Localization in coupled heterogeneously disordered transport channels on the Bethe lattice

Hong-Yi Xie, M. Müller
2013 Physical Review B  
We study the Anderson localization in systems, in which transport channels with rather different properties are coupled together. This problem arises naturally in systems of hybrid particles, such as exciton-polaritons, where it is not obvious which transport channel dominates the coupled system. Here we address the question of whether the coupling between a strongly and a weakly disordered channel will result in localized (insulating) or delocalized (metallic) behavior. Complementing an
more » ... lementing an earlier study in 1D [H. Y. Xie, V. E. Kravtsov, and M. M\"uller, Phys. Rev. B \textbf{86} 014205 (2012)], the problem is solved here on a bilayer Bethe lattice with parametrically different parameters. The comparison with the analytical solution in 1D shows that dimensionality plays a crucial role. In D=1 localization is in general dominated by the dirtier channel, which sets the backscattering rate. In contrast, on the Bethe lattice a delocalized channel remains almost always delocalized, even when coupled to strongly localized channels. We conjecture that this phenomenology holds true for finite dimensions $D>2$ as well. Possible implications for interacting many-body systems are discussed.
doi:10.1103/physrevb.87.094202 fatcat:3sgoqe3a2zffhaaofumg42roeu