Percolation transitions in bilayer graphene encapsulated by hexagonal boron nitride

Abstract

We studied the plateau-plateau transitions that characterize the electrical transport in the quantum Hall regime in a high mobility bilayer graphene flake encapsulated by hexagonal boron nitride at magnetic fields up to 9 T and temperatures above 300 mK. We measured independently the exponent $\ensuremath{\kappa}$ of the temperature-induced transition broadening, the critical exponent $\ensuremath{\gamma}$ of the localization length, and the exponent $p$ ruling the temperature scaling of the coherence length, finding consistency with the relation $\ensuremath{\gamma}=p/2\ensuremath{\kappa}$. The observed value of $\ensuremath{\kappa}=0.30(0.28,0.32)$ deviates from that of the quantum Hall critical point. The obtained $\ensuremath{\gamma}=1.25(0.96,1.54)$ questions the validity of a pure Anderson transition, and reveals percolation as the underlying driving mechanism.