10.6084/m9.figshare.1012169.v1 D N Maksimov D N Maksimov I Yu Chesnokov I Yu Chesnokov D V Makarov D V Makarov A R Kolovsky A R Kolovsky Squared absolute value of the continuous wavefunction Ψ(<em>x</em>, <em>y</em>, <em>t</em>), left, and squared absolute values of the amplitudes ψ<sub><em>l</em>, <em>m</em></sub>(<em>t</em>), right, for <em>t</em> = 300 IOP Publishing 2013 phenomenon Hall configuration analyse dynamics quantum particle tunnelling square lattice system parameters landau direction orthogonal gauge field Atomic Physics Molecular Physics 2013-06-13 00:00:00 Figure https://iop.figshare.com/articles/figure/_Squared_absolute_value_of_the_continuous_wavefunction_em_x_em_em_y_em_em_t_em_left_and_squared_abso/1012169 <p><strong>Figure 1.</strong> Squared absolute value of the continuous wavefunction Ψ(<em>x</em>, <em>y</em>, <em>t</em>), left, and squared absolute values of the amplitudes ψ<sub><em>l</em>, <em>m</em></sub>(<em>t</em>), right, for <em>t</em> = 300. The system parameters are <em>v<sub>x</sub></em> = <em>v<sub>y</sub></em> = 0.5, <em>F</em> = 0 and α = 1/8.</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>