Dynamic localization and transport in complex crystals

The behavior of a Bloch particle in a complex crystal with PT symmetry subjected to a sinusoidal ac force is theoretically investigated. For unbroken PT symmetry and in the single-band approximation, it is shown that time reversal symmetry of the ac force preserves the reality of the quasienergy spectrum. Like in ordinary crystals, exact band collapse, corresponding to dynamic localization, is attained for a sinusoidal band shape. The wave packet dynamics turns out to be deeply modified at the PT symmetry breaking point, where band merging occurs and Bragg scattering in the crystal becomes highly non-reciprocal.