[Wannier] The meaning of wannier_hr.dat
Mostofi, Arash
a.mostofi at imperial.ac.uk
Sun Dec 14 12:28:55 CET 2014
Dear Hassan,
Each line in hr.dat refers to an element of H_{mn}(R) = <w_m(0)|H|w_n(R)>. The first three entries in each line give the translation vector R, the next two give the WF indices m and n, and the last two are the real and imaginary parts of the matrix element itself. See the User Guide Sec. 8.18, for example. The order of the indices m and n are the same order in which the WFs appear at the end of the wannier90 output file (*.wout), so which atoms are referred to by a particular hopping matrix element with indices m and n depends on where the wannier functions w_m and w_n are centred in the cell.
Whilst the WFs themselves are orthogonal, you would not expect the matrix representation of the Hamiltonian in the WF basis to be diagonal in the m and n indices because the WFs are not eigenstates of H. The WFs are, however, localised, so you would expect the matrix elements of H to reflect this.
Hope this helps,
Arash
—
Dr Arash Mostofi — www.mostofigroup.org<http://www.mostofigroup.org>
Imperial College London
Director, Thomas Young Centre @Imperial
Assistant Director, CDT in Theory & Simulation of Materials
Warden, Wilkinson & Weeks Hall
On 14 Dec 2014, at 06:32, Hassan Tahini <hat343 at gmail.com<mailto:hat343 at gmail.com>> wrote:
Dear All,
We are having a problem interpreting the output of wannier_hr.dat. This file is supposed to contain the on-site energies and hopping elements from one orbital on one site to another.
We have a perovskite system (space group R-3c) with octahedral tilting and we are interested in the eg bands, we define our projections as:
num_wann = 4
num_bands = 144
begin projections
Mn:l=2,mr=1,4
end projections
Part of the wannier90.up_hr.dat looks like this:
0 0 0 1 1 11.382484 0.000000
0 0 0 2 1 -0.435842 0.000000
0 0 0 3 1 0.017151 0.000000
0 0 0 4 1 0.170537 0.000000
0 0 0 1 2 -0.435842 0.000000
0 0 0 2 2 11.966686 0.000000
0 0 0 3 2 -0.067861 0.000000
0 0 0 4 2 -0.613858 0.000000
We are finding it difficult to interpret the above. Can we say for instance that there is “hopping” between the dz2 orbital on atom one to a dx2-y2 on the same atom (=-0.435 eV)? Or can we say that the hopping between dz2 on atom 1 to dx2-y2 on atom 2 is 0.17 eV? Shouldn't the hopping between orthogonal orbitals be equal to zero? Should we use different projection settings?
Your help is highly appreciated.
Hassan
p.s. The band structure obtained with wannier90 looks just like the one we obtain from ab-initio calculations.
--
Dr Hassan A. Tahini
PhD, DIC
Physical Sciences and Engineering,
Computational Physics & Materials Science Group,
KAUST
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