[Wannier] A question on the Hamiltonian with spinors from Wannier90

Ivo Souza ivo_souza at ehu.es
Wed Nov 14 19:00:42 CET 2012 

Dear Binghai,

   Glad to hear that you solved your problem.

   Let me follow up on the remarks by Julen about the maxloc WFs being 
real. This statement is correct without spin-orbit. For spinor WFs I 
believe the corresponding statement would be that maxloc WFs come in 
time-reversal (TR) pairs. But I think in general they are complex.

   There is however a counter-example to the statement above, maybe you 
know this already: the valence bands of topological insulators are still 
Wannier-representable, as in ordinary insulators, but the gauge where the 
WFs are localized must break TR. This is discussed in a series of papers 
by Alexey Soluyanov and David Vanderbilt.

   (If you include conduction bands in the set of states to be wannierized, 
then I guess it again becomes possible to find a set of WFs which come in 
TR-pairs,even for topological insulators.)

   These things are subtle, and I hope I did not make any wrong statements!

   Best,

   Ivo


On Wed, 14 Nov 2012, Yan, Binghai wrote:

> Dear Julen
>
> Thank you for your suggestions. Finally, I have got a satisfying 
> Hamiltonian, which respects the time-reversal symmetry. In my case, the 
> convergence of DFT calculation is found to be a problem. Wannier90 
> requires wavefunctions on a full k-point grid, while my DFT calculation 
> uses a reduced k-points and interpolates the wavefunctions to a full k 
> grid. Here the interpolated wavefunction and eigen energies are not 
> accurate enough. (For calculations without spinors, normal interpolation 
> is found to be enough) Therefore, I switch off the symmetry and use a 
> full k-grid to extract the wannier parameters. Consequently, this 
> improves my wannier90 results dramatically. This might be a well-known 
> trick for wannier90. However, I spent a lot of time to realize it.
>
> BTW, I knew that the imaginary parts of _hr.dat are zero for 
> calculations without SOC. However, my SOC hr.dat still has the imaginary 
> components.
>
> All the best,
> Binghai
> ________________________________________
> From: julen.azpiroz at gmail.com [julen.azpiroz at gmail.com] on behalf of Julen Ibanez Azpiroz [julen.ibanez at ehu.es]
> Sent: Monday, November 12, 2012 9:01 PM
> To: Yan, Binghai
> Cc: wannier at quantum-espresso.org
> Subject: Re: [Wannier] A question on the Hamiltonian with spinors from Wannier90
>
> Dear Binghai,
>
> Maybe the issue is related to the convergence, the off-diagonal matrix 
> elements you show have a non-null imaginary part, as far as I know this 
> means that the Wannier functions you got are not still the maximally 
> localized ones since these should be real in a system with TR symmetry 
> (see PRL 98, 046402 (2007)). Maybe you could try to wannierise till the 
> imaginary part of the matrix elements are null to be sure that you got 
> the MLWF, and then check the on-site and off-diagonal matrix elements. 
> Just a question, the 16 bands you are including, are they all below the 
> Fermi level?
>
> Cheers,
>
> Julen
>
>
> On Fri, Nov 9, 2012 at 11:44 AM, Yan, Binghai 
> <yanb at uni-mainz.de<mailto:yanb at uni-mainz.de>> wrote: Dear Wannier 
> developers
>
> I am new user of wannier90. I extract wannier functions from a DFT 
> calculation (I use vasp) including spin orbit coupling (SOC). Then I 
> switch on spinors=T and double the num_bands. My systems have no spin 
> polarization, respecting the time reversal symmetry. A wannier function 
> is expected to be represented by two functions, which have the same 
> center but different spins. I expect these two functions have the same 
> onsite energies and the hopping term between them are exactly zero. 
> However, I get different onsite energies and nonzero hopping terms, 
> although the band structure is well reproduced. The wannier cenceters 
> are also very different.
>
> The following is an example of my inputs for bulk HgTe calculations. 
> (zincblende structure)
>
> ==========
> num_wann          =   16
> num_bands         =   38
> #exclude_bands     =   3-12
>
> dis_win_max       =  15.0
> dis_froz_max      =  9
> dis_num_iter      =  2000
> dis_mix_ratio     = 1.d0
>
> num_iter          = 1000
> num_print_cycles  = 10
>
> Begin Projections
> Hg : sp3
> Te : sp3
> End Projections
>
> spinors = .true.
>
> begin unit_cell_cart
>     3.2300000     3.2300000     0.0000000
>     0.0000000     3.2300000     3.2300000
>     3.2300000     0.0000000     3.2300000
> end unit_cell_cart
>
> begin atoms_cart
> Hg       2.4225000     2.4225000     2.4225000
> Te       4.0375000     4.0375000     4.0375000
> end atoms_cart
>
> mp_grid =    12    12    12
>
> begin kpoints
>      0.000000000000      0.000000000000      0.000000000000
>      0.083333333333      0.000000000000      0.000000000000
>      0.166666666667      0.000000000000      0.000000000000
>      0.250000000000      0.000000000000      0.000000000000
> ................
> ========================
>
> The optimized wannier centers are :
> Cycle:   1000
>  WF centre and spread    1  (  1.125081,  2.105459,  2.107134 )     7.50544434
>  WF centre and spread    2  (  2.108857,  1.123510,  2.103942 )     7.50493864
>  WF centre and spread    3  (  2.106035,  2.107794,  1.122418 )     7.50768700
>  WF centre and spread    4  (  1.124096,  1.124214,  1.123910 )     7.52064335
>  WF centre and spread    5  (  3.522963,  3.524601,  3.524535 )     4.48040046
>  WF centre and spread    6  (  3.526018,  2.934456,  2.939037 )     4.47399171
>  WF centre and spread    7  (  2.939672,  3.523541,  2.932669 )     4.46863560
>  WF centre and spread    8  (  2.934153,  2.938291,  3.522491 )     4.47010302
>  WF centre and spread    9  (  2.107155,  2.105137,  1.125272 )     7.64204572
>  WF centre and spread   10  (  1.123133,  1.123929,  1.123907 )     7.64532973
>  WF centre and spread   11  (  1.122550,  2.106696,  2.105047 )     7.63263662
>  WF centre and spread   12  (  2.104217,  1.123646,  2.107754 )     7.63564195
>  WF centre and spread   13  (  3.524860,  3.524017,  3.523515 )     4.51698438
>  WF centre and spread   14  (  3.522838,  2.936705,  2.934278 )     4.51145886
>  WF centre and spread   15  (  2.933391,  3.524025,  2.938085 )     4.50864047
>  WF centre and spread   16  (  2.937251,  2.934720,  3.525198 )     4.51260402
>  Sum of centres and spreads ( 38.762270, 38.760740, 38.759191 )    96.53718585
>
> For example, the matrix elements between WF 8 and WF 16 are
>
>    0    0    0    8    8    0.863620    0.000000
> -
>    0    0    0   16   16    0.932080    0.000000
> -
>    0    0    0   16    8   -0.032312   -0.000905
> -
>    0    0    0    8   16   -0.032312    0.000905
>
>
> Is this problem due to a bad projection? Actually, I used sp3 for non-SOC case, it seems pretty well.
> Is there a way to constrain different spins have the same wannier centers?
>
> Thank you very much in advance!
> Binghai
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>
> --
> ========================================
> Julen Ibañez Azpiroz
> Materia Kondentsatuaren Fisika Saila
> Zientzia eta Teknologia Fakultatea
> Euskal Herriko Unibertsitatea
> ========================================
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