Theoretical solid state physics

[Niles]

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,

[sokrates]

Non-Equilibrium Green's Function Formalism (NEGF) is one.

It is widely used even among engineers. Easy to use, and deep sound theory.

[t!m]

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.

[Erythro73]

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.

[hiyok]

Can you tell me if there is any difference between NEGF and those used in linear response theory ?

Thanks

[sokrates]

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?

[hiyok]

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.

[hiyok]

Or would you exemplify the difference by a direct example ?

Thanks

[sokrates]

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...

[hiyok]

Nonetheless, the principles that lead to Kubo formalism are not at all applicable to only linear response (small bias case). One can actually consider higher order effects that are not included in the conventional Kubo jargon. For details please see this link http://books.google.com.hk/books?id=qgU50X9vtIoC&pg=PR7&lpg=PR7&dq=introduction+to+solid+state+theory&source=bl&ots=cJu7EtMlHU&sig=EAmXCke594FKspGSCkzya90lRwg&hl=zh-TW&ei=kqXSSojfLI-ZkQXM8MWCBA&sa=X&oi=book_result&ct=result&resnum=6&ved=0CCEQ6AEwBQ#v=onepage&q=&f=false