Dielectric function with band theory

Click For Summary

Discussion Overview

The discussion revolves around the relationship between dielectric function and band structure in solids, particularly focusing on how a local property like dielectric function can be derived from a global property such as band structure. The scope includes theoretical considerations and complexities involved in calculating dielectric functions for non-translationally invariant systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that while dielectric function can be computed from band structure, it raises questions about how a local property can be derived from a global property.
  • Another participant explains that calculating dielectric function for non-translationally invariant systems is complex, as it depends on both position variables r and r', and cannot be derived solely from bulk band structure.
  • This participant notes that for points inside the bulk, the dielectric function depends on the distance (r-r') and typically decays rapidly over atomic or lattice spacing.
  • Fourier transformation is mentioned as a method to obtain ε(k), which can be calculated using k-dependent Bloch states, with the macroscopic dielectric constant usually reported as ε(k=0).
  • A request for literature on the topic is made, indicating a need for further resources.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of calculating dielectric function from band structure, with some acknowledging the complexity and limitations involved. The discussion does not reach a consensus on the methods or implications of these calculations.

Contextual Notes

The discussion highlights limitations related to the assumptions of translational invariance and the specific conditions under which dielectric function can be computed from band structure. The dependence on spatial variables and the decay of the dielectric function over short distances are also noted as significant factors.

Who May Find This Useful

This discussion may be of interest to researchers and students in condensed matter physics, materials science, and those studying the electronic properties of solids.

taishizhiqiu
Messages
61
Reaction score
4
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?
 
Physics news on Phys.org
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?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 3 ·
Replies
3
Views
15K