Logarithm of |Ψ(<em>x</em>, <em>y</em>, <em>t</em>)|<sup>2</sup> at <em>t</em> = 10 000 for a vanishing magnetic field

<p><strong>Figure 4.</strong> Logarithm of |Ψ(<em>x</em>, <em>y</em>, <em>t</em>)|<sup>2</sup> at <em>t</em> = 10 000 for a vanishing magnetic field. The system parameters are <em>v<sub>x</sub></em> = <em>v<sub>y</sub></em> = 0.5, <em>F<sub>y</sub></em> = 0.015 and <em>F<sub>x</sub></em> = 0.</p> <p><strong>Abstract</strong></p> <p>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.</p>