Texts on Topological Effects/Phases in Materials

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SUMMARY

The discussion focuses on acquiring resources related to topological effects and phases in solids, specifically emphasizing the application of algebraic topology and homotopy classes. Recommended texts include Altland and Simons's textbook on Quantum Field Theory in condensed matter theory, which contains a chapter on topology, and David Tong's lecture notes on the fractional quantum Hall effect, although the latter lacks depth in algebraic topology. Additionally, S. Girvin's textbook on modern condensed matter theory was mentioned, but access to its content was limited. A promising online course on topological condensed matter can be found at topocondmat.org.

PREREQUISITES
  • Understanding of algebraic topology concepts
  • Familiarity with Quantum Field Theory (QFT)
  • Knowledge of condensed matter theory (CMT)
  • Basic principles of homotopy classes
NEXT STEPS
  • Explore the textbook "Quantum Field Theory in Condensed Matter Theory" by Altland and Simons
  • Review David Tong's lecture notes on the fractional quantum Hall effect for foundational concepts
  • Investigate S. Girvin's textbook on modern condensed matter theory for advanced topics
  • Enroll in the online course available at topocondmat.org for comprehensive learning
USEFUL FOR

Researchers, graduate students, and educators in condensed matter physics, particularly those interested in the intersection of topology and material science.

doggydan42
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I am looking to learn about these topological effects or phases in solids. More specifically, I'm trying to find a set of lecture notes or a textbook or some other text that do not shy away from discussing homotopy classes and the application algebraic topology to describe these materials.

I know Altland and Simons's textbook on QFT in condensed matter theory has a chapter on topology. David Tong's lectures notes on the fractional quantum hall effect has been recommended to me, but Tong seems to try to avoid discussing the relevant algebraic topology. I have also been recommended "S. Girvin textbook on modern CMT", but I could only get the table of contents, which wasn't helpful to me.

Any recommendations for other texts or comments on the texts I mentioned would be appreciated!
 
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