## Flat band states: disorder and nonlinearity    [PDF]

Daniel Leykam, Sergej Flach, Omri Bahat-Treidel, Anton S. Desyatnikov
We reveal the critical behaviour of Anderson localized modes near intersecting flat and dispersive bands in the quasi-one-dimensional diamond ladder with weak diagonal disorder $W$. The localization length $\xi$ of the flat band states scales with disorder as $\xi \sim W^{-\gamma}$, with $\gamma = 1.30 \pm 0.01$, in contrast to the dispersive bands with $\gamma =2$. A small fraction of dispersive modes mixed with the flat band states is responsible for the unusual scaling. Anderson localization is therefore controlled by two different length scales. Nonlinearity couples these critical modes, resulting in qualitatively different wave spreading regimes, from enhanced expansion to resonant tunneling and self-trapping.
View original: http://arxiv.org/abs/1305.7287