Controlled engineering of extended states in disordered systems

TL;DR

This paper presents a method to engineer wavefunction delocalization in disordered systems, enabling controlled coexistence of extended and localized states, with potential applications in quantum wave devices.

Contribution

It introduces a simple potential structure and parameter tuning to achieve resonant ballistic transport and coexistence of states in disordered systems.

Findings

Extended states persist in the thermodynamic limit.

Robustness of extended states against parameter deviations.

Engineered anisotropic localization and transport properties.

Abstract

We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suitably chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.