[Wannier] why hopping parameters of equivalent WF is different

[Lin Xie]

Dear all
   I am calculating the hopping parameters of monolayer and bulk MoS2 using
Wannier90. I have got good convergence of the MLWF basis for both cases.
The Hamiltonian in WF basis for the monolayer is fine and the matrix
element (hopping parameters) looks like:

    0    0    0    1    1   -7.812224    0.000000
    0    0    0    2    1    0.378757    0.000000
    0    0    0    3    1   -0.161374    0.000000
    0    0    0    4    1    0.378757    0.000000
    0    0    0    5    1    0.378757    0.000000
    0    0    0    6    1   -0.161374    0.000000
    0    0    0    7    1    0.378757    0.000000

There are three WFs for each S atom (2 S atoms in total) and one WFs for Mo
atom. From this table it is clear that the hopping parameters for
equivalent hoppings (e.g. hopping from WF 2 to WF 1 and hopping from WF 4
to WF 1) are identical.

However, for the bulk MoS2, I got the following hopping parameters:

    0    0    0    1    1    6.788221    0.000000
    0    0    0    2    1    0.002303    0.000000
    0    0    0    3    1    0.167082    0.000000
    0    0    0    4    1   -0.375031    0.000000
    0    0    0    5    1    0.374977    0.000000
    0    0    0    6    1    0.167082    0.000000
    0    0    0    7    1   -0.375031    0.000000
    0    0    0    8    1    0.374977    0.000000
    0    0    0    9    1   -0.000013    0.000000
    0    0    0   10    1    0.000201    0.000000
    0    0    0   11    1   -0.000201    0.000000
    0    0    0   12    1   -0.010587    0.000000
    0    0    0   13    1   -0.005480    0.000000
    0    0    0   14    1    0.005477    0.000000

What puzzles me is that now I get a complete different hopping parameters
for equivalent hoppings, e.g. hopping from WF 4 to WF 1 and that from WF 5
to WF 1. I have try many possible sets of initial projections but they give
similar results. Could some one help if my understand of the Hamiltonian in
WF basis is incorrect.

Best regards!
-- 
Lin Xie
Beijing National Center for Electron Microscopy
Department of Material Science and Engineering
Tsinghua University
Beijing, PR of China
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