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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)

   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. Dirac lines and loop at the Fermi level in the time-reversal symmetry breaking superconductor LaNiGa2

   https://doi.org/10.1038/s42005-021-00771-5  

   Badger, Jackson R. ; Quan, Yundi ; Staab, Matthew C. ; Sumita, Shuntaro ; Rossi, Antonio ; Devlin, Kasey P. ; Neubauer, Kelly ; Shulman, Daniel S. ; Fettinger, James C. ; Klavins, Peter ; et al ( December 2022 , Communications Physics)

   Abstract Unconventional superconductors have Cooper pairs with lower symmetries than in conventional superconductors. In most unconventional superconductors, the additional symmetry breaking occurs in relation to typical ingredients such as strongly correlated Fermi liquid phases, magnetic fluctuations, or strong spin-orbit coupling in noncentrosymmetric structures. In this article, we show that the time-reversal symmetry breaking in the superconductor LaNiGa 2 is enabled by its previously unknown topological electronic band structure, with Dirac lines and a Dirac loop at the Fermi level. Two symmetry related Dirac points even remain degenerate under spin-orbit coupling. These unique topological features enable an unconventional superconducting gap in which time-reversal symmetry can be broken in the absence of other typical ingredients. Our findings provide a route to identify a new type of unconventional superconductors based on nonsymmorphic symmetries and will enable future discoveries of topological crystalline superconductors. 

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3. Time-reversal symmetry breaking superconductivity between twisted cuprate superconductors

   https://doi.org/10.1126/science.abl8371  

   Zhao, S. Y. ; Cui, Xiaomeng ; Volkov, Pavel A. ; Yoo, Hyobin ; Lee, Sangmin ; Gardener, Jules A. ; Akey, Austin J. ; Engelke, Rebecca ; Ronen, Yuval ; Zhong, Ruidan ; et al ( December 2023 , Science)

   Twisted interfaces between stacked van der Waals (vdW) cuprate crystals present a platform for engineering superconducting order parameters by adjusting stacking angles. Using a cryogenic assembly technique, we construct twisted vdW Josephson junctions (JJs) at atomically sharp interfaces between Bi₂Sr₂CaCu₂O_8+xcrystals, with quality approaching the limit set by intrinsic JJs. Near 45° twist angle, we observe fractional Shapiro steps and Fraunhofer patterns, consistent with the existence of two degenerate Josephson ground states related by time-reversal symmetry (TRS). By programming the JJ current bias sequence, we controllably break TRS to place the JJ into either of the two ground states, realizing reversible Josephson diodes without external magnetic fields. Our results open a path to engineering topological devices at higher temperatures.

    

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4. Anomalous metals: From “failed superconductor” to “failed insulator”

   https://doi.org/10.1073/pnas.2202496119  

   Zhang, Xinyang ; Palevski, Alexander ; Kapitulnik, Aharon ( July 2022 , Proceedings of the National Academy of Sciences)

   Resistivity saturation is found on both superconducting and insulating sides of an “avoided” magnetic-field-tuned superconductor-to-insulator transition (H-SIT) in a two-dimensional In/InO x composite, where the anomalous metallic behavior cuts off conductivity or resistivity divergence in the zero-temperature limit. The granular morphology of the material implies a system of Josephson junctions (JJs) with a broad distribution of Josephson coupling E J and charging energy E C , with an H-SIT determined by the competition between E J and E C . By virtue of self-duality across the true H-SIT, we invoke macroscopic quantum tunneling effects to explain the temperature-independent resistance where the “failed superconductor” side is a consequence of phase fluctuations and the “failed insulator” side results from charge fluctuations. While true self-duality is lost in the avoided transition, its vestiges are argued to persist, owing to the incipient duality of the percolative nature of the dissipative path in the underlying random JJ system. 

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5. Magnetic-field-free nonreciprocal transport in graphene multiterminal Josephson junctions

   https://doi.org/10.1103/PhysRevApplied.21.034011  

   Zhang, Fan ; Rashid, Asmaul Smitha ; Tanhayi Ahari, Mostafa ; de Coster, George J. ; Taniguchi, Takashi ; Watanabe, Kenji ; Gilbert, Matthew J. ; Samarth, Nitin ; Kayyalha, Morteza ( March 2024 , Physical Review Applied)

   Nonreciprocal superconducting devices have attracted growing interest in recent years as they potentially enable directional charge transport for applications in superconducting quantum circuits. Specifically, the superconducting diode effect has been explored in two-terminal devices that exhibit superconducting transport in one current direction while showing dissipative transport in the opposite direction. Here, we exploit multiterminal Josephson junctions (MTJJs) to engineer magnetic-field-free nonreciprocity in multiport networks. We show that when treated as a two-port electrical network, a three terminal Josephson junction (JJ) with an asymmetric graphene region exhibits reconfigurable two-port nonreciprocity. We observe nonreciprocal (reciprocal) transport between superconducting terminals with broken (preserved) spatial mirror symmetry. We explain our observations by considering a circuit network of JJs with different critical currents. 

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