A Majorana perspective on understanding and identifying axion insulators

Abstract

An axion insulator is theoretically introduced to harbor unique surface states with half-integer Chern number {{{{{{{mathcal{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 {{{{{{{mathcal{C}}}}}}}}=frac{1}{2} axion state corresponds to a topological state with Chern number {{{{{{{mathcal{N}}}}}}}}=1 in the Majorana basis. In proximity to an s − wave superconductor, a topological phase transition to an {{{{{{{mathcal{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 {{{{{{{mathcal{N}}}}}}}}=1 and {{{{{{{mathcal{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 {{{{{{{mathcal{C}}}}}}}}=frac{1}{2} ({{{{{{{mathcal{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.