[Wannier] Extracting the tight-binding elements from Wannier90
Giovanni Pizzi
giovanni.pizzi at epfl.ch
Thu May 3 22:12:04 CEST 2018
Dear Alex,
No, it’s not required a priori that they have the same center.
Indeed, the WF you find are quite displaced: 1,2,3,4,5,8 are along the +/- x,y,z direction, while 6,7,9 are in the origin. As expected (which is a good additional check to verify convergence, also), the on term sites are the same for the two groups; the hoppings within the first group have a value for those aligned along the same axis (e.g. 1-4) that is different than the value for those aligned on different axes (1-2,1-3,1-8), and even different (almost zero) with the hoppings for the second group; hoppings between same-centre orbitals 6,7,9 are zero. So, to me the Hamiltonian matrix elements look reasonable.
Best,
Giovanni
--
Giovanni Pizzi
Theory and Simulation of Materials and MARVEL, EPFL
http://people.epfl.ch/giovanni.pizzi
http://nccr-marvel.ch/en/people/profile/giovanni-pizzi
On 1 May 2018, at 21:43, Alex.Durie <alex.durie at open.ac.uk<mailto:alex.durie at open.ac.uk>> wrote:
Thanks Giovanni,
I have compared the bandstructure produced by Wannier90 with use_ws_distance = true, and use_ws_distance = false and seem to conclude in this case that it has little effect.
The Hamiltonian at 000 is the following 9x9 Matrix (apologies if it doesn't format well);
1.54787 -0.0622846 -0.0622845 -0.426436 -0.0622842 -2.93994e-07 0 -0.0622843 2.93994e-07
-0.0622846 1.54787 0.0622846 -0.0622845 -0.426436 1.46997e-07 7.34986e-08 0.0622845 -7.34986e-08
-0.0622845 0.0622846 1.54787 -0.0622846 0.0622845 2.20496e-07 0 -0.426436 7.34986e-08
-0.426436 -0.0622845 -0.0622846 1.54787 -0.0622845 -2.20496e-07 0 -0.0622843 1.46997e-07
-0.0622842 -0.426436 0.0622845 -0.0622845 1.54787 2.93994e-07 7.34986e-08 0.0622844 -7.34986e-08
-2.93994e-07 1.46997e-07 2.20496e-07 -2.20496e-07 2.93994e-07 1.00461 0 2.93994e-07 0
0 7.34986e-08 0 0 7.34986e-08 0 1.00461 0 0
-0.0622843 0.0622845 -0.426436 -0.0622843 0.0622844 2.93994e-07 0 1.54787 1.46997e-07
2.93994e-07 -7.34986e-08 7.34986e-08 1.46997e-07 -7.34986e-08 0 0 1.46997e-07 1.00461
if it's relevant, here is the Wannier90 output;
Final State
WF centre and spread 1 ( 0.000985, 0.685469, -0.000344 ) 1.10271947
WF centre and spread 2 ( 0.000151, 0.000345, 0.685467 ) 1.10267618
WF centre and spread 3 ( -0.685461, 0.000990, 0.000152 ) 1.10266654
WF centre and spread 4 ( -0.000992, -0.685461, 0.000345 ) 1.10264952
WF centre and spread 5 ( -0.000155, -0.000348, -0.685468 ) 1.10269372
WF centre and spread 6 ( 0.000001, 0.000000, 0.000000 ) 0.41116932
WF centre and spread 7 ( 0.000001, 0.000001, 0.000000 ) 0.41116778
WF centre and spread 8 ( 0.685471, -0.000997, -0.000152 ) 1.10270517
WF centre and spread 9 ( 0.000000, 0.000002, 0.000000 ) 0.41116957
Sum of centres and spreads ( 0.000000, 0.000001, 0.000000 ) 7.84961726
Spreads (Ang^2) Omega I = 5.946718268
================ Omega D = 0.014524748
Omega OD = 1.888374247
Final Spread (Ang^2) Omega Total = 7.849617263
Translated centres
translation centre in fractional coordinate: 0.000000 0.000000 0.000000
WF centre 1 ( 0.000985, 0.685469, -0.000344 )
WF centre 2 ( 0.000151, 0.000345, 0.685467 )
WF centre 3 ( -0.685461, 0.000990, 0.000152 )
WF centre 4 ( -0.000992, -0.685461, 0.000345 )
WF centre 5 ( -0.000155, -0.000348, -0.685468 )
WF centre 6 ( 0.000001, 0.000000, 0.000000 )
WF centre 7 ( 0.000001, 0.000001, 0.000000 )
WF centre 8 ( 0.685471, -0.000997, -0.000152 )
WF centre 9 ( 0.000000, 0.000002, 0.000000 )
Forgive my naive question, but would it be expected that the Wannier functions have the same centre?
Many thanks,
Alex
________________________________
From: Giovanni Pizzi <giovanni.pizzi at epfl.ch<mailto:giovanni.pizzi at epfl.ch>>
Sent: 30 April 2018 11:15:44
To: Alex.Durie
Cc: wannier at lists.quantum-espresso.org<mailto:wannier at lists.quantum-espresso.org>
Subject: Re: [Wannier] Extracting the tight-binding elements from Wannier90
Dear Alex,
Maybe this reply answers only partially to your questions, but anyway:
- to get the same interpolation, you should also use the content of the seedname_wsvec.dat file, see se. 8.21 of the user guide http://wannier.org/doc/user_guide.pdf as well as Sec. 9 “Some notes on the interpolation”
Anyway, the difference if you discard these elements should be small (the same as running with use_ws_distance=false or true).
For the non-diagonal elements at R=000: these would be hoping between different Wannier functions (that you project initially with different symmetry). The first option that comes to my mind: are the Wannier functions all at the same center? If not, this might be one cause for a non-zero element. Also, how big are these non-zero elements?
Giovanni
--
Giovanni Pizzi
Theory and Simulation of Materials and MARVEL, EPFL
http://people.epfl.ch/giovanni.pizzi
http://nccr-marvel.ch/en/people/profile/giovanni-pizzi
On 29 Apr 2018, at 23:09, Alex.Durie <alex.durie at open.ac.uk<mailto:alex.durie at open.ac.uk>> wrote:
Dear all,
Forgive the nature of this question, as I know there has been much previous discussion. I am new to Wannier90 and wish to extract the tight-binding parameters to use within my existing C++ code. I am attempting to compare against results that I have obtained using potentials within 'The Handbook of the Bandstructure of Elemental Solids' by D. Papaconstantopoulos.
I thought a good place to start would be bcc Fe spin up. To that end, I have started with input files from example08 with the following additions;
write_hr = true
use_ws_distance = true
bands_plot_mode = cut
dist_cutoff = 5
as I was hoping to use up to second nearest neighbour interactions, and wanted to check the bandstructure was sufficiently accurate.
I have attempted to use the relevant data within seedname_hr.dat to reconstruct the bandstructure in my C++ code to make sure I was building the Hamiltonians correctly and seem to be running into difficulty.
I assumed these were the lines of seedname_hr.dat that were relevant;
0 0 0 n m real imag
1 1 1 n m real imag
-1 1 1 n m real imag
1 -1 1 n m real imag
1 1 -1 n m real imag
-1 -1 1 n m real imag
1 -1 -1 n m real imag
-1 1 -1 n m real imag
-1 -1 -1 n m real imag
2 0 0 n m real imag
-2 0 0 n m real imag
0 2 0 n m real imag
0 -2 0 n m real imag
0 0 2 n m real imag
0 0 -2 n m real imag
but using these values does not yield the same bandstructure as that in iron_up_band.gnu.
Is there some form of reordering required that I have not considered?
Also, at R = 0,0,0 I am getting non-zero off-diagonal elements. Is that an error in output?
Also, I would have expected dist_cutoff = 2.942225 to be suitable to calculate the bandstructure up to second nearest-neighbour, but found that I needed dist_cutoff = 5 to observe non-zero second nearest-neighbour terms in iron_up.wout, under
"Maximum absolute value of Real-space Hamiltonian at each lattice point"
unless I am misinterpreting the information?
Thanks in advance to anyone who can put me on the right track.
Alex Durie
PhD student
The Open University
United Kingdom
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