Phase Diagram for Anderson Disorder: beyond Single-Parameter Scaling
arXiv:cond-mat/0509550 · doi:10.1103/PhysRevB.73.045118
Abstract
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams in all physical dimensions, a plethora of additional, weaker Anderson transitions are found, characterized by the long-distance behavior of states. Critical disorders are found for Anderson transitions at which the asymptotically dominant sector of augmented space changes for all states at the same disorder. At fixed disorder, critical energies are also found at which the localization properties of states are singular. Under the approximation of single-parameter scaling, this phase diagram reduces to the widely-accepted one in 1, 2 and 3 dimensions. In two dimensions, in addition to the Anderson transition at infinitesimal disorder, there is a transition between two localized states, characterized by a change in the nature of wave function decay.
arXiv comment51 pages including 4 figures, revised 30 November 2005
References in corpus (7)
- Typical medium theory of Anderson localization: A local order parameter approach to strong disorder effects
- Localization Bounds for an Electron Gas
- Topology dependent quantities at the Anderson transition
- Reentrant behaviour and universality in the Anderson transition
- Analytical realization of finite-size scaling for Anderson localization: Is there transition in the 2D case?
- The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents
- Analytic Trajectories for Mobility Edges in the Anderson Model