# Dielectric function with band theory

As far as I am concerned, dielectric function can be computed by band structure. However, band structure is a global property of solids, while dielectric function is a local property. How a local property can be computed from a global property.

Put it another way, if I want to calculate dielectric function for a specific point(for example, on the surface or deep in the bulk), how can I do it with band structure? Or there is a concept called local band structure?

## Answers and Replies

DrDu
Science Advisor
The calculation of a dielectric function for non-translationally invariant systems is very complicated as it will depend on both r and r' as ##D(r)=\int dr' \epsilon(r,r') E(r')##(dependence on omega understood) and cannot be done from a bulk band structure. For a point inside the bulk, epsilon will only depend on the distance (r-r') and this dependence decays normally rapidly to zero on a distance of the order of the atomic or lattice spacing.
Fourier transforming gives ##\epsilon(k)## which can be calculated using the k-dependent Bloch states. The macroscopic dielectric constant which is usually reported is epsilon(k=0).

The calculation of a dielectric function for non-translationally invariant systems is very complicated as it will depend on both r and r' as ##D(r)=\int dr' \epsilon(r,r') E(r')##(dependence on omega understood) and cannot be done from a bulk band structure. For a point inside the bulk, epsilon will only depend on the distance (r-r') and this dependence decays normally rapidly to zero on a distance of the order of the atomic or lattice spacing.
Fourier transforming gives ##\epsilon(k)## which can be calculated using the k-dependent Bloch states. The macroscopic dielectric constant which is usually reported is epsilon(k=0).
Can you provide me with some literature?