Logarithm of |Ψ(x, y, t)|² at t = 10 000

Figure 6. Logarithm of |Ψ(x, y, t)|² at t = 10 000. Parameters are v_x = v_y = 0.5, α = 1/8 (B ≈ 0.02), F_y = 0.015 and F_x = 0.

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.