Single impurity-induced localization transitions in electronic systems

TL;DR

This paper explores how a single impurity in a low-dimensional electronic system can induce a transition in the impurity-bound state from extended to localized, revealing localized states without global system localization.

Contribution

It introduces a detailed analysis of impurity-induced localization transitions focusing on bound states in low-dimensional systems, a novel perspective beyond traditional multi-impurity studies.

Findings

Impurity can host a bound state that transitions from extended to localized as impurity strength increases.

The transition affects only the impurity state, not the bulk states of the system.

Different spatial profiles of bound states are characterized, showing diverse decay behaviors.

Abstract

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.