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Planar Josephson junction (JJs) provide an attractive platform to realize topological superconductivity and implement fault-tolerant quantum computing [1,2]. By embedding two gate-tunable Al/InAs JJs in a loop geometry, we measure a π jump in the junction phase with an increasing in-plane magnetic field [3]. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic with in-plane field [3]. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana bound states (MBS). While the key element for the fault-tolerant quantum computing is the non-Abelian statistics of MBS, its demonstration is conspicuously missing. By extending our work [3], we propose how to demonstrate the non-Abelian statistics through MBS fusion in mini-gate controlled JJs [1]. Surprisingly, we show that with a gate-tunable spin-orbit coupling (SOC), the same planar JJs, sought after for topological superconductivity, could also support a much broader range of applications. The time-dependent SOC offers unexplored mechanisms for switching JJs, accompanied by the 2π-phase jumps and the voltage pulses corresponding to the single-flux-quantum transitions, key to high-speed and low-power superconducting electronics. In a constant applied magnetic field, with SOC, anharmonic current-phase relations, calculated microscopically in these JJs, yield a nonreciprocal transport and superconducting diode effect [4-6]. Together with the time-dependent SOC, this allows us to identify a switching mechanism at no applied current bias and supporting fractional-flux-quantum superconducting circuits [6].
[1] T. Zhou, M. C. Dartiailh, K. Sardashti, J. E. Han, A. Matos-Abiague, J. Shabani, and I. Zutic, Nat. Commun. 13, 1738 (2022).
[2] T. Zhou, M. C. Dartiailh, W. Mayer, J. E. Han, A. Matos-Abiague, J. Shabani, and I. Zutic, Phys. Rev. Lett. 124, 137001 (2020)
[3] M. C. Dartiailh,W. Mayer, J. Yuan, K. S. Wickramasinghe, A. Matos-Abiague, I. Zutic, and J. Shabani, Phys. Rev. Lett. 126, 036802 (2021).
[4] M. Amundsen, J. Linder, J. W. A. Robinson, I. Zutic, and N. Banerjee, arXiv:2210.03549, under review in Rev. Mod. Phys.
[5] D. Monroe, M. Alidoust, and I. Zutic, Phys. Rev. Applied 18, L031001 (2022),
[6] D. Monroe, D. Tringali, M. Alidoust, and I. Zutic, preprint.
