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1. Evidence for 4e charge of Cooper quartets in a biased multi-terminal graphene-based Josephson junction

   https://doi.org/10.1038/s41467-022-30732-7  

   Huang, Ko-Fan; Ronen, Yuval; Mélin, Régis; Feinberg, Denis; Watanabe, Kenji; Taniguchi, Takashi; Kim, Philip (May 2022, Nature Communications)

   Abstract In a Josephson junction (JJ) at zero bias, Cooper pairs are transported between two superconducting contacts via the Andreev bound states (ABSs) formed in the Josephson channel. Extending JJs to multiple superconducting contacts, the ABSs in the Josephson channel can coherently hybridize Cooper pairs among different superconducting electrodes. Biasing three-terminal JJs with antisymmetric voltages, for example, results in a direct current (DC) of Cooper quartet (CQ), which involves a four-fermion entanglement. Here, we report half a flux periodicity in the interference of CQ formed in graphene based multi-terminal (MT) JJs with a magnetic flux loop. We observe that the quartet differential conductance associated with supercurrent exhibits magneto-oscillations associated with a charge of 4e, thereby presenting evidence for interference between different CQ processes. The CQ critical current shows non-monotonic bias dependent behavior, which can be modeled by transitions between Floquet-ABSs. Our experimental observation for voltage-tunable non-equilibrium CQ-ABS in flux-loop-JJs significantly extends our understanding of MT-JJs, enabling future design of topologically unique ABS spectrum. 

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2. Phase Diffusion in Low-EJ Josephson Junctions at Milli-Kelvin Temperatures

   https://doi.org/10.3390/electronics12020416  

   Lu, Wen-Sen; Kalashnikov, Konstantin; Kamenov, Plamen; DiNapoli, Thomas J.; Gershenson, Michael E. (January 2023, Electronics)

   Josephson junctions (JJs) with Josephson energy EJ≲1 K are widely employed as non-linear elements in superconducting circuits for quantum computing operating at milli-Kelvin temperatures. In the qubits with small charging energy EC ( EJ/EC≫1 ), such as the transmon, the incoherent phase slips (IPS) might become the dominant source of dissipation with decreasing EJ. In this work, a systematic study of the IPS in low-EJ JJs at milli-Kelvin temperatures is reported. Strong suppression of the critical (switching) current and a very rapid growth of the zero-bias resistance due to the IPS are observed with decreasing EJ below 1 K. With further improvement of coherence of superconducting qubits, the observed IPS-induced dissipation might limit the performance of qubits based on low-EJ junctions. These results point the way to future improvements of such qubits. 

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3. Theory of Josephson scanning microscopy with $s$ -wave tip on unconventional superconducting surface: Application to ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$

   https://doi.org/10.1103/PhysRevB.110.184519  

   Choubey, Peayush; Hirschfeld, P J (November 2024, Physical Review B)

   Josephson scanning tunneling microscopy (JSTM) is a powerful probe of the local superconducting order parameter, but studies have been largely limited to cases where the superconducting sample and superconducting tip both have the same gap symmetry—either s-wave or d-wave. It has been generally assumed that, in an ideal s-to-d JSTM experiment, the critical current would vanish everywhere, as expected for ideal c-axis planar junctions. We show here that this is not the case. Employing first-principlesWannier functions for Bi2Sr2CaCu2O8+δ , we develop a scheme to compute the Josephson critical current (Ic) and quasiparticle tunneling current measured by JSTM with subangstrom resolution. We demonstrate that the critical current for tunneling between an s-wave tip and a superconducting cuprate sample has the largest magnitude above O sites and it vanishes above Cu sites. Ic changes sign under π/2 rotation and its average over a unit cell vanishes, as a direct consequence of the d-wave gap symmetry in cuprates. Further, we show that Ic is strongly suppressed in the close vicinity of a Zn-like impurity owing to suppression of the superconducting order parameter. More interestingly, Ic acquires nonvanishing values above the Cu sites near the impurity. The critical current modulations produced by the impurity occur at characteristic wave vectors distinct from the quasiparticle interference (QPI) analog. Furthermore, the quasiparticle tunneling spectra in the JSTM setup shows coherence peaks and impurity-induced resonances shifted by the s-wave tip gap. We discuss the similarities and differences in JSTM observables and conventional STM observables, making specific predictions that can be tested in future JSTM experiments. 

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4. Josephson Detection of Time Reversal Symmetry Breaking s +/- is Superconductivity in SnTe Nanowires

   Trimble, C.; Wei, M. T.; Kalantre, S. S.; Yuan, N. F.; Liu, P.; Cha, J. J.; Fu, L.; Williams, J. R. (January 2019, ArXiv.org)

   Exotic superconductivity, such as high TC, topological, and heavy-fermion superconductors, often rely on phase sensitive measurements to determine the underlying pairing. Here we investigate the proximity-induced superconductivity in nanowires of SnTe, where a s±is′ superconducting state is produced that lacks the time-reversal and valley-exchange symmetry of the parent SnTe. A systematic breakdown of three conventional characteristics of Josephson junctions -- the DC Josephson effect, the AC Josephson effect, and the magnetic diffraction pattern -- fabricated from SnTe nanowire weak links elucidates this novel superconducting state. Further, the AC Josephson effect reveals evidence of a Majorana bound state, tuned by a perpendicular magnetic field. This work represents the definitive phase-sensitive measurement of novel s±is′ superconductivity, providing a new route to the investigation of fractional vortices, topological superconductivity, topological phase transitions, and new types of Josephson-based devices. 

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5. Enhanced topological superconductivity in spatially modulated planar Josephson junctions

   https://doi.org/10.1103/PhysRevB.104.155428  

   Paudel, Purna P.; Cole, Trey; Woods, Benjamin D.; Stanescu, Tudor D. (October 2021, Physical Review B)

   We propose a semiconductor-superconductor hybrid device for realizing topological superconductivity and Majorana zero modes consisting of a planar Josephson junction structure with periodically modulated junction width. By performing a numerical analysis of the effective model describing the low-energy physics of the hybrid structure, we demonstrate that the modulation of the junction width results in a substantial enhancement of the topological gap and, consequently, of the robustness of the topological superconducting phase and associated Majorana zero modes. This enhancement is due to the formation of minibands with strongly renormalized effective parameters, including stronger spin-orbit coupling, generated by the effective periodic potential induced by the modulated structure. In addition to a larger topological gap, the proposed device supports a topological superconducting phase that covers a significant fraction of the parameter space, including the low Zeeman field regime, in the absence of a superconducting phase difference across the junction. Furthermore, the optimal regime for operating the device can be conveniently accessed by tuning the potential in the junction region using, for example, a top gate. 

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