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

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posted on 13.06.2013 by D N Maksimov, I Yu Chesnokov, D V Makarov, A R Kolovsky

Figure 6. Logarithm of |Ψ(x, y, t)|2 at t = 10 000. Parameters are vx = vy = 0.5, α = 1/8 (B ≈ 0.02), Fy = 0.015 and Fx = 0.


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.