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We analyze the Wannier-Stark spectrum of a quantum particle in tiltedtwo-dimensional lattices with the Bloch spectrum consisting of two subbands,which could be either separated by a finite gap or connected at the Diracpoints. For rational orientations of the static field given by an arbitrarysuperposition of the translation vectors the spectrum is a ladder of energybands. We obtain asymptotic expressions for the energy bands in the limit oflarge and weak static fields and study them numerically for intermediate fieldstrength. We show that the structure of energy bands determines the rate ofspreading of a localized wave packets which is the quantity measured inlaboratory experiments. It is shown that wave-packet dispersion becomes afractal function of the field orientation in the long-time regime of ballisticspreading.

Wannier-Stark states in double-periodic lattices II: two-dimensional lattices