What theories in solid state should every physicist know?

Click For Summary

Discussion Overview

The discussion centers on essential theories and concepts in solid state and condensed matter physics that every physicist should be familiar with. Participants explore various theoretical frameworks, their implications, and connections within the field.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests foundational theories such as BCS theory, Ginzburg-Landau theory, Landau theory of phase transitions, and Fermi liquid theory as essential knowledge in condensed matter physics.
  • Another participant emphasizes the importance of understanding band structure, including the connections between determinant wave functions, Hartree-Fock/Kohn-Sham methods, and their relation to molecular and atomic orbitals.
  • A different viewpoint highlights the conceptual distinction between molecular and solid state physics, particularly in treating crystals as infinite objects, which allows for the emergence of concepts like phase transitions.
  • Additional theories proposed include mean-field theory, scaling, the renormalization group, and the fluctuation-dissipation theorem.
  • Participants express interest in specific reading materials and resources related to these theories.

Areas of Agreement / Disagreement

Participants present multiple competing views on what constitutes essential knowledge in solid state physics, with no consensus reached on a definitive list of theories or concepts.

Contextual Notes

Some discussions involve nuanced distinctions between related concepts, and there is an acknowledgment of the varying interpretations of terms like "solid state" and "condensed matter." The discussion also reflects the complexity of the subject matter, with references to advanced theoretical frameworks.

Who May Find This Useful

This discussion may be of interest to graduate students and researchers in physics, particularly those focusing on condensed matter and solid state physics, as well as educators seeking to understand key concepts in the field.

Kurret
Messages
141
Reaction score
0
[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?
 
Last edited by a moderator:
Physics news on Phys.org
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.
 
  • Like
Likes   Reactions: atyy
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.
 
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
 
Thanks for your replies. If you know any specific reading material, don't hesitate to post them :).
 

Similar threads

Graduate Looking for study group to hack on basic theory in condensed matter
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Reproducibility in condensed matter
  • · Replies 1 ·
Replies
1
Views
3K
Solid State Minimal background books for Condensed Matter Theory
  • · Replies 7 ·
Replies
7
Views
4K
Graduate How Do Landau Levels Function in Solid State Band Theory?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Fraunhofer's multiple slits versus atomic scatteres (diffraction theory)
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Which condensed matter experiment PhD group is the most fun?
  • · Replies 8 ·
Replies
8
Views
3K
"The theoritical minimum" modern equivalent for solid state?
  • · Replies 6 ·
Replies
6
Views
3K
Solid State Should I buy Kittel's Introduction to Solid State Physics?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad What Is the Most Current Model in Solid State Physics?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What frequencies allow for the long wavelength limit in solid state physics?
  • · Replies 1 ·
Replies
1
Views
5K