The ABINIT Users Mailing List ( CLOSED )

[Xavier Gonze <xavier.gonze@uclouvain.be>]

Dear T Gao,

On 13 Apr 2009, at 21:46, gaotaoscu@hotmail.com wrote:

> Hello everybody,
>
> When  read the paper 'Lattice dynamics and dielectric properties of  
> TiO2
> anatase: A first-principles study' published PHYSICAL REVIEW B 66,  
> 155213
> (2002).  there is one point I can not undserstand, i.e., why there  
> is a LO-TO
> splitting for the IR active A2u?
>
> To my best of knowledge, A2u is only a one dimmensional  
> representation for
> group D4h(4/mmm). It is quiet easy to find the LO-TO splitting  for Eu
> representation in ABINIT calculation, because it is a two dimmensional
> representation. so it could have the LO-TO splitting. And the same A2u
> Splitting also exists in article 'Lattice dynamics and Dielectric  
> Properties of
> SiO2 Stishovite' published on PRL, vo72, p1686,1994.Why there is a  
> LO-TO
> splitting for the IR active one dimmenstional representation A2u  
> mode?	Could
> it be splitted in optical measurement?  


The frequency of this A2u (at Gamma q=0 in principle) will depend on  
the way the limit q->0 is taken.
Indeed, there is a non-analytic contribution to the dynamical matrix,  
and, for different
branches of the phonon dispersion curves, the limit of the A2u mode  
frequency at Gamma will be different.
So, along some directions, the electric field will not couple (TO),  
while for one direction,
there will be a full coupling to the electric field (LO). This can be  
seen in neutron experiments.
For the equations, see section VIII B of Phys. Rev. B 55, 10355 (1997).

Best regards,
Xavier