A Majorana perspective on understanding and identifying axion insulators

n axion insulator is theoretically introduced to harbor unique surface states with half-integer Chern number 𝒞 . Recently, experimental progress has been made in different candidate systems, while a unique Hall response to directly reflect the half-integer Chern number is still lacking to distinguish an axion state from other possible insulators. Here we show that the 𝒞=1/2 axion state corresponds to a topological state with Chern number 𝒩=1 in the Majorana basis. In proximity to an s − wave superconductor, a topological phase transition to an 𝒩=0 phase takes place at critical superconducting pairing strength. Our theoretical analysis shows that a chiral Majorana hinge mode emerges at the boundary of 𝒩=1 and 𝒩=0 regions on the surface of an axion insulator. Furthermore, we propose a half-integer quantized thermal Hall conductance via a thermal transport measurement, which is a signature of the gapless chiral Majorana mode and thus confirms the 𝒞=1/2 ( 𝒩=1 ) topological nature of an axion state. Our proposals help to theoretically comprehend and experimentally identify the axion insulator and may benefit the research of topological quantum computation.