, A1, A2 and A3 are my HEXAGONAL lattice vectors and j is the  
index for the jth R-vector. Having R, I then take its x-component as  
Rx, namely Rx=R(1).

3) I construct a fine k-mesh, and finally calculate Jx at each k using  
the above equation.

While this procedure seems to be very straightforward, it doesn't  
appear to be giving me correct Jx results. For example, If construct  
H(R) from a 10x10x10 ab-initio k-mesh the calculated Jx would somehow  
differ from that obtained form another H(R) made from 16x16x16 k-mesh  
(note that this k-mesh differs from what I described in step 3).  
Moreover, due to the hexagonal symmetry of my structure, I expect that  
the Jx should be invariant under 60 deg rotation, but it doesn't seems  
so.

I suspect that the problem should be somehow related to the way I  
calculate Rx. The reason is simply because I can properly construct  
H(k) and by that reproduce the ab-intio band dispersions without any  
problem.

I was wondering if somebody in this forum could let me know If I'm  
missing something.

I would greatly appreciate your comments and suggestions.

Sincerely,
Saeed
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Saeed Bahramy
Correlated Electron Research Group
Advanced Science Institute, RIKEN
Saitama 351-0198 JAPAN
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