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Physical Review A

Transition from particlelike to wavelike behavior for an electron in one-dimensional nonuniform lattice systems

Longyan Gong, Bingjie Xue, Wenjia Li, W. W. Cheng, Shengmei Zhao

Published Sep 28, 2016• 6 citations
Publisher

Abstract

We explore a distinguishability $D$ and a visibility $V$, satisfying the relation ${D}^{2}+{V}^{2}=1$, to measure a single electron's particlelike and wavelike behaviors, respectively. For several typical one-dimensional nonuniform lattice systems, we find that ${D}^{2}$ is less than, equal to, and greater than ${V}^{2}$ for delocalized, critical, and localized states, respectively. In this sense, the Anderson transition can be viewed as a transition from relatively more particlelike behavior to relatively more wavelike behavior.

DOI
10.1103/physreva.94.032125

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Anderson localization is a fundamental phenomenon in disordered quantum systems, where transport is suppressed by wave interference from extensive randomness. Moving beyond traditional multi-impurity scenarios, we investigate impurity-induced localization phenomena in low-dimensional tight-binding systems by focusing on the properties of impurity-generated bound states. By introducing a single on-site impurity into an otherwise extended lattice, we demonstrate that the impurity can host a bound state whose spatial character undergoes a transition from extended to localized as the impurity strength surpasses a critical value. This transition pertains solely to the impurity state, while the bulk states of the host system remain extended. We characterize the localization behavior by analyzing two distinct spatial profiles of the bound states: one with symmetric decay and another with exponential decay from the impurity site. Our results highlight how a local perturbation can induce nontrivial localization behavior at the level of individual eigenstates, without implying a global localization transition of the underlying electronic system.
We present a detailed analysis of the critical behavior close to the Mott-Anderson transition. Our findings are based on a combination of numerical and analytical results obtained within the framework of typical-medium theory-the simplest extension of dynamical mean field theory capable of incorporating Anderson localization effects. By making use of previous scaling studies of Anderson impurity models close to the metal-insulator transition, we solve this problem analytically and reveal the dependence of the critical behavior on the particle-hole symmetry. Our main result is that, for sufficiently strong disorder, the Mott-Anderson transition is characterized by a precisely defined two-fluid behavior, in which only a fraction of the electrons undergo a "site selective" Mott localization; the rest become Anderson-localized quasiparticles.