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We analyze dynamics of a quantum particle in a square lattice in the Hallconfiguration beyond the single-band approximation. For vanishing gauge(magnetic) field this dynamics is defined by the inter-band Landau-Zenertunneling, which is responsible for the phenomenon known as the electricbreakdown. We show that in the presence of a gauge field this phenomenon isabsent, at least, in its common sense. Instead, the Landau-Zener tunnelingleads to appearance of a finite current which flows in the direction orthogonalto the vector of a potential (electric) field.

Landau-Zener tunneling in 2D periodic structures in the presence of a gauge field II: Electric breakdown