Closing the gap in the Andreev spectrum in a three-terminal superconducting junction

Quasiclassical circuit theory [1] is used to investigate transport in a mesoscopic junction with three superconducting terminals. Our study reveals the closing of the gap in the Andreev spectrum for a wide range of phase-biases and transparencies, in agreement with previous work [2]. In this regime a superconducting current flows in the junction, while the proximity mini-gap is closed. The corresponding parameter region is studied systematically, both analytically in the low transparency limit and numerically. We provide a microscopic explanation for the closing of the gap in terms of multiple pair processes that correlate the superconducting currents flowing between different pairs of terminals [3]. We show that multi-terminal superconducting junctions provide unique opportunities for applications in quantum devices based on Josephson and/or Majorana physics. \\[4pt] [1] Yu. V. Nazarov, Superlattices Microstruct. 25, 1221-1231 (1999). \\[0pt] [2] B. van Heck, S. Mi, and A. R. Akhmerov, Phys. Rev. B 90, 155450 (2014).\\[0pt] [3] A. Freyn, B. Dou\c{c}ot, D. Feinberg and R. M\'{e}lin, Phys. Rev. Lett. 106, 257005 (2011).