Theoretical solid state physics

In summary, the conversation discusses various theories and principles in theoretical solid state physics that have had a wide impact, such as Non-Equilibrium Green's Function Formalism, Density Functional Theory, and the GW approximation. The advantages of NEGF over Kubo formalism in dealing with high-bias scenarios and including contact effects are also mentioned. The conversation also touches on the use of NEGF in calculating tunneling current and its applicability to real experiments and devices. Overall, the conversation highlights the importance and versatility of NEGF in theoretical solid state physics.
  • #1
Niles
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Hi all

Do you know of any interesting subjects in theoretical solid state physics? Are there any theories that have had a wide impact, e.g. in computers and such?

Thanks in advance,
 
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  • #2
Non-Equilibrium Green's Function Formalism (NEGF) is one.

It is widely used even among engineers. Easy to use, and deep sound theory.
 
  • #3
How about the transistor effect? 1956 Nobel Prize, undeniably important for "computers and such." Bardeen and Shockley (and others) had to do a whole lot of theory to explain it.
 
  • #4
Niles said:
Hi all

Do you know of any interesting subjects in theoretical solid state physics? Are there any theories that have had a wide impact, e.g. in computers and such?

Thanks in advance,

Density Functional Theory is perhaps one of the most widely used theoretical principle in solid state physics now in computational physics.The GW approximation too is a widely used theoretical principle.
 
  • #5
Can you tell me if there is any difference between NEGF and those used in linear response theory ?

Thanks
 
  • #6
NEGF is a quantum-transport model that can incorporate "high-bias" scenarios if properly implemented with an equation like Poisson, to get the energy bands right...

I didn't see what you are trying to compare NEGF with in linear response theory?

Do you mean Kubo Formalism? or Landauer-Buttiker formalism of transport?
 
  • #7
Hi, Socrates

I mean Kubo formalism. For the moment I'm studying tunneling effects of Luttinger liquid into a metal or vacuum. Some authors suggest using NEGF formalism (The Keldysh formalism ?) to calculate the tunneling current. However, I don't see what advantages it makes than the usual Kubo theory. The Green's functions used in NEGF are the same as Kubo, anyway.
 
  • #8
Or would you exemplify the difference by a direct example ?

Thanks
 
  • #9
As far as I know Kubo Formalism implies that conductance is proportional to the noise (fluctuation-dissipation theorem) in the conductor... So it really applies to very small bias scenarios.

NEGF (Keldysh), on the other hand is NOT limited to linear response, it can deal with high-bias scenarios INCLUDING the perturbative effects of contacts (broadening, spilling states into the channel)..

A good example is the analysis of a MOSFET where linear response is not the relevant mode of operation and the only meaningful analysis is the high-bias response. It can be fairly easily done by NEGF, say, for a ballistic device, but Kubo would not even be applicable.

Also in tunneling problems; the contact can play a major role so it must be somehow included in the model (something that cannot be done by Kubo), although no one really knows the exact shape of a 'real' contact, a phenomenological model is always possible...

So if your work is somehow connected with real experiments and devices; there are a number of reasons where NEGF is superior over Kubo; considering its power and its endearing simplicity...
 
  • #10

Related to Theoretical solid state physics

1. What is theoretical solid state physics?

Theoretical solid state physics is a branch of physics that studies the properties of solid materials, such as metals, semiconductors, and insulators, at a microscopic level. It uses mathematical models and theories to understand and predict the behavior of these materials.

2. What are the main areas of research in theoretical solid state physics?

The main areas of research in theoretical solid state physics include the study of electronic, magnetic, and optical properties of materials, as well as the development of computational methods and models to simulate and analyze these properties.

3. How does theoretical solid state physics contribute to technological advancements?

Theoretical solid state physics plays a crucial role in the development of new technologies, such as semiconductors for computer chips, solar cells for renewable energy, and magnetic materials for data storage. It provides insights into the fundamental properties of materials and guides the design and optimization of new materials for specific applications.

4. What are some key concepts in theoretical solid state physics?

Some key concepts in theoretical solid state physics include band theory, which explains the behavior of electrons in solids, and crystal structure, which describes the arrangement of atoms in a material. Other important concepts include phonons, which describe the vibrations of atoms in a material, and defects, which can significantly affect the properties of a material.

5. What are some current challenges in theoretical solid state physics?

Some current challenges in theoretical solid state physics include understanding and predicting the behavior of complex materials, such as high-temperature superconductors, and developing more accurate and efficient computational methods to simulate and analyze these materials. There is also a growing interest in studying the properties of materials at the nanoscale, which presents unique challenges and opportunities for theoretical solid state physicists.

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