Quantum anomalous Hall effect in chiral semimetals

The quantum anomalous Hall (QAH) effect is conventionally understood to exist only in Chern insulators, while a recent study has shown that ferromagnetic metals can also host the QAH effect. Between insulators and metals, we demonstrate that QAH can persist even in a chiral semimetal, where conduction and valence bands touch at zero energy. Transport calculations demonstrate that the Hall conductivity of such a system can be quantized in the presence of dephasing. Interestingly, its longitudinal conductivity remains finite and exhibits semimetallic behavior, in contrast to Chern insulators. This unusual transport behavior originates from the quantization of the Berry curvature integral over occupied states and the semimetallic band structure. This chiral semimetal can transition into a Chern insulator, accompanied by the vanishing of longitudinal conductivity and a reduction of the intrinsic length scale of the Hall response. Our results extend the concept of QAH and uncover the semimetallic QAH transport signatures.