Imaging the work, dissipation and topological protection in the quantum Hall state

Topology is a powerful concept asserting that quantum states can be globally protected against local perturbation. These states are of major fundamental interest as well as of practical importance in metrology and quantum information technology. However, topological protection in realistic devices it is often fragile against dissipative mechanisms, which are difficult to probe directly. Using scanning nanothermometry, we visualize microscopic mechanisms undermining the topological protection in the quantum Hall state in graphene. Our simultaneous nanoscale thermal and scanning gate microscopy reveals that the dissipation is governed by crosstalk between counterpropagating downstream and upstream channels that appear at graphene boundaries because of edge reconstruction. The dissipation mechanism comprises two distinct and spatially separated processes. The work generating process that we image directly and which involves elastic tunneling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. The heat generating process, in contrast, occurs nonlocally upon inelastic resonant scattering off single atomic defects at the edges. Our findings offer a crucial insight into the mechanisms that conceal the true topological protection and suggest venues for engineering more robust quantum states.