Connection between topological pumping effect and chiral anomaly in Weyl semimetals

Abstract

While the semiclassical Boltzmann approach has been widely adopted to study chiral-anomaly-related transport in Weyl semimetals (WSMs), it predicts an unphysical diverging electrical conductivity when ${E}_{F}\ensuremath{\rightarrow}0$, where ${E}_{F}$ is the Fermi energy. Here, we develop a modified semiclassical equation of motion which includes both the diagonal and off-diagonal contributions of the Berry curvature. On this basis, we derive an undivergent classical formula for the positive longitudinal magnetoconductivity in a WSM which resolves the conflict between the classical and ultraquantum approaches. We demonstrate that the chiral anomaly is closely related to the topological pumping effect and it can be realized even in the absence of a magnetic field. With our findings we propose a different perspective to understand the topological properties of WSMs and suggest a way to measure the chiral anomaly using transport.