Reduced probability ρ(y) at t = 10 000 in the logarithmic scale

Figure 7. Reduced probability ρ(y) at t = 10 000 in the logarithmic scale. The solid and dashed lines correspond to α = 1/8 and α = 0, respectively.

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.