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Recent transport experiments have revealed the activation of longitudinalmagnetoresistance of Weyl semimetals in the quantum limit, suggesting thebreakdown of chiral anomaly in a strong magnetic field. Here we provide ageneral mechanism for gapping the zeroth chiral Landau levels applicable forboth Dirac and Weyl semimetals. Our result shows that the zeroth Landau levelsanticross when the magnetic axis is perpendicular to the Dirac/Weyl nodeseparation and when the inverse magnetic length $l_B^{-1}$ is comparable to thenode separation scale $\Delta k$. The induced bulk gap increases rapidly beyonda threshold field in Weyl semimetals, but has no threshold and is non-monotonicin 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 Weylsystems host counterpropagating edge states between the zeroth Landau levels,leading to a state with metallic side walls and zero Hall conductance.

Emergence of Gapped Bulk and Metallic Side Walls in the Zeroth Landau level in Dirac and Weyl semimetals