## Squared absolute value of the continuous wavefunction Ψ(*x*, *y*, *t*), left, and squared absolute values of the amplitudes ψ_{l, m}(*t*), right, for *t* = 300

**Figure 1.** Squared absolute value of the continuous wavefunction Ψ(*x*, *y*, *t*), left, and squared absolute values of the amplitudes ψ_{l, m}(*t*), right, for *t* = 300. The system parameters are *v _{x}* =

*v*= 0.5,

_{y}*F*= 0 and α = 1/8.

**Abstract**

We analyse dynamics of a quantum particle in a square lattice in the Hall configuration beyond the single-band approximation. For vanishing gauge (magnetic) field this dynamics is defined by the inter-band Landau–Zener tunnelling, which is responsible for the phenomenon known as the electric breakdown. We show that in the presence of a gauge field this phenomenon is absent, at least, in its common sense. Instead, the Landau–Zener tunnelling leads to the appearance of a finite current which flows in the direction orthogonal to the vector of a potential (electric) field.