## Survival probability as the function of time for *eFa*/2π = 0.05*E*_{R} (*E*_{R} = *h*^{2}/*Ma*^{2}) and *B* = 0, dashed line, and *a*^{2}*B* = Φ_{0}/8 (Φ_{0} = *hc*/*e*), solid line

_{R}

_{R}

**Figure 1.** Survival probability as the function of time for *eFa*/2π = 0.05*E _{R}* (

*E*=

_{R}*h*

^{2}/

*Ma*

^{2}) and

*B*= 0, dashed line, and

*a*

^{2}

*B*= Φ

_{0}/8 (Φ

_{0}=

*hc*/

*e*), solid line. The lattice parameters are

*v*= 0.5

_{x}*E*(

_{R}*J*= 0.0431

_{x}*E*) and

_{R}*v*= 0.25

_{y}*E*(

_{R}*J*= 0.0741

_{y}*E*). The time is measured in units of the Bloch period

_{R}*T*=

_{B}*h*/

*eFa*. Inset shows the data in the semi-logarithmic scale.

**Abstract**

We study the interband Landau–Zener tunnelling of a quantum particle in the Hall configuration, i.e., in the presence of gauge field (for example, magnetic field for a charged particle) and in-plane potential field (electric field for a charged particle) normal to the lattice plane. The interband tunnelling is induced by the potential field and for the vanishing gauge field is described by the common Landau–Zener theory. We generalize this theory for a nonzero gauge field. The depletion rates of low-energy bands are calculated by using a semi-analytical method of the truncated Floquet matrix.