# Dielectric function with band theory

• taishizhiqiu
In summary, the dielectric function of non-translationally invariant systems is a complicated calculation that cannot be done directly from a bulk band structure. It depends on both r and r' and can be expressed as an integral with an omega-dependent term. However, for a point inside the bulk, epsilon will only depend on the distance between r and r' and can be calculated using Fourier transforming and k-dependent Bloch states. The commonly reported macroscopic dielectric constant is epsilon(k=0). For further reading, "Dielectric function" by Maradudin is a recommended resource.
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?

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).

DrDu said:
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?

## 1. What is the dielectric function with band theory?

The dielectric function with band theory is a mathematical concept used in condensed matter physics to describe the response of a material to an external electric field. It takes into account the electronic band structure of the material and the interactions between the electrons and the lattice.

## 2. How is the dielectric function with band theory calculated?

The dielectric function with band theory is calculated using quantum mechanical calculations, such as density functional theory (DFT), to determine the electronic band structure of a material. This information is then used to calculate the response of the material to an external electric field.

## 3. What is the significance of the dielectric function with band theory?

The dielectric function with band theory is important in understanding the optical and electronic properties of materials. It can be used to predict the behavior of materials in various applications, such as in electronic devices and solar cells.

## 4. How does the dielectric function with band theory differ from classical dielectric theory?

Classical dielectric theory only takes into account the motion of free electrons in a material, while the dielectric function with band theory considers the behavior of both free electrons and bound electrons in the material's electronic band structure. This makes it a more accurate description of the dielectric response of a material.

## 5. What factors can affect the dielectric function with band theory?

The dielectric function with band theory can be affected by various factors, such as the electronic band structure of the material, the temperature, and external influences such as electric fields or pressure. Additionally, impurities and defects in the material can also impact the dielectric function.

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