Quasicrystalline Resonant States and Nonlinear Landau Fan Diagram in van der Waals Superlattices

Explore the fascinating world of quasicrystalline resonant states and nonlinear Landau fan diagrams in van der Waals superlattices in this comprehensive 1-hour 13-minute lecture. Delve into the emergence of quasicrystalline resonant states in dodecagonal and octagonal van der Waals quasicrystals, examining the conditions for their formation and the theoretical models used to calculate their electronic structures. Investigate the unique geometry of van der Waals quasicrystals and the challenges in identifying their "precise center" due to mathematical constraints. Analyze conductance oscillations in graphene electrons exposed to moiré potentials, understanding their deviation from the linear Landau fan diagram and the underlying causes. Learn about a novel method for extracting spectral gaps in multiband systems using the density of states of open orbits, applicable to various electronic systems beyond van der Waals materials.