Emergence of gapped bulk and metallic side walls in the zeroth Landau level in Dirac and Weyl semimetals

Abstract

Recent transport experiments have revealed the activation of longitudinal magnetoresistance of Weyl semimetals in the quantum limit, suggesting the breakdown of chiral anomaly in a strong magnetic field. Here we provide a general mechanism for gapping the zeroth chiral Landau levels applicable for both Dirac and Weyl semimetals. Our result shows that the zeroth Landau levels anticross when the magnetic axis is perpendicular to the Dirac/Weyl node separation and when the inverse magnetic length $l_B^{-1}$ is comparable to the node separation scale $\Delta k$. The induced bulk gap increases rapidly beyond a threshold field in Weyl semimetals, but has no threshold and is non-monotonic in Dirac systems due to the crossover between $l_B^{-1}>\Delta k$ and $l_B^{-1}<\Delta k$ regions. We also find that the Dirac and possibly Weyl systems host counterpropagating edge states between the zeroth Landau levels, leading to a state with metallic side walls and zero Hall conductance.