The density of states of proximitized normal nanowires interrupting superconducting rings can be tuned by the magnetic flux piercing the loop. Using these as the contacts of a single-electron transistor allows us to control the energetic mirror asymmetry of the conductor, thus introducing rectification properties. In particular, we show that the system works as a diode that rectifies both charge and heat currents and whose polarity can be reversed by the magnetic field and a gate voltage. We emphasize the role of dissipation at the island. The coupling to substrate phonons enhances the effect and furthermore introduces a channel for phase tunable conversion of heat exchanged with the environment into electrical current.
We thank discussions and comments from A. Levy Yeyati, C. Urbina, and F. Giazotto. This work was supported by the Spanish Ministerio de Economía, Industria y Competitividad (MINECO) via the Ramón y Cajal Program No. RYC-2016-20778 and the “María de Maeztu” Programme for Units of Excellence in R&D (No. MDM-2014-0377). We also acknowledge the Université Paris-Saclay international grants, the EU Erasmus program. [Full article]