Propagation of a quantum particle through two dimensional percolating systems

TL;DR

This study investigates quantum particle transmission in two-dimensional percolating systems, revealing localized regimes, potential delocalization at low disorder, and introducing a visualization method for wave packet dynamics.

Contribution

It introduces a visualization technique for wave packet evolution and identifies two localization regimes, advancing understanding of quantum percolation phenomena.

Findings

Existence of exponential and power law localization regimes

Potential delocalized state at very low disorder

Finite size scaling analysis up to 70x70 systems

Abstract

We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is determined by the disorder and interference effects, leading to interesting sharp features in conductance as the energy, disorder, and boundary conditions are varied. To aid understanding of this phenomenon, we develop a visualization method whereby the progression of a wave packet entering the cluster through a lead on one side and exiting from another lead on the other side can be tracked dynamically. Using this method, we investigate the evolution of the wave packet through transmission and reflection under clusters of various disorder, sizes, boundary conditions, and energies. Our results indicate the existence of two different kinds of localized regimes, namely exponential and power law localization, depending on the amount of disorder. Our study further suggests that there may be a delocalized state in the 2D quantum percolation system at very low disorder. These results are based on a finite size scaling analysis of the systems of size up to 70 x 70 (containing 4900 sites) on the square lattice.