Interplay between interaction and chiral anomaly: Anisotropy in the electrical resistivity of interacting Weyl metals

We predict that long-range interactions give rise to anisotropy in the electrical resistivity of Weyl metals at low temperatures, where the electrical resistivity becomes much reduced when electric fields are applied to the direction of the momentum vector to connect two paired Weyl points. Performing the renormalization group analysis, we find that the distance between two Weyl points becomes enhanced logarithmically at low temperatures although the coupling constant of such interactions vanishes inverse-logarithmically. Considering the Adler-Bell-Jackiw anomaly, scattering between these two Weyl points becomes suppressed to increase electrical conductivity in the "longitudinal" direction, counter-intuitive in the respect that interactions are expected to reduce metallicity. We also propose that the anomalous contribution in the Hall effect shows the logarithmic enhancement as a function of temperature, originating from the fact that the anomalous Hall coefficient turns out to be proportional to the distance between two paired Weyl points. Correlations with topological constraints allow unexpected and exotic transport properties.