[Wannier] understanding the output of Wannier90

[Gianluca Giovannetti]

Dear All,

i`m having a problem in understanding the output of wannier90 (file hr.dat).

i have made a calculation for a molecular crystal.

the unit cell consists of molecular sites (A and B) along the stacking
direction a (with a lattice vector) as illustrated in the following:

-----> a

|o   o | o   o | ......
 A   B  A  B

(here i`m plotting schematically two unit cells)

Let label the molecules in this way:

-----> a

|o    o | o    o | ......
 A1 B1 A2 B2

now the bonds B1-A2 are shorter while bonds A2-B2 are longer (the system is
dimerized).

the HOMOs (highest occupied molecular orbitals) of the two molecules A,B
contained in the unit cell hybridize, giving rise to bonding and
antinbonding bands around the Fermi level. then at Fermi level i have two
states.

the calculations performed with PW and W90 looks fine and the agreement of
PW and W90 bands is good.

once i plot using xcrystalden the Wannier functions of the such states at
Fermi one is located at A2 and the other one is located to B1 (basically one
is in the unit cell and the other one is located at the NN unit cell along
a).

now i go to look at the hr.dat file and i find:

    0    0    0    1    1    3.334228    0.000000
    0    0    0    2    1    0.222024    0.000000
    0    0    0    1    2    0.222024    0.000000
    0    0    0    2    2    3.334221    0.000000

    1    0    0    1    1    0.000243    0.000000
    1    0    0    2    1    0.203498    0.000000
    1    0    0    1    2    0.000122    0.000000
    1    0    0    2    2    0.000242    0.000000

   -1    0    0    1    1    0.000243    0.000000
   -1    0    0    2    1    0.000122    0.000000
   -1    0    0    1    2    0.203498    0.000000
   -1    0    0    2    2    0.000242    0.000000

i have some doubts in understanding the hopping parameters.

i see the kinetic terms are different 0.222024/0.203498 as one would expect
in a dimerized structure. this is fine.

the values 3.334228 are the on-site energies of the tight-binding problem.

my problem is the following.
is 0.222024 referring to the the hopping between A1 and B1 (also between A2
and B2)  or between B1 and A2?

because the Wannier functions plotted in real space are sitting between
adjacent different unit cells i would expect 0.222024 referring to hopping
between B1 and A2 and 0.203498  referring to hopping between A1 and B1 (also
between A2 and B2).
then at smaller distances would correspond larger hoppings and at larger
distances would correspond smaller hoppings.

could you please confirm this way to interpret the file hr.dat? :-)

i thank you in advance for our time.

cheers,

Gianluca Giovannetti
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