The projection (8) on the subspace spanned by the ground Wannier states for F = 0 (solid line) and F = 0.015 (dashed line)

Figure 3. The projection (8) on the subspace spanned by the ground Wannier states for F = 0 (solid line) and F = 0.015 (dashed line). The dash-dotted line shows the decrease of total probability in the case F = 0.015 due to absorbing boundary conditions.

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.