Edge currents shunt the insulating bulk in gapped graphene

An energy gap can be opened in the electronic spectrum of graphene by lifting its sublattice symmetry. In bilayers, it is possible to open gaps as large as 0.2 eV. However, these gaps rarely lead to a highly insulating state expected for such semiconductors at low temperatures. This long-standing puzzle is usually explained by charge inhomogeneity. Here we investigate spatial distributions of proximity-induced superconducting currents in gapped graphene and, also, compare measurements in the Hall bar and Corbino geometries in the normal state. By gradually opening the gap in bilayer graphene, we find that the supercurrent at the charge neutrality point changes from uniform to such that it propagates along narrow stripes near graphene edges. Similar stripes are found in gapped monolayers. These observations are corroborated by using the "edgeless" Corbino geometry in which case resistivity at the neutrality point increases exponentially with increasing the gap, as expected for an ordinary semiconductor. This is in contrast to the Hall bar geometry where resistivity measured under similar conditions saturates to values of only about a few resistance quanta. We attribute the metallic-like edge conductance to a nontrivial topology of gapped Dirac spectra.