  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 reveals 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.
