Localization in coupled heterogeneously disordered transport channels on the Bethe lattice
arXiv:1302.6376 · doi:10.1103/PhysRevB.87.094202
Abstract
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 earlier study in 1D [H. Y. Xie, V. E. Kravtsov, and M. Müller, 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 as well. Possible implications for interacting many-body systems are discussed.
10 pages, 4 figures
References in corpus (11)
- Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
- Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
- Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
- Anderson model on Bethe lattices: density of states, localization properties and isolated eigenvalue
- Effect of interface disorder on quantum well excitons and microcavity polaritons
- Induced vs Spontaneous Breakdown of S-matrix Unitarity: Probability of No Return in Quantum Chaotic and Disordered Systems
- Extended States in a Lifshitz Tail Regime for Random Schrödinger Operators on Trees
- Weak Disorder Expansion for the Anderson Model on a Tree
- Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
- Anderson localization of one-dimensional hybrid particles
- Disorder induced field effect transistor in bilayer and trilayer graphene