CMSA Topological Quantum Matter Seminar: Anomalous Landau level analog in solids: search and implications for 2d heterostructures

The recent experimental observation of fractional Chen insulators — the analog of fractional quantum Hall states realized in absence of any applied magnetic field — calls for more detailed theoretical investigations of the special conditions allowing their emergence. To gain some insight on this problem, we can rely on (i) our extensive knowledge of the physical properties of Landau levels, and (ii) the identification of their exact solid state analogs.
In this talk, (i-ii) will be discussed in the case of ''anomalous Landau levels", which are protected by an index theorem, and whose most famous representative are the zero-th Landau levels of graphene. In particular, I will derive the generic form of Bloch wave functions realizing the analog of such anomalous Landau levels, and argue that twisted transition metal dichalcogenides homobilayers (in which fractional Chern insulators were first discovered) almost realize such anomalous bands.