From ballistic Andreev interferometers to ballistic multiterminal Josephson junctions

The progress in nanofabrication technology now allows fabricating all kinds of Josephson weak links connecting an arbitrary number of terminals. As soon as 2011, I generalized with my collaborators to three terminals the Anderson and Josephson works which establish a connection between gauge invariance, the superconducting phase variables and the supercurrent [1]. The resulting quartets involve a transient state supporting correlations among four fermions and coupling to the three-body quartet phase. This produces DC-resonance lines when the differential conductance is plotted as a function of the two independent bias voltages, which was observed in the three successive collaborations that were developed with the Lefloch’s group (Grenoble) in metallic devices [2], with the Heiblum’s group (Weizmann Institute) in semi-conducting nanowires [3] and with the Kim’s group (Harvard) in graphene [4].

In this talk, I will propose a general picture [5] for the voltage-biased ballistic 2D metal-based devices, that captures both features of the Kayyalha’s group experiment (Penn State) on three-terminal Andreev interferometers [6] and the Kim’s group experiment (Harvard) on four-terminal Josephson junctions [4]. This new approach is based on the spectrum and the electronic populations, starting from the long-junction limit. Their coupling to the two- or three-body Josephson or quartet modes is operated via a new nonlocal Keldysh process that we call as "phase-Andreev reflection" [6,7]. This extends the physics of Andreev interferometers to the ballistic limit and to multiterminal Josephson junctions.

[1] A. Freyn, B. Douçot, D. Feinberg R. Mélin, Phys. Rev. Lett. 106, 257005 (2011)

[2] A.H. Pfeffer, J.E. Duvauchelle, H. Courtois, R. Mélin, D. Feinberg and F. Lefloch, Phys. Rev. B 90, 075401 (2014)

[3] Y. Cohen, Y. Ronen, J.H. Kang, M. Heiblum, D. Feinberg, R. Mélin and H. Shtrikman, PNAS 3, 2018, 115 (27) 6991

[4] K.F. Huang, Y. Ronen, R. Mélin, D. Feinberg, K. Watanabe, T. Taniguchi and P. Kim, Nature Communications 13, 3032 (2022)

[5] R. Mélin, A.S. Rashid and M. Kayyalha, arXiv:2403.13669 (2024)

[6] A.S. Rashid, L. Yi, T. Taniguchi, K. Watanabe, N. Samarth, R. Mélin and M. Kayyalha, arXiv:2405.02975 (2024)