Microscopic charge fluctuations in hexagonal boron nitride

We present an ab initio approach to the electron dynamics through the calculation of the total polarizability matrix, including the off-diagonal elements. The charge density induced in a system by an external perturbation is computed in real space and time, following the idea of Abbamonte et al. The difference between our approach and the one from Ref. [1] is that we can calculate not only the diagonal response $\chi $(q,q,$\omega )$, but also the off-diagonal elements of the matrix $\chi $(q,q',$\omega )$. Hence, we have access to the microscopic charge oscillations which are induced by the local-field effects. We have studied these charge oscillations at various frequencies comprising interband-transition and plasmon-excitation energies. The real-space approach allows us to see which electrons (or orbitals) contribute to which kind of excitation. The final goal is to offer theoretical support and benchmark to future inelastic x-ray scattering experiments that may measure also the off-diagonal elements of the polarizability. The method is applied to hexagonal boron nitride (h-BN) which is the most stable of the three existing structures (hexagonal, cubic, and wurtzite) at room temperature and ambient pressure.