Ballistic-to-diffusive transition in engineered counterpropagating quantum Hall channels

Exotic quantum Hall systems hosting counterpropagating edge states can show seemingly nonuniversal transport regimes, usually depending on the size of the sample. We experimentally probe transport in a quantum Hall sample engineered to host a tunable number of counterpropagating edge states. The latter are coupled by Landauer reservoirs, which force charge equilibration over a tunable effective length. We show that charge transport is determined by the balance of up- and downstream channels, with a ballistic regime emerging for unequal numbers of channels. For equal numbers, we observe a transition to a critical diffusive regime, characterized by a diverging equilibration length. Our approach allows simulating the equilibration of hole-conjugate states and other exotic quantum Hall effects with fully controlled parameters using well-understood quantum Hall states.