[Pw_forum] about born effective charge tensors

[hai wang]

>
> I'm not sure about whether the born effective charge tensor should be
> symmetric in crystals. Does it dependent on the structural symmetry of
> crystal itself ?


~~~~~~~~~

Born effective charge, alias transverse charge, can be computed from three
different techniques (linear response, difference of polarization under
finite atomic displacement, and difference of force under finite electric
field ). Linear-response methods provide an efficient means for computing
quantities that an be expressed as derivatives of the total energy E with
respect to a perturbation, such as that produced by displacement via of an
atom or a homogeneous electric field E.

The effective charges are somewhat sensitive to the structural details,
include the symmetric of crystals. Cubic local environments imply diagonal,
isotropic Born effective charge. In non-cubic structures, it may be with
off-diagonal components. For example, in the orthorhombic CaTiO3 structures,
the relatively large off-diagonal components of the Ti Born effective charge
tensors and their asymmetries were unexpected because the TiO6 octahedra are
nearly ideal. The large offdiagonal components show that Born effective
charge is not determined solely by nearest-neighbor Ti-O interactions, but
is strongly influenced by further-neighbor interactions which more strongly
break cubic symmetry(PRB62,3735).
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