Supermetallic and Trapped States in Periodically Driven Lattices

The gapless metallic phases of periodically driven lattices are shown\footnote{Indubala I. Satija and Bala Sundaram, arXiv:0783264, cond-mat-quant-gas} to exhibit unusual resonant transport characteristics where every resonance is accompanied by a pair of anti-resonances. These anti-resonances describe highly coherent, dynamically localized or {\it trapped} states, in sharp contrast with the resonant or {\it supermetallic} states where the quantum dynamics describes free propagation. The supermetallic states are related to the integer winding of the quasienergy spectrum and are characterized by a band structure that is topologically a circle. In the context of novel phases of matter, our study elucidates important distinctions between static and driven systems that pave the way for engineering a variety of band structures resulting in free, trapped as well as flat band states.