Texts on Topological Effects/Phases in Materials

In summary, the conversation was about someone looking for resources to learn about topological effects in solids, specifically those that discuss homotopy classes and algebraic topology. Some recommended resources were Altland and Simons's textbook on QFT, David Tong's lecture notes on the fractional quantum hall effect, and S. Girvin's textbook on modern CMT. The person also mentioned finding an online course with a lot of information. They were recommended to check out a book by Springer and a website called topocondmat.org.
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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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  • #3
I found this, looks good! An online course with tons of information https://topocondmat.org/
 
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Likes atyy, vanhees71 and Delta2

1. What is the significance of studying topological effects/phases in materials?

Studying topological effects/phases in materials is important because it can lead to the discovery of new physical phenomena and potential applications in various fields, such as electronics, photonics, and quantum computing. It can also provide a deeper understanding of the fundamental properties of materials.

2. How do topological effects/phases manifest in materials?

Topological effects/phases can manifest in materials in various ways, such as the emergence of protected surface states, the presence of topological defects, and the appearance of exotic physical properties, such as non-locality and robustness against disorder.

3. What techniques are commonly used to study topological effects/phases in materials?

Some commonly used techniques to study topological effects/phases in materials include angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), and transport measurements. Theoretical methods, such as density functional theory (DFT) and topological band theory, are also widely used.

4. What are some examples of materials that exhibit topological effects/phases?

One well-known example is topological insulators, which are materials that have insulating bulk states but conductive surface states due to their non-trivial band topology. Other examples include topological semimetals, topological superconductors, and topological magnets.

5. How can topological effects/phases be manipulated or controlled in materials?

Topological effects/phases can be manipulated or controlled in materials through various means, such as applying external magnetic or electric fields, changing the material's composition or structure, and inducing strain or defects. These methods can alter the band structure and topology of the material, leading to different topological phases or effects.

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