What theories in solid state should every physicist know?

[Kurret]

[Moderator's Note: Changed level of thread to "Advanced" based on the topics being asked about, all are graduate level topics.]

I feel that I have an inadequate understanding of many important concepts in condensed matter physics, so I want to try to learn at least the most basic parts. So what concepts/theories/papers in condensed/solid state physics should every physicist know? I can think of the following

BCS theory and Ginzburg Landau theory

Landau theory of phase transitions

The fermi liquid theory

What else?

 

[cgk]

This is not a theory, but one thing I would hope physicists would learn is the real meaning of "band structure". I.e., the connection between determinant wave functions, Hartree-Fock/Kohn-Sham, and then canonical molecular orbitals and electron bands on one side (which transform according to irreps of the spatial symmetry group), and localized molecular orbitals, atomic orbitals, and Wannier functions on the other side (which do not). One should think that this lies at the very basis of solid state electronic structure theory, but in practice even theorists are sometimes confused about these topics and their connections.

There is a good introductory article by Roald Hoffmann (Solids and surfaces: a chemist's view of bonding in extended structures, pdf on net) relating these things (and other) to each other. If anyone else has a good textbook suggestion, I'd also like to hear it.

 

[DrDu]

Maybe the largest conceptual difference between molecular and solid state physics lies in treating a crystal as an object of infinite extent. Only in this limit concepts like phase transitions emerge and get a precise meaning. This goes in hand with quantum field theoretical techniques becoming powerful.
In this limit, it is possible to have different ground states which live in completely different Hilbert spaces. Superconductivity is but one example.

 

[Andy Resnick]

The title says 'solid state', but the post says 'condensed matter'. In that spirit, I would add:

Mean-field theory, scaling, and the renormalization group
Fluctuation-dissipation theorem

 

[Kurret]

Thanks for your replies. If you know any specific reading material, don't hesitate to post them :).

 

[atyy]

For the RG, I like Kardar's lectures.

http://dspace.mit.edu/bitstream/han...ysics/8-334Spring-2004/LectureNotes/index.htm

https://www.youtube.com/playlist?list=PLUl4u3cNGP63HkEHvYaNJiO0UCUmY0Ts7