Seminarium KMMF "Teoria Dwoistości"

Magic angles refer to a remarkable theoretical(Bistritzer--MacDonald, 2011) and experimental (Cao et al 2018)discovery, that two sheets of graphene twisted by certain (magic)angles display unusual electronic properties such assuperconductivity.Mathematically, this is related to having flat bands of nontrivialtopology for the corresponding periodic Hamiltonian and theirexistence was shown in the chiral model of twisted bilayer graphene(Tarnopolsky-Kruchkov-Vishwanath, 2019). A spectral characterizationof magic angles (Becker--Embree--Wittsten--Z, 2021, Galkowski--Z,2023) also produces complex values and the distribution of theirreciprocals looks remarkably like a distribution of scatteringresonances, with the real magic angles corresponding to anti-boundstates. I will provide a gentle introduction to the subject andhighlight some recent results.The talk is based on joint works with S Becker, M Embree, J Galkowski,M Hitrik, T Humbert, Z Tao, J Wittsten and H Zeng.