Quantum coherent transport in a three-arm beam splitter and a Braess paradox

The Braess paradox encountered in classical user-optimized network system, such as a transportation network, is a counter intuitive phenomenon when the travel cost (time) for every user can be increased by adding a new road or, more generally, when the overall net performance can degrade after addition of an extra available choice. In this work, we discuss the possibility of a similar effect in a phase-coherent quantum transport and demonstrate it by example of a simple Y-shaped metallic fork. To reveal the Braess-like partial suppression of the charge flow in such device, it is proposed to transfer two outgoing arms into a superconducting state. We show that the differential conductance-vs. voltage spectrum of the hybrid fork structure varies considerably when the extra link between the two superconducting leads is added and it can serve as an indicator of quantum correlations which manifest themselves in the quantum Braess paradox.