Kohn's localization in the insulating state: one-dimensional lattices, crystalline versus disordered

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• The distinction between insulators and metals is traditionally linked to low-lying electronic excitations.
• Kohn's theory posits that ground-state electron organization (localized vs. delocalized) also differentiates these materials.
• A quantitative measure, the localization length (lambda), is finite for insulators and divergent for metals.

Purpose of the Study:

• To quantitatively assess electron localization in different material types.
• To investigate the differences in localization mechanisms between band insulators and Anderson insulators.
• To explore the organization of electrons in the many-body ground state.

Main Methods:

• Simulations of a one-dimensional binary alloy model within a tight-binding scheme.
• Analysis of electron localization using a defined "localization length" (lambda).
• Examination of ground-state electron organization via density matrices and Boys' theory.

Main Results:

• Simulations confirmed localized ground states in insulators and delocalized states in metals.
• A significant quantitative difference in localization length (lambda) was found between band and Anderson insulators.
• Different scattering mechanisms were identified as responsible for the distinct insulating behaviors.

Conclusions:

• The localization length effectively distinguishes between metallic and insulating electronic ground states.
• Band and Anderson insulators exhibit fundamentally different electron localization mechanisms, impacting their properties.
• Further investigation into many-body ground states provides deeper insights into electron localization phenomena.