Licentiate seminar: Distinguishing zero-energy states in topological and moiré systems

Zero-energy states (ZESs) appear as edge states in topological materials and can lead to the emergence of unique thermodynamic phases in interacting systems. Here, we investigate two scenarios where ZESs play an important role. We first consider semiconductor-superconductor heterostructures, where topological zero-energy Majorana bound states (MBSs) have been predicted to appear. A great obstacle in detecting MBSs is the presence of trivial ZESs, particularly Andreev bound states. We propose a method based on phase-biased transport measurements to distinguish these two kinds of ZESs. We next consider twisted bilayer graphene (TBG), where ZESs appear as moiré flat bands. In graphene-based systems, quasilocalized ZESs are also known to appear around vacancies and impurities. We investigate the interplay between these two kinds of ZESs through atomistic modeling of defects in the twisted bilayer lattice, where we find both a conventional graphene-like behavior and a non-local response in the moiré scale. We explain the latter through exquisite band removal and replacement processes, which we expect to strongly impact the exotic orders of TBG.