Abstract:Année de publication : 2018
We investigate Anderson localization on various 1D structures having flat bands. The main focus is on the scaling laws obeyed by the localization length at weak disorder in the vicinity of flat-band energies. A careful distinction is made between situations where the scaling functions are universal (i.e., depend on the disorder distribution only through its width) and where they depend on the full shape of the disorder distribution. Three examples are analyzed in detail. On the stub chain, the flat band is isolated from the dispersive ones. The localization length remains microscopic at weak disorder and exhibits disorder-specific features. On the pyrochlore ladder, the two flat bands are tangent to one of the dispersive ones. The localization length diverges with exponent 1/2 and a non-universal scaling law, whose dependence on the disorder distribution is predicted analytically. On the diamond chain, the central flat band is tangent to two symmetric dispersive ones. The localization length exhibits two successive scaling regimes, diverging first with exponent 4/3 and a universal law, and then (i.e., further away from the pristine flat band) with exponent 1 and a non-universal law. Both scaling functions are also derived by analytical means.