# Dielectric function with band theory

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1. Jun 19, 2015

### taishizhiqiu

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?

2. Jun 20, 2015

### DrDu

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).

3. Jun 20, 2015

### taishizhiqiu

Can you provide me with some literature?

4. Jun 20, 2015