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# Logarithm of |Ψ(*x*, *y*, *t*)|^{2} at *t* = 10 000 for a vanishing magnetic field

figure

posted on 2013-06-13, 00:00 authored by D N Maksimov, I Yu Chesnokov, D V Makarov, A R Kolovsky**Figure 4.** Logarithm of |Ψ(*x*, *y*, *t*)|^{2} at *t* = 10 000 for a vanishing magnetic field. The system parameters are *v _{x}* =

*v*= 0.5,

_{y}*F*= 0.015 and

_{y}*F*= 0.

_{x}**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.