Quasiparticle poisoning in trivial and topological Josephson junctions

We study theoretically a short single-channel Josephson junction between superconductors in the trivial and topological phases. The junction is assumed to be biased by a small current and subjected to quasiparticle poisoning. We find that the presence of quasiparticles leads to a voltage signal from the Josephson junction that can be observed both in the trivial and in the topological phase. Quite remarkably, these voltage signatures are sufficiently different in the two phases such that they can serve as means to clearly distinguish between trivial Andreev and topological Majorana bound states in the system. Moreover, these voltage signatures, in the trivial and topological phase, would allow one to measure directly the quasiparticle poisoning rates and to test various approaches for protection against quasiparticle poisoning

Critical current for an insulating regime of an underdamped current-biased topological Josephson junction

We study analytically an underdamped current-biased topological Josephson junction. First, we consider a simplified model at zero temperature, where the parity of the non-local fermionic state formed by Majorana bound states (MBSs) localized on the junction is fixed, and show that a transition from insulating to conducting state in this case is governed by single-quasiparticle tunneling rather than by Cooper pair tunneling in contrast to a non-topological Josephson junction. This results in a significantly lower critical current for the transition from insulating to conducting state. We propose that, if the length of the system is finite, the transition from insulating to conducting state occurs at exponentially higher bias current due to hybridization of the states with different parities as a result of the overlap of MBSs localized on the junction and at the edges of the topological nanowire forming the junction. Finally, we discuss how the appearance of MBSs can be established experimentally by measuring the critical current for an insulating regime at different values of the applied magnetic field

Enhancement of the Kondo effect in a quantum dot formed in a full-shell nanowire

We analyze results of a recent experiment [D. Razmadze et al., Phys. Rev. Lett., 125, 116803 (2020)] on transport through a quantum dot between two full-shell nanowires and show that the observed effects are caused by the Kondo effect enhancement due to a nontrivial geometry (magnetic flux in a full-shell nanowire) rather than the presence of Majorana bound states. Moreover, we propose that such a setup presents a unique and convenient system to study the competition between superconductivity and the Kondo effect and has significant advantages in comparison to other known approaches, as the important parameter is controlled by the magnetic flux through the full-shell nanowire, which can be significantly varied with small changes of magnetic field, and does not require additional gates. This competition is of fundamental interest as it results in a quantum phase transition between an unscreened doublet and a many-body Kondo singlet ground states of the system

Theory of coherent quantum phase-slips in Josephson junction chains with periodic spatial modulations

We study coherent quantum phase-slips which lift the ground state degeneracy in a Josephson junction ring, pierced by a magnetic flux of the magnitude equal to half of a flux quantum. The quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Sch\"on modes). These, in turn, are affected by spatial inhomogeneities in the ring. We analyze the case of weak periodic modulations of the system parameters and calculate the corresponding modification of the quantum phase-slip amplitude

Insulating regime of an underdamped current-biased Josephson junction supporting Z(3) and Z(4) parafermions

We study analytically a current-biased topological Josephson junction supporting Z(n) parafermions. First, we show that in an infinite-size system a pair of parafermions on the junction can be in n different states; the 2 pi n periodicity of the phase potential of the junction results in a significant suppression of the maximum current I-m for an insulating regime of the underdamped junction. Second, we study the behavior of a realistic finite-size system with avoided level crossings characterized by splitting delta. We consider two limiting cases: when the phase evolution may be considered adiabatic, which results in the 2 pi periodicity of the effective potential, and the opposite case, when Landau-Zener transitions restore the 2 pi n periodicity of the phase potential. We also study the case with time-reversal symmetry and show that breaking this symmetry gives different phase periodicity reductions. resulting current I-m is exponentially different in the opposite limits, which allows us to propose another detection method to establish the appearance of parafermions in the system experimentally, based on measuring I-m at different values of the splitting delta

Demonstration of the Nonlocal Josephson Effect in Andreev Molecules

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current–phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.ISSN:1530-6984ISSN:1530-699

Phase-engineering the Andreev band structure of a three-terminal Josephson junction

Data and code upload for publication of the same name. Folder 'Data' contains raw, processed and simulated data for all figures of Main Text and Supplementary Information. Folder 'Code' contains the MATLAB scripts used to generate the simulated data. In each folder, a description complementing the information available in the manuscript is provided in the 'readme.txt' file.Additional funding: Deutsche Forschungsgemeinschaft (DFG) via SFD 1432, ID 425217212 and BE 3803/14-1, ID 467596333; Spanish Ministry of Science and Innovation, PID2020-114880GB-I00