Year: 2013
Type: article
Abstract: We study the critical behavior 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 $\ensuremath{\xi}$ of the flat band states scales with disorder as $\ensuremath{\xi}\ensuremath{\sim}{W}^{\ensuremath{-}\ensuremath{\gamma}}$, with $\ensuremath{\gamma}\ensuremath{\approx}1.3$, in contrast to the dispersive bands with $\ensuremath{\gamma}=2$. 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 can produce qualitatively different wave spreading regimes, from enhanced expansion to resonant tunneling and self-trapping.
Source: Physical Review B
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2117638296