Three-Dimensional Quantum Percolation Studied by Level Statistics

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.