An external orbital magnetic field applied perpendicular to the separation vector of a pair of Weyl points can couple them and induce a gap in the electronic spectrum. In this work, we investigate the gap-opening behavior in the presence of a lattice, revealing rich phenomenology absent in the continuum picture. Specifically, we address the emergence of layered Chern insulating states, examining how the anisotropy of the Weyl cone dispersion influences the sequence of phase transitions, and establishing connections to the continuum limit. We analyze the evolution of surface Fermi-arc states across these regimes, highlighting their distinct behaviors during the gap-opening transitions.

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• Landau levels
• Surface states
• Symmetry protected topological states
• Weyl semimetal
• Band structure methods
• Tight-binding model
• k dot p method