Logarithm of |Ψ(x, y, t)|2 at t = 10 000 for α = 0 (left panel) and α = 1/8 (right panel)

Figure 8. Logarithm of |Ψ(x, y, t)|2 at t = 10 000 for α = 0 (left panel) and α = 1/8 (right panel). The other parameters are vx = vy = 0.5, F = 0.015 and F_x/F_y=(\sqrt{5}-1)/4.

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.