The ABINIT Users Mailing List ( CLOSED )

[David Vanderbilt <dhv@physics.rutgers.edu>]

Tularam, Riad,

The problem goes deeper than this.  For materials like III-V
semiconductors, the "formal" electric polarization (the one
obtained from the Berry-phase theory) is not zero in the
high-symmetry structure, even after taking the quantum into
account.  See, e.g., Sec. III.E of
http://link.aps.org/doi/10.1103/PhysRevB.48.4442
and the discussion in Sec. 3.4 of
http://www.physics.rutgers.edu/~dhv/pubs/pub_list.html#198

David

On Tue, 27 Jan 2009, Riad Shaltaf wrote:

> Dear Tularam,
>
> Within modern theory of polarization, the total polarization may only be
> determined up to an integer multiple of the polarization quantum. So I
> guess
> that you need to subtract the value of polarization quantum or one of its
> multiples from the the ABINIT result.
>
> for more details: Neaton et al, PRB 71, 014113 (2005)
>
> Riad
>
> > Dear all,
> >
> > I am trying the spontaneous polarization of the III-V nitrides. Here is my
> > input file for the GaN
> > # Specific to calculation of Berry Phase.
> >   berryopt -1
> >   rfdir 1 1 1
> > #Definition of the planewave basis set
> >   ecut    100.0
> >   ectusm  0.5
> >   dilatmx 1.05
> >   diemac  6.0
> >
> > #Specific to ground state calculation
> >   iscf   5
> >   nstep  60
> >
> > #Definition of the unit cell
> > acell  6.026 6.026  9.798276
> > angdeg 90 90 120
> >
> > #Definition of the atom types
> > ntypat 2
> > znucl 31 7
> >
> > #Definition of the atoms
> > natom 4
> > typat 1 1 2 2
> > xred  0.0  0.0  0.0
> >       2/3  1/3  1/2
> >       0    0    0.377
> >       2/3 1/3   0.877
> >
> > #Gives the number of band, explicitely (do not take the default)
> > nband  18               # For an insulator (if described correctly as an
> > insulator
> >
> > #Exchange-correlation functional
> > ixc 1
> >
> > #Definition of the k-point grid
> > ngkpt 4 4 8
> > nshiftk 1
> > shiftk 0 0 .5
> > kptopt    3
> > toldfe    1.0d-12
> > nbdbuf 0
> >
> > I used hgh pseudopotential, hence used high cutoff. But my result for the
> > zz
> > part of polarization is as follow
> >  Computing the polarization (Berry phase) for reciprocal vector:
> >   0.00000  0.00000  0.12500 (in reduced coordinates)
> >   0.00000  0.00000  0.01276 (in cartesian coordinates - atomic units)
> >  Number of strings:    16
> >  Number of k points in string:    8
> >
> >  Summary of the results
> >  Electronic Berry phase     9.622896788E-01
> >             Ionic phase     7.700000000E-01
> >             Total phase     1.732289679E+00
> >     Remapping in [-1,1]    -2.677103212E-01
> >
> >            Polarization    -8.512874458E-03 (a.u. of charge)/bohr^2
> >            Polarization    -4.870620906E-01 C/m^2
> >
> >
> >  Polarization in cartesian coordinates (a.u.):
> >  (the sum of the electronic and ionic Berry phase has been fold into [-1,
> > 1])
> >      Electronic:  0.399941195E-12  -0.113753605E-11   0.305996840E-01
> >      Ionic:       0.318961478E-16  -0.868508257E-17   0.244850976E-01
> >      Total:       0.399969197E-12  -0.113755148E-11  -0.851287446E-02
> >
> >  Polarization in cartesian coordinates (C/m^2):
> >  (the sum of the electronic and ionic Berry phase has been fold into [-1,
> > 1])
> >      Electronic:  0.228825405E-10  -0.650838549E-10   0.175075365E+01
> >      Ionic:       0.182493052E-14  -0.496914937E-15   0.140090904E+01
> >      Total:       0.228841426E-10  -0.650847378E-10  -0.487062091E+00
> >
> > But the total zz polarization of-0.48 is more then a order of magnitude
> > greater
> > then reported p_zz of -0.029 reported in Phys. Rev B 56, R10024. I don't
> > understand the differences as both of them are similar first principle
> > calculation.   So I am wondering, if I am wrong ?. I played with the fhi
> > psedudopotential and obvious tests with the cutoff kpoints , Berryopt, but
> > the
> > result is same.
> >
> > I would appreciate if anyone help me how to calculate the spontaneous
> > polarization correctly.
> >
> > Thanks in an advance.
> >
> > Tularam
> --
> Dr. Riad Shaltaf                   UCL/SE/FSA/MAPR/PCPM
> Tel: +32 (0)10 47 36 30            B?timent Boltzmann, a+1
> Fax: +32 (0)10 47 34 52            1 place Croix du Sud
> Mel: riad.shaltaf@uclouvain.be     1348 Louvain-la-Neuve (Belgique)

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Prof. David Vanderbilt               Phone: (732) 445-5500 x2514
Department of Physics and Astronomy  Fax:   (732) 445-4400
Rutgers University                   Email:  dhv@physics.rutgers.edu
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