Probing the percolation in the quantum anomalous Hall insulator

Abstract

Abstract The percolation plays an essential role in the physics of plateau transition, localization, and breakdown in quantum Hall (QH) systems. In practice, it always exists probably due to sample imperfections and has to be addressed before realizing the full potentials of topological electronics and qubits. Here, we investigate the cause, distribution, and number of the percolation in a quantum anomalous Hall (QAH) insulator of an anti-Hall bar geometry with two perimeters, which allows for probing both the inter- and intra-perimeter percolations by injecting currents into either or both perimeters. We discover the dual-QAH effect with opposite chiralities from these two perimeters, which exhibits linear modulations by the currents applied to both perimeters. By solving the formulation of such modulations with the Landauer–Büttiker formalism, the distribution and number of the inter-perimeter percolative channels could be identified. Strikingly, a dissipative constituent is detected in the transport of the QAH state, as revealed by the linear scalings in longitudinal conductivities versus the sum of currents injected to both perimeters, similar to that in the trivial-insulating state. Such a behavior unveils the quasi-2D nature of the intra-perimeter percolation, which superimposes onto and perturbs the dissipationless chiral edge transport. The formation of percolations is ascribed to the joint effect of the electric field, finite conductivity, and sample imperfections.