Berry phases and finite electric fields: Difference between revisions

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== Berry phase expression for the macroscopic polarization ==
== Berry phase expression for the macroscopic polarization ==
Calculating the change in dipole moment per unit cell under PBC's, is a
nontrivial task. In general one {\it cannot} define it as the first moment of
the induced change in charge density δ('''r'''), through
:<math>
\Delta \mathbf{P}= \frac{1}{\Omega_{0}} \int_{\Omega_{0}} \mathbf{r} \delta
\left(
\mathbf{r} \right) d^{3}r
</math>
without introducing a dependency on the shape of &Omega;<sub>0</sub>, the
chosen unit cell (see for instance Ref.\ \cite{Vogl78}).
Recently King-Smith and Vanderbilt\ \cite{Vanderbilt93I}, building on the work
of Resta\ \cite{Resta92}, showed that the electronic contribution to the
difference in polarization $\Delta \mathbf{P}_{e}$, due to a finite adiabatic
change in the Hamiltonian of a system, can be identified as a {\it geometric
quantum phase} or {\it Berry phase} of the valence wave functions. We will
briefly summarize the essential results (for a review of geometric quantum
phases in polarization theory see Refs.\ \cite{Resta94} and \cite{Resta96}).


== Self-consistent response to finite electric fields ==
== Self-consistent response to finite electric fields ==

Revision as of 14:01, 6 March 2011

Berry phase expression for the macroscopic polarization

Calculating the change in dipole moment per unit cell under PBC's, is a nontrivial task. In general one {\it cannot} define it as the first moment of the induced change in charge density δ(r), through

without introducing a dependency on the shape of Ω0, the chosen unit cell (see for instance Ref.\ \cite{Vogl78}).

Recently King-Smith and Vanderbilt\ \cite{Vanderbilt93I}, building on the work of Resta\ \cite{Resta92}, showed that the electronic contribution to the difference in polarization $\Delta \mathbf{P}_{e}$, due to a finite adiabatic change in the Hamiltonian of a system, can be identified as a {\it geometric quantum phase} or {\it Berry phase} of the valence wave functions. We will briefly summarize the essential results (for a review of geometric quantum phases in polarization theory see Refs.\ \cite{Resta94} and \cite{Resta96}).

Self-consistent response to finite electric fields

Related Tags and Sections

LBERRY, IGPAR, NPPSTR, LPEAD, IPEAD, LCALCPOL, LCALCEPS, EFIELD_PEAD, DIPOL

References


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