Chiral Majorana Edge Modes and Vortex MajoranaZero Modes in Superconducting Antiferromagnetic TopologicalInsulator

The antiferromagnetic topological insulator (AFTI) is topologically protected by the combined time-reversal and translational symmetry $\mathcal{T}_c$. In this paper we investigate the effects of the $s$-wave superconducting pairings on the multilayers of AFTI, which breaks $\mathcal{T}_c$ symmetry and can realize quantum anomalous Hall insulator with unit Chern number. For the weakly coupled pairings, the system corresponds to the topological superconductor (TSC) with the Chern number $C=\pm 2$. We answer the following questions whether the local Chern numbers and chiral Majorana edge modes of such a TSC distribute around the surface layers. By the numerical calculations based on a theoretic model of AFTI, we find that when the local Chern numbers are always dominated by the surface layers, the wavefunctions of chiral Majorana edge modes must not localize on the surface layers and show a smooth crossover from spatially occupying all layers to only distributing near the surface layers, similar to the hinge states in a three dimensional second-order topological phases. The latter phase, denoted by the hinged TSC, can be distinguished from the former phase by the measurements of the local density of state. In addition we also study the superconducting vortex phase transition in this system and find that the exchange field in the AFTI not only enlarges the phase space of topological vortex phase but also enhances its topological stability. These conclusions will stimulate the investigations on superconducting effects of AFTI and drive the studies on chiral Majorana edge modes and vortex Majorana zero modes into a new era.

A Majorana perspective on understanding and identifying axion insulators

An axion insulator is theoretically introduced to harbor unique surface states with half-integer Chern number $${{{{{{{\mathcal{C}}}}}}}}$$ 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 $${{{{{{{\mathcal{C}}}}}}}}=\frac{1}{2}$$ C = 1 2 axion state corresponds to a topological state with Chern number $${{{{{{{\mathcal{N}}}}}}}}=1$$ N = 1 in the Majorana basis. In proximity to an s − wave superconductor, a topological phase transition to an $${{{{{{{\mathcal{N}}}}}}}}=0$$ 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 $${{{{{{{\mathcal{N}}}}}}}}=1$$ N = 1 and $${{{{{{{\mathcal{N}}}}}}}}=0$$ 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 $${{{{{{{\mathcal{C}}}}}}}}=\frac{1}{2}$$ C = 1 2 ($${{{{{{{\mathcal{N}}}}}}}}=1$$ 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.