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

TL;DR

This paper explores a quantum analog of the Braess paradox in a phase-coherent transport system, demonstrating that adding an extra link can suppress charge flow, with potential indicators observable in conductance spectra.

Contribution

It introduces the concept of a quantum Braess paradox in a Y-shaped metallic fork with superconducting links, revealing counterintuitive flow suppression due to quantum correlations.

Findings

Adding a superconducting link alters the conductance spectrum significantly.

The quantum Braess paradox manifests as partial suppression of charge flow.

Differential conductance spectra can serve as indicators of quantum correlations.

Abstract

The Braess paradox encountered in classical networks is a counterintuitive phenomenon when the flow in a road network can be impeded by adding a new road or, more generally, 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.