Squared absolute value of the continuous wavefunction Ψ(x, y, t), left, and squared absolute values of the amplitudes ψl, m(t), right, for t = 300

Figure 1. Squared absolute value of the continuous wavefunction Ψ(x, y, t), left, and squared absolute values of the amplitudes ψl, m(t), right, for t = 300. The system parameters are vx = vy = 0.5, F = 0 and α = 1/8.

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.