Localization in 2D Quantum percolation

TL;DR

This paper investigates quantum transport in 2D percolation systems across various regimes, revealing persistent localization near the band center, novel conductance quantization in small systems, and confirming Pendry's conjecture on rare conducting states.

Contribution

It provides a comprehensive numerical analysis of localization, conductance distributions, and rare resonant states in 2D quantum percolation, including new observations of conductance quantization and validation of Pendry's conjecture.

Findings

Persistent Anderson localization near the band center.

Observation of partial conductance quantization in small systems.

Confirmation of Pendry's conjecture on rare conducting samples.

Abstract

Quantum site percolation as a limiting case of binary alloy is studied numerically in 2D within the tight-binding model. We address the transport properties in all regimes - ballistic, diffusive (metallic), localized and crossover between the latter two. Special attention is given to the region close to the conduction band center, but even there the Anderson localization persists, without signs of metal - insulator transition. We found standard localization for sufficiently large samples. For smaller systems, novel partial quantization of Landauer conductances, i. e. most values close to small integers in arbitrary units is observed at band center. The crossover types of conductance distributions (outside the band center) are found to be similar to systems with corrugated surfaces. Universal conductance fluctuations in metallic regime are shown to approach the known, theoretically predicted value. The resonances in localized regime are Pendry necklaces. We tested Pendry's conjecture on the probability of such rare conducting samples and it proved consistent with our numerical results.