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Stacking two-dimensional van der Waals (vdW) materials rotated with respect to each other show versatility for studying exotic quantum phenomena. In particular, anisotropic layered materials have great potential for such twistronics applications, providing high tunability. Here, we report anisotropic superconducting order parameters in twisted Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212) vdW junctions with an atomically clean vdW interface, achieved using the microcleave-and-stack technique. The vdW junctions with twist angles of 0°and 90°showed the maximum Josephson coupling, comparable to that of intrinsic Josephson junctions. As the twist angle approaches 45°, Josephson coupling is suppressed, and eventually disappears at 45°. The observed twist angle dependence of the Josephson coupling can be explained quantitatively by theoretical calculation with the d-wave superconducting order parameter of Bi-2212 and finite tunneling incoherence of the junction. Our results revealed the anisotropic nature of Bi-2212 and provided a novel fabrication technique for vdW-based twistronics platforms compatible with air-sensitive vdW materials.

We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely, twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, sub-nanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau level (N = 1). Notably the energy gaps for these states are of order 1 K, which is several orders of magnitude greater than those in GaAs. Furthermore, a variety of quantum Hall phase transitions are observed experimentally. All the experimental observations are largely consistent with our phenomenological model calculations. Hence, we establish that a large twist angle system is an excellent platform for high-temperature excitonic condensation.

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The Majorana zero-energy modes (MZMs) residing at the boundary of topological superconductors have attracted a great deal of interest recently, as they provide a platform to explore fundamental physics such as non-Abelian statistics, as well as fault-tolerant quantum computation. Period doubling of Shapiro steps in a Josephson junction under microwave irradiation has been regarded as strong evidence for the emergence of the MZMs at the junction edges. However, questions remain as to how the Shapiro steps respond to the presence of a 4πperiodic Josephson current. In this study, we investigated the characteristic features of Shapiro steps with respect to the ratio (𝛼) of the 4π-periodic current to the topologically trivial 2πperiodic one, as well as the reduced microwave frequency Ω and McCumber parameter 𝛽 of the junction. Our analysis reproduced Shapiro steps similar to those observed experimentally for specific parameter sets of 𝛼, Ω ≲ 0.1 , and 𝛽 ≳ 1.0 . Full suppression of the first lobe of the 𝑛 1 step guarantees the presence of a 4π-periodic Josephson current. In addition, we discuss the range of Ω and 𝛽 needed for full suppression of the first lobe of the 𝑛 1 step, even for small 𝛼 0.1 . To observe "period-doubled Shapiro steps", even with a small 𝛼, the junction should have a large 𝐼 𝑅 product and sufficiently large junction capacitance.