Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport

Recent experiments on multilayer graphene have unearthed a number of interesting phenomena in the regime where Integer (IQAH) and Fractional (FQAH) Quantum Anomalous Hall phenomena were previously reported. Specifically at low temperature and low applied currents, an “Extended” Integer Quantum Anomalous Hall (EIQAH) is seen over a wide range of the phase diagram. As the current is increased, the EIQAH undergoes a phase transition into a metallic state at generic fillings, and to the FQAH state at the Jain fillings; increasing temperature at the Jain fillings also leads to an evolution out of the EIQAH to the Jain state. In this talk, we will provide a theoretical interpretation of the phenomenology (the phases, phase transitions, and transport signatures) in terms of electronic crystals with non-trivial topology.