# Definition In the modern theory of polarization, charge polarization is defined in terms of the [[Berry connection]] $\pmb{A}_n(\pmb{k})$ as: $ \begin{align} P_\rho = \int_{\text{BZ}} \frac{\text{d}\pmb{k}}{(2\pi)^3} \sum_{n=1}^{n_b} A_{n}(\pmb{k}) .\end{align} $ $n_b$ indicates the number of occupied [[Band Structure|bands]] and the integration is done over the first [[Brillouin zone]].