# Double Path Interference and Magnetic Oscillations in Cooper Pair Transport through a Single Nanowire

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1 LOMA - Laboratoire Ondes et Matière d-Aquitaine 2 IPM - Institute for Physics of Microstructures 3 UNN - Lobachevsky State University of Nizhny Novgorod

Abstract : We show that the critical current of the Josephson junction consisting of superconducting electrodes coupled through a nanowire with two conductive channels can reveal the multiperiodic magnetic oscillations. The multiperiodicity originates from the quantum mechanical interference between the channels affected by both the strong spin-orbit coupling and the Zeeman interaction. This minimal two-channel model is shown to explain the complicated interference phenomena observed recently in Josephson transport through Bi nanowires. The systems with a few conductive channels provide a unique possibility for constructing nanoelectronic devices with tunable transport properties at the quantum length scale. One of the promising realizations of these devices is based on the localized electronic states appearing, for example, at the surface of topological insulators 1, at the edges of graphene nanoribbons 2, and in InAs, InSb, and Bi nanowires 3–6. The physics of the charge transport through these states appears to be extremely rich due to strong spin-orbit coupling, large anisotropic g-factors, etc. The unique normal state properties naturally also cause unusual proximity phenomena revealing themselves for the edge states coupled to the bulk superconducting leads 1,3. Such a coupling provides a possibility for constructing new types of Josephson devices where an external magnetic field H can effectively control the current-phase relation 7,8 and provide favorable conditions for the appearance of Majorana fermions 9–11. In this Letter we provide a theoretical description of the magnetotransport phenomena in a Josephson system containing a few conductive channels which model the edge states localized, e.g., at the surface of a single nanowire see Fig. 1. Specifically, we propose a generic model accounting for only two interfering electron paths or conductive channels and strong spin-orbit and Zeeman interactions. This model allows us to describe both orbital and spin mechanisms of the magnetic field effect and to uncover the microscopical mechanisms responsible for the formation of the nontrivial ground state of the Josephson junction with a nonzero superconducting phase difference. The Zeeman interaction produces the spatial oscillation of the Cooper pair wave function at the scale ℏv F =gμ B H similar to the ones in superconductor-ferromagnet structures 7 which results in the magnetic oscillations of the critical current with the period ℏv F =gμ B L, where L is the channel length. The orbital effect causes a standard phase gain ∼2πHS=Φ 0 Φ 0 ¼ πℏc=jej is the flux quantum in the electronic wave function similar to the one appearing in the Aharonov-Bohm AB effect. Here S is the area enclosed by the pair of interfering paths projected on the plane perpendicular to the magnetic field. The interfering quantum mechanical amplitudes in this case cause the magnetic oscillations in the total transmission amplitude with the period 2Φ 0 =S. The Andreev reflection at the superconducting boundaries can double the effective charge in the oscillation period 12, and we show that, in the general case, the resulting critical current oscillates with the competing periods 2Φ 0 =S and Φ 0 =S. The above physical picture should, of course, be modified in the presence of the spin-orbit coupling which can produce the spontaneous Josephson phase difference φ 0 8. Despite the fact that this anomalous Josephson effect was found within several different theoretical models 13–19, its microscopical origin still remains disputable. We clarify this question and show that the key ingredient for the φ 0-junction formation is the nonparabolicity of the electron energy spectrum, which in the presence of spin-orbit coupling gives rise to the dependence of the Fermi velocity on momentum direction. Under the influence of the Zeeman field, such specific dependence results in the spontaneous Josephson ground state phase φ 0 and in the renormalization of the above magnetic oscillation periods. Turning to the existing experimental data, we must note that the multiperiodic magnetic oscillations have recently been observed in measurements of the Josephson critical

Keywords : Proximity effects Andreev reflection SN and SNS junctions Quantum wires Mesoscopic and nanoscale systems

Autor: ** Sergei V. Mironov - Alexandre S. Mel-Nikov - Alexandre I. Buzdin - **

Fuente: https://hal.archives-ouvertes.fr/