By combining quantum simulations of electron transport and scanning-gate microscopy, we have shown that the current transmitted through a semiconductor two-path rectangular network in the ballistic and coherent regimes of transport can be paradoxical
ly degraded by adding a third path to the network. This is analogous to the Braess paradox occurring in classical networks. Simulations reported here enlighten the role played by congestion in the network.
We present evidence for a counter-intuitive behavior of semiconductor mesoscopic networks that is the analog of the Braess paradox encountered in classical networks. A numerical simulation of quantum transport in a two-branch mesoscopic network revea
ls that adding a third branch can paradoxically induce transport inefficiency that manifests itself in a sizable conductance drop of the network. A scanning-probe experiment using a biased tip to modulate the transmission of one branch in the network reveals the occurrence of this paradox by mapping the conductance variation as a function of the tip voltage and position.
