One-dimensional models of disordered quantum wires: general formalism

Abstract

In this work we describe, compile and generalize a set of tools that can be used to analyse the electronic properties (distribution of states, nature of states, ...) of one-dimensional disordered compositions of potentials. In particular, we derive an ensemble of universal functional equations which characterize the thermodynamic limit of all one-dimensional models and which only depend formally on the distributions that define the disorder. The equations are useful to obtain relevant quantities of the system such as density of states or localization length in the thermodynamic limit.

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Cited by in corpus (10)

• Controlled engineering of extended states in disordered systems
• Complete absence of localization in a family of disordered lattices
• Energy structure, density of states and transmission properties of the periodic 1D Tight-Binding lattice with a generic unit cell of $u$ sites
• Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices
• Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one dimensionality
• Absolutely continuous energy bands in the electronic spectrum of quasiperiodic ladder networks
• Localization of wave packets in one-dimensional random potentials
• Transfer efficiency enhancement and eigenstate properties in locally symmetric disordered finite chains
• One-dimensional transport revisited: A simple and exact solution for phase disorder
• Engineering electronic states of periodic and quasiperiodic chains by buckling