Three-Dimensional Quantum Percolation Studied by Level Statistics

TL;DR

This study investigates three-dimensional quantum percolation through energy level statistics, revealing the quantum percolation threshold's dependence on magnetic fields and its universality class similarity to the Anderson transition.

Contribution

It provides new insights into the quantum percolation threshold's behavior under magnetic fields and establishes its universality class alignment with the Anderson transition.

Findings

Quantum percolation threshold decreases with magnetic field.

Critical exponents match those of the Anderson model.

Novel level statistics observed at the percolation threshold.

Abstract

Three-dimensional quantum percolation problems are studied by analyzing energy level statistics of electrons on maximally connected percolating clusters. The quantum percolation threshold $\pq$, which is larger than the classical percolation threshold $\pc$, becomes smaller when magnetic fields are applied, i.e., $\pq(B=0)>\pq(B\ne 0)>\pc$. The critical exponents are found to be consistent with the recently obtained values of the Anderson model, supporting the conjecture that the quantum percolation is classified onto the same universality classes of the Anderson transition. Novel critical level statistics at the percolation threshold is also reported.