Special CM Seminar | Robert-Jan Slager | Max Planck | "Crystalline symmetries and topological band theory. ." | Jadwin 303

Mon, Oct 23, 2017, 4:00 pm
Jadwin 303


Topological phases of matter entail a prominent research theme,
featuring distinct characteristics that include protected metallic edge
states and the possibility of fractionalized excitations.
With the advent of symmetry protected topological (SPT) phases, many of
these phenomena have effectively become accessible in the form of
readily available band structures. Whereas the role of (anti-)unitary
symmetries in such SPT states has been thoroughly understood, the
inclusion of lattice symmetries provides for an active area of research.

In this talk, I will present a short overview of results on defects in
SPT states that directly motivate the existence of additional physics
beyond the characterization based on (anti-)unitary symmetries. More
importantly, I will then connect these ideas to recent work in which we
were able to map out all different gapped phases of free fermion systems
in the presence of solely lattice symmetries. This revolves around a
very simple algorithm that matches a rather involved mathematical
perspective in terms of a framework called K-theory. I will then discuss
the implications of these combinatorial arguments, such as their impact
on the description of Weyl phases, and sketch related ideas and future