Physics of Topological Insulators and Superconductors

In summary, topology is a broad and complex field in mathematics that is also relevant in physics research, particularly in the study of topological states of matter. While some physicists may delve into the more mathematical aspects of topology, it is not necessary to have an in-depth understanding of topology at the level of a mathematician in order to work on topological insulators and superconductors. Different theorists may have different approaches, but there have been notable contributions made by physicists without a strong background in topology.
  • #1
cuppls
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Hello there!
Topological insulators and supercontuctors nowadays are very active field in physics research. I am looking for a Phd in theoretical matter physics, and these arguments could interest me. But I have a question: phisicists that study topological superconductors, insulators and similar know topology almost 'as a matematician'? They study topology in deep manner? Or this word is used as in the feynmann diagram for example, in which one says that two diagrams give a different contribution if they are topologically distinct (but without a deep mathematic meaning of the word 'topology').
 
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  • #2
Topology is a very broad term and a very big field in Mathematics:

https://en.wikipedia.org/wiki/Topology

Initial forays into the subject from a mathematical perspective will start with Point Set Topology which for me was very very abstract. Basically a set of interlinked definitions that had no apparent analog in the real world. I was one Physics major struggling in a sea of many senior Math majors during this course.

Physicists are more interested in the geometric aspects of topology as in Differential Topology and Geometric Topology. I never got that far my lifejacket gave out and I retreated back to physics and then computers.
 
  • #3
No, you do not need to know topology at the level of a mathematician to work on topological states of matter. Different theorists have different styles: some theorists work on the more mathematical side of the field and need to know the advanced mathematics, while others may not explicitly need the advanced mathematics but they like it and learn/use advanced techniques anyways. But there are brilliant physicists who have made groundbreaking contributions to the field without knowing what the fundamental group is.
 

FAQ: Physics of Topological Insulators and Superconductors

1. What are topological insulators and superconductors?

Topological insulators and superconductors are materials that have unique electronic properties due to their topological nature. These materials have an insulating or superconducting behavior on their surface or edges, while their bulk remains conductive. This is because of the presence of topologically protected surface states, which are robust against impurities and defects.

2. How do topological insulators and superconductors differ from traditional materials?

Topological insulators and superconductors have properties that are fundamentally different from those of traditional materials. Unlike traditional insulators, which have an energy gap in their bulk, topological insulators have a gapless bulk but have gapped surface states. Similarly, superconductors have zero resistance at low temperatures, while topological superconductors have surface states that are immune to scattering and are therefore highly conductive.

3. What is the importance of topological insulators and superconductors in modern physics?

The study of topological insulators and superconductors is crucial for understanding many phenomena in modern physics. These materials have unique properties that have potential applications in quantum computing, spintronics, and other advanced technologies. Additionally, they can provide insights into the behavior of electrons in condensed matter systems and have implications for our understanding of fundamental physics principles.

4. How are topological insulators and superconductors discovered and studied?

Topological insulators and superconductors are often discovered through theoretical predictions and then confirmed through experiments. These materials are studied using a variety of techniques, including angle-resolved photoemission spectroscopy, scanning tunneling microscopy, and transport measurements. Theoretical models and simulations are also used to understand the behavior of these materials and predict new properties.

5. What are the potential applications of topological insulators and superconductors?

Topological insulators and superconductors have potential applications in various fields, including quantum computing, spintronics, and energy storage. The unique properties of these materials, such as their robust surface states and low dissipation, make them promising candidates for new technologies. Additionally, the study of topological materials may lead to new discoveries and advances in fundamental physics, ultimately benefiting society as a whole.

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