[Wannier] spread WFs to locate localized and delocalized states

[Gianluca Giovannetti]

Dear All,

i have a question.
I performed spin-polarized calculations with PW and then Wannier90 for a
system including Fe sites.
They are fine and convergence is good.
Looking at the bands close to Fermi level there are d states coming from Fe.
So i project the Hlda into Wannier states with d character (i also included
more states but things don`t change).
In the "file".wout i can grep the spread of Wannier functions (WFs) and this
is what i get:

  WF centre and spread    1  (  0.000000,  2.668451,  0.000000 )
0.87609658
  WF centre and spread    2  (  0.000000,  2.668451,  0.000000 )
1.14524506
  WF centre and spread    3  (  0.000000,  2.668451,  0.000000 )
1.08451112
  WF centre and spread    4  (  0.000000,  2.668451,  0.000000 )
0.89621460
  WF centre and spread    5  (  0.000000,  2.668451,  0.000000 )
1.07608158

  WF centre and spread    6  (  5.336902,  0.000000,  0.000000 )
0.56879195
  WF centre and spread    7  (  5.336902,  0.000000,  0.000000 )
0.68008849
  WF centre and spread    8  (  5.336902,  0.000000,  0.000000 )
0.68984086
  WF centre and spread    9  (  5.336902,  0.000000,  0.000000 )
0.59443634
  WF centre and spread   10  (  5.336902,  0.000000,  0.000000 )
0.66826689

>From 1 to 5 there are WFs of minority component while from 6 to 10 there are
WFs of majority component.
Can i say that minority component is more delocazied (for WFs 2,3,5) respect
to other WFs 6-10, 1,4?
There is a physical meaning i can associate to the value of spread to
understand if Wannier states are more metallic or insulating?
In my head i have majority component "close" to be more insulating and other
states "close" to be more metallic.
I`m not sure however about it.
Is this true?  Is this a correct statement?
Can you suggest some references to look at this point?

I thank you in advance.

cheers,

Gianluca Giovannetti
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