Flavors of noise in a magnetic Weyl semimetal

Weyl semimetals (WSMs) are a relatively new class of topological quantum materials that exhibit exotic transport phenomena such as the chiral anomaly, the chiral magnetic effect and the anomalous Hall effect etc. Many magnetic-WSM materials are discovered recently, opening more possibilities for spintronic applications. To model the transport in a magnetic WSM, at least three degrees of freedom---charge, valley and spin---need to be considered. In this work, we investigate the magnetic noise induced by the fluctuations of the charge current, the valley (chiral) current and the spin density, respectively. In particular, the valley current behaves like spins in generating a magnetic field by the demagnetization kernel. In a simple treatment in the diffusive regime, we show that the three contributions have very different frequency dependence, which could be used to extract the valley related properties in a quantum-impurity relaxometry measurement. Our approach could be generalized to discuss WSMs with broke time-reversal symmetry and may inspire further study of transport in topological semimetals in general by non-invasive means.