[Wannier] What's a good way to define the localization length?

[Raul Laasner]

Hi
I performed the minimization procedure for the 24 topmost valence bands of
my system. The resulting WFs have the spreads

1.18495  1.18450  1.13896
1.18495  1.18450  1.13895
1.18494  1.18449  1.13895
1.18492  1.18449  1.13892
1.18492  1.18449  1.13892
1.18490  1.18448  1.13889
1.18489  1.18448  1.13888
1.18489  1.18448  1.13888

Near the VB maximum, there should be 16 states of O 2p character, and
toward the VB bottom, there should be 8 states that are also of mainly O 2p
character, but have some mixture of W 5d states. By taking the sqrt of each
spread and averaging, I can say that the states in the lower half of the VB
are more localized (1.067) than in the upper half (1.088). However, In
several papers I've seen the localization length defined as the sqrt of the
total spread, divided by the number of states. By that logic, the upper
half of the VB would be more localized (sqrt(sum over the selected
spreads)/16=0.272) than the lower half in my system (0.377).

I'm confused over exactly what the spreads represent. Is it reasonable to
speak of the localization length of each WF separately?

-- 
Raul Laasner
Institute of Physics
University of Tartu
Ravila 14c, 50411, Tartu, Estonia
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