I will introduce an analytic family of non normal operator $D(\alpha)$ (for $\alpha \in \mathbb{C}$) such that $\alpha\mapsto \mathrm{Spec}(D(\alpha))$ is very highly discontinuous. The points of discontinuity are called "magic angles" and I will show that there are infinitely many of them. This is joint work with Simon Becker and Maciej Zworski.

The existence of these angles were predicted by Bistritzer–MacDonald in 2011 and were observed experimentally in 2018. They correspond to specific "twisting angles" between two sheets of graphene for which we observe supraconductivity.