The ABINIT Users Mailing List ( CLOSED )

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

Dear all,

The Berry phase does not have to be zero in a system with inversion
symmetry.  For example, consider a 1D system where the "+1 ions"
are at x=0, a, 2a, etc, and the electron Wannier centers are at
x=-a/2, a/2, 3a/2, etc.  Then the Berry phase is pi, not zero.

Something similar happens for centrosymmetric ionic systems.  For
example, the Berry phases of CsCl and KNbO3 are pi, and not zero,
In such cases, one should be practical and report an "effective
polarization" that is defined relative to that of the
centrosymmetric structure (so that it is zero by definition in the
centrosymmetric structure).  But one still needs to be aware that
the raw Berry-phase polarizations coming out of the calculation
will not be zero.

Raffaele Resta and I have written two manuscripts that attempt to
explain some of the tricky physical issues associated with the
theory of polarization.  These are intended to be published as book
chapters; for copyright reasons, I have not posted them on my
publications web site, but I will be more than happy to send a
draft preprint (for personal use only) to anybody who requests
it.  See

  http://www.physics.rutgers.edu/~dhv/pub_list.html#182
  http://www.physics.rutgers.edu/~dhv/pub_list.html#190

The latter one addresses more specifically the issue raised in
this thread.

David Vanderbilt


On Thu, 9 Feb 2006, Vincenzo Fiorentini wrote:

> I am not an expert on how abinit computes Berry phases,
> but I suspect this results is consistent with your
> expectation. The Berry phase is defined modulo a lattice
> translation (Phys. Rev. B 47, 1651 (1993)), so probably
> your number *is* indeed zero in that convention.
>
> best - V. Fiorentini
>
>
> On 9 Feb 2006, at 2:12 PM, Konstantin Rushchanskii wrote:
>
> > Dear all,
> >
> > I'm trying to calculate the polarization of a low-symmetry monoclinic
> > compound
> > Sn2P2S6 (space group Nom. 14), containing the inversion symmetry.
> > In this case, the resulting polarization should be zero.
> >
> > Unfortunately, it is zero only for the ionic part, but not for the
> > electron one.
> > Electronic Berry phase is exatly equal to 1, and as a result the total
> > polarization
> > is non-zero.  The input file with simplyfied conditions is given below
> > (the case with berryopt -1).
> > Moreover, the results are similar also for berryopt 1.
> >
> > ABINIT identifies the space group correctly.
> >
> > How can I treat this result?
> > Does it mean that the problem is related  to the setting of the
> > crystalline structure?
> >
> > I have found similar problem in the letter of Jian ZHOU (16 Jun 2005),
> > but there were no answers to this question.
> >
> >
> > Thank you in advance,
> > K.Rushchanskii
> >
> >
> >
> > log_file -----------------------------
> >  Computing the polarization (Berry phase) for reciprocal vector:
> >  0.00000  0.25000  0.00000 (in reduced coordinates)
> >  0.00000  0.01766  0.00000 (in cartesian coordinates - atomic units)
> >  Number of strings:    16
> >  Number of k points in string:    4
> >
> >  Compute the electronic contribution to polarization
> >
> >          istr          polberry(istr)
> >             1       0.100000000E+01
> >             2       0.100000000E+01
> >             3       0.100000000E+01
> >             4       0.100000000E+01
> >             5       0.100000000E+01
> >             6       0.100000000E+01
> >             7       0.100000000E+01
> >             8       0.100000000E+01
> >             9       0.100000000E+01
> >            10       0.100000000E+01
> >            11       0.100000000E+01
> >            12       0.100000000E+01
> >            13       0.100000000E+01
> >            14       0.100000000E+01
> >            15       0.100000000E+01
> >            16       0.100000000E+01
> >         total       0.100000000E+01 (isppol=   1)
> >
> >  Compute the ionic contributions
> > ...
> >
> >  Summary of the results
> >  Electronic Berry phase     1.000000000E+00
> >            Ionic phase    -1.221245327E-15
> >            Total phase     1.000000000E+00
> >    Remapping in [-1,1]     1.000000000E+00
> >
> >           Polarization     4.567594984E-03 (a.u. of charge)/bohr^2
> >           Polarization     2.613338624E-01 C/m^2
> >
> > log_file -----------------------------
> >
> >
> >
> >
> > -------------------------
> > input.ini
> > -------------------------
> >
> >
> > ndtset  2
> > nstep 10
> >
> >
> > acell 9.362 7.493 6.55 Angstrom
> > angdeg 90 91.2 90
> >
> > xred
> >     0.24310       0.36920       0.95890
> >     0.25690       0.86920       0.54110
> >     0.75690       0.63080       0.04110
> >     0.74310       0.13080       0.45890
> >     0.06710       0.39140       0.43940
> >     0.43290       0.89140       0.06060
> >     0.93290       0.60860       0.56060
> >     0.56710       0.10860       0.93940
> >     0.26290       0.49750       0.39910
> >     0.23710       0.99750       0.10090
> >     0.73710       0.50250       0.60090
> >     0.76290       0.00250       0.89910
> >     0.96720       0.30900       0.17720
> >     0.53280       0.80900       0.32280
> >     0.03280       0.69100       0.82280
> >     0.46720       0.19100       0.67720
> >     0.05700       0.19760       0.65580
> >     0.44300       0.69760       0.84420
> >     0.94300       0.80240       0.34420
> >     0.55700       0.30240       0.15580
> >
> > ntypat 3
> > znucl 50 15 16
> > natom 20
> > typat 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
> > nband  54
> >
> > ngkpt 2  2  2
> > ecut 2 Ha
> >
> >
> >   kptopt1   1
> >   toldfe1   1.0d-3
> >   iscf1   5
> >   prtden1 1
> >
> >   berryopt2 -1
> >   rfdir2 0 1 0
> >   iscf2 -2
> >   kptopt2 1
> >   ngkpt2 4 4 4
> >   getden2 1
> >   tolwfr2 1.0d-4

------------------------------------------------------------------------
Prof. David Vanderbilt               Phone: (732) 445-2514
Department of Physics and Astronomy  Fax:   (732) 445-4400
Rutgers University                   Email:  dhv@physics.rutgers.edu
136 Frelinghuysen Road               http://www.physics.rutgers.edu/~dhv
Piscataway, NJ 08854-8019   USA
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