Upper panel: participation ratio (7) as functions of time for the parameters of figure 1

Figure 2. Upper panel: participation ratio (7) as functions of time for the parameters of figure 1. Lower panel: the same yet F = 0.015, F_x/F_y=(\sqrt{5}-1)/4\approx 0.309. Dashed lines show the participation ratio calculated by using the tight-binding model.

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.