Tunneling Spectroscopy of Quantum Hall States in Bilayer Graphene PN Networks

Two dimensional electronic systems under strong magnetic field form quantum Hall (QH) edge states, which propagate along the boundary of a sample with a dissipationless current. Engineering the pathway of these propagating one-dimensional chiral modes enables the investigation of quantum tunneling between adjacent QH states. Here, we report tunneling transport in spatially controlled networks of QH edge states in bilayer graphene. We observe resonant tunneling between co-propagating QH edges across barriers formed by electrically defining incompressible strips. Employing spectroscopic tunneling measurements enable the direct probing of the spatial profile, density of states, and compressibility of the QH edge states with an unprecedented energy resolution. The capability to engineer the QH edge network provides an opportunity to build future quantum electronic devices supported by rich underline physics.