Quantum Matter Study Group invited Prof. Christopher Bourne to give a talk on aperiodic and amorphous topological phases on May 12th, 2021. In the beginning, he reviewed topological phases in lattice systems and introduced integer Chern numbers. To generalize the topological phases, we extend the lattice to Delone sets, including quasicrystal and amorphous solid. The main talk focused on the topological phases for those types of solid. He provided examples to show the amorphous patterns exhibit gapped phases. He showed that the invariants can be defined as noncommutative Chern number and computed the non-zero Chern number in the gapped phase. It is interesting to see that quasicrystal and amorphous solid share similar integer Chern numbers, and the idea can be further extended to different spatial dimensions with symmetries. We thank Prof. Bourne for giving a wonderful talk.

Reported by Ching-Kai Chiu