Past Events

Abstract

It has already been shown by the pioneering work of G.E. Volovik that there exists three universality classes for (3+1)-dimensional fermionic spectrum: vacua with Fermi surfaces, vacua with Fermi points, and fully gapped spectrum. For gapless systems, it is well-known that the Fermi zero modes with odd codimension are stable under perturbation because of the non-trivial topology at the singularities of the Green function. Similarly, the fully gapped spectrum can be a topologically stable system if the topology of the momentum space is non-trivial. Besides, recent founding showed that for every spatial dimension there exists five kinds of topological insulators and topological superconductors with respect to different anti-unitary symmetries the system possesses. Therefore, the topological characteristics of Fermi surfaces and momentum space can be classified with respect to the (co)dimension and the anti-unitary symmetries respectively. Furthermore, these two classifications can be both derived in terms of the famous topological K-theory. In this seminar, I will introduce the K-theory-based classification for the gapless and gapped fermionic systems, and corresponding topological invariants in these classifications and the connection between these two classifications will also be derived and discussed.