Josephson current in a normal-metal nanowire coupled to superconductor/ferromagnet/superconductor junction

Abstract

We consider superconducting nanowire proximity coupled to superconductor / ferromagnet / superconductor junction, where the magnetization penetrates into superconducting segment in nanowire decaying as $\sim \exp [-\frac{\mid n\mid }{\xi }]$ with site index $n$ and the decay length $\xi$. We tune chemical potential and spin-orbit coupling so that topological superconducting regime hosting Majorana fermion is realized for long $\xi$. We find that when $\xi$ becomes shorter, zero energy state at the interface between superconductor and ferromagnet splits into two away from zero energy. Accordingly, the behavior of Josephson current is drastically changed due to this "zero mode-non-zero mode crossover". By tuning the model parameters, we find an almost second-harmonic current-phase relation, $\sin 2\phi$, with phase difference $\phi$. Based on the analysis of Andreev bound state (ABS), we clarify that current-phase relation is determined by coupling of the states within the energy gap. We find that the emergence of crossing points of ABS is a key ingredient to generate $\sin 2\phi$ dependence in current-phase relation. We further study both the energy and $\phi$ dependence of pair amplitudes in the ferromagnetic region. For long $\xi$, odd-frequency spin-triplet $s$-wave component is dominant. The magnitude of the odd-frequency pair amplitude is enhanced at the energy level of ABS.

13 pages, 17 figures

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Cited by in corpus (7)

• The Role of Odd-Frequency Pairing in Multiband Superconductors
• Theory of time reversal topological superconductivity in double Rashba wires -- symmetries of Cooper pair and Andreev bound states
• Spin-polarized Andreev tunneling through the Rashba chain
• Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model
• Theory of proximity effect in two-dimensional unconventional superconductor with Rashba spin-orbit interaction
• Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping
• Local density of states in two-dimensional topological superconductors under a magnetic field: signature of an exterior Majorana bound state