Physics of Topological Insulators and Superconductors

[cuppls]

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').

 

[jedishrfu]

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.

 

[king vitamin]

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.