Mastering DFT: Calculating Band Structures for Heterostructures

In summary, the conversation discusses the use of Density Functional Theory (DFT) for calculating band structures in different heterostructures. The speaker is using a combination of learning the theory from a book and using various software packages to calculate band structures. However, there is confusion on how to connect the theory with the program and how to map the ground state density to the band structure. It is mentioned that DFT can determine any property of a system given a functional, but in practice, no functional exists for calculating excitation energies. This leads to the use of Kohn-Sham orbitals as an input for other methods, such as the GW method, for calculating excited state properties.
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I'm teaching myself how to do DFT for my master's project, where I want to use it for calculating band structures for different heterostructures. Now to learn DFT I am on one hand reading a book on the basic theory, on the other hand using different freeware packages to try and calculate the band structure for some simple systems like bulk silicon.
One thing that bothers me however, is how to connect the theory I learn in the book, with how the program works. As far as I can understand the idea of DFT is to map a many body problem to a non-interacting problem, using some exchange correlation function, which will produce the same ground state density. To do so a range of methods like the LDA and different choices for the xc-potential is avaiable.
However, I don't understand how to basically go from a theory that allows you to calculate the ground state density to the band structure. Band structure is basically the dispersion of the energy of your system, i.e. E(k), which, for a noninteracting electron gas for example, is a parabola. But how can I get this from the ground state density?
I think the Kohn-sham eigenvalues are not the true eigenvalues of the system and neither are the kohn-sham orbitals.
 
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  • #2
It is commonly believed that DFT is a theory to predict ground state properties of a system only (e.g. the total energy, atomic structure, etc.), and that excited state properties cannot be determined by DFT. This is a misconception. In principle, DFT can determine any property (ground state or excited state) of a system given a functional that maps the ground state density to that property. This is the essence of the Hohenburg–Kohn theorem. In practice, however, no known functional exists that maps the ground state density to excitation energies of electrons within a material. Thus, what in the literature is quoted as a DFT band plot is a representation of the DFT Kohn–Sham energies, i.e., the energies of a fictive non-interacting system, the Kohn–Sham system, which has no physical interpretation at all. The Kohn–Sham electronic structure must not be confused with the real, quasiparticle electronic structure of a system, and there is no Koopman's theorem holding for Kohn–Sham energies, as there is for Hartree–Fock energies, which can be truly considered as an approximation for https://en.wikipedia.org/w/index.php?title=Quasiparticle_energies&action=edit&redlink=1 [Broken]. Hence, in principle, Kohn–Sham based DFT is not a band theory, i.e., not a theory suitable for calculating bands and band-plots. In principle time-dependent DFT can be used to calculate the true band structure although in practice this is often difficult. A popular approach is the use of hybrid functionals, which incorporate a portion of Hartree–Fock exact exchange; this produces a substantial improvement in predicted bandgaps of semiconductors, but is less reliable for metals and wide-bandgap materials.
(SOURCE: WIKIPEDIA)
 
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  • #3
There is no such thing as a band structure on a fundamental level for an interacting electron system. Hence it can not be calculated neither with DFT nor with other methods. What you can calculate is the dependence of the Fermi energy on the number of particles for the ground state. From this you can infer the band gap.
However, most exchange correlation functionals don't perform well in this respect.
What one usually does is to use DFT Kohn Sham orbitals as an input for other methods like the GW method if one is interested in excited state properties.
 

1. What is DFT and why is it important in studying band structures for heterostructures?

DFT stands for Density Functional Theory, which is a mathematical framework used to study the electronic properties of materials. It is important in studying band structures for heterostructures because it allows us to accurately calculate the electronic band structure of a material, which is crucial in understanding its properties and potential applications.

2. How does DFT differ from other methods of calculating band structures?

DFT differs from other methods, such as tight-binding and empirical pseudopotential calculations, in that it is based on first-principles, meaning it does not rely on any experimental data or assumptions. It also takes into account the electron-electron interactions, which is crucial in accurately predicting band structures for complex materials, such as heterostructures.

3. What are some common challenges in mastering DFT for calculating band structures for heterostructures?

Some common challenges include understanding the underlying mathematical concepts and equations involved in DFT, choosing the appropriate exchange-correlation functional, and correctly setting up the simulation parameters. Additionally, correctly interpreting and analyzing the results can also be a challenge.

4. Can DFT accurately predict the band structures of all types of heterostructures?

No, DFT is not a perfect method and has its limitations. It works best for systems with a well-defined periodicity and can accurately predict band structures for most types of heterostructures. However, it may not be suitable for highly disordered or amorphous materials.

5. How can I improve my skills in mastering DFT for calculating band structures for heterostructures?

To improve your skills, it is important to have a strong understanding of the underlying theory and mathematical concepts, as well as regularly practicing and experimenting with different simulation parameters and methods. It can also be helpful to attend workshops or courses on DFT and seek guidance from experienced researchers in the field.

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