%0 Figure %A N Maksimov, D %A Yu Chesnokov, I %A V Makarov, D %A R Kolovsky, A %D 2013 %T 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 %U 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 %R 10.6084/m9.figshare.1012169.v1 %2 https://iop.figshare.com/ndownloader/files/1479991 %K phenomenon %K Hall configuration %K analyse dynamics %K quantum particle %K tunnelling %K square lattice %K system parameters %K landau %K direction orthogonal %K gauge field %K Atomic Physics %K Molecular Physics %X

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.

%I IOP Publishing