Zhe Hou

The emergence of higher order topological insulators (TIs) has attracted considerable interest recently due to the exotic topological corner states or hinge states which are governed by a new bulk-edge correspondence. Here we consider a three dimensional TI and drive it into a second order TI by simultaneously introducing the quantum anomalous Hall (QAH) effect with a Zeeman field, and the quantum Hall effect (QH) with an external magnetic field. We show that the second order three dimensional TI provides a perfect platform for investigating the interplay between the QAH and QH effects in the unified framework. The cancellation or coexistence between the QAH and QH states at the same hinges, leads to abundant phenomenon both in the design of topological hinge states and in electronic transport. The model presented here also realises a coexisting and spatially distinguished QAH and QH effects in the same material, which has potential applications in exploiting new topological electronics.