In solid materials, non-trivial topological states, electron correlations and magnetism are central ingredients for realizing quantum properties, including unconventional superconductivity, charge and spin density waves and quantum spin liquids. The kagome lattice, made up of corner-sharing triangles, can host these three ingredients simultaneously and has proved to be a fertile platform for studying diverse quantum phenomena including those stemming from the interplay of these ingredients. This Review introduces the fundamental properties of the kagome lattice and discusses the complex phenomena observed in several materials systems, including the intertwining of charge order and superconductivity in some kagome metals, the modulation of magnetism and topology in some kagome magnets, and the combination of symmetry breaking and Mott physics in ‘breathing’ kagome insulators. The Review also highlights open questions in the field and future research directions in kagome systems.

Materials with Kagome nets are of particular importance for their potential combination of strong correlation, exotic magnetism, and electronic topology. KV3Sb5 was discovered to be a layered topological metal with a Kagome net of vanadium. Here, we fabricated Josephson Junctions of K1-xV3Sb5 and induced superconductivity over long junction lengths. Through magnetoresistance and current versus phase measurements, we observed a magnetic field sweeping direction-dependent magnetoresistance and an anisotropic interference pattern with a Fraunhofer pattern for in-plane magnetic field but a suppression of critical current for out-of-plane magnetic field. These results indicate an anisotropic internal magnetic field in K1-xV3Sb5 that influences the superconducting coupling in the junction, possibly giving rise to spin-triplet superconductivity. In addition, the observation of long-lived fast oscillations shows evidence of spatially localized conducting channels arising from edge states. These observations pave the way for studying unconventional superconductivity and Josephson device based on Kagome metals with electron correlation and topology.

The superconducting analogue to the semiconducting diode, the Josephson diode, has long been sought with multiple avenues to realization being proposed by theorists^1–3. Showing magnetic-field-free, single-directional superconductivity with Josephson coupling, it would serve as the building block for next-generation superconducting circuit technology. Here we realized the Josephson diode by fabricating an inversion symmetry breaking van der Waals heterostructure of NbSe₂/Nb₃Br₈/NbSe₂. We demonstrate that even without a magnetic field, the junction can be superconducting with a positive current while being resistive with a negative current. The ΔI_c behaviour (the difference between positive and negative critical currents) with magnetic field is symmetric and Josephson coupling is proved through the Fraunhofer pattern. Also, stable half-wave rectification of a square-wave excitation was achieved with a very low switching current density, high rectification ratio and high robustness. This non-reciprocal behaviour strongly violates the known Josephson relations and opens the door to discover new mechanisms and physical phenomena through integration of quantum materials with Josephson junctions, and provides new avenues for superconducting quantum devices.

The Kagome lattice is an important fundamental structure in condensed matter physics for investigating the interplay of electron correlation, topology, and frustrated magnetism. Recent work on Kagome metals in the AV3Sb5 (A = K, Rb, and Cs) family has shown a multitude of correlation-driven distortions, including symmetry breaking charge density waves and nematic superconductivity at low temperatures. Here, we study the new Kagome metal Yb0.5Co3Ge3 and find a temperature-dependent kink in the resistivity that is highly similar to the AV3Sb5 behavior and is commensurate with an in-plane structural distortion of the Co Kagome lattice along with a doubling of the c-axis. The symmetry is lower below the transition temperature, with a breaking the in-plane mirror planes and C6 rotation, while gaining a screw axis along the c-direction. At very low temperatures, anisotropic negative magnetoresistance is observed, which may be related to anisotropic magnetism. This raises questions about the types of the distortions in Kagome nets and their resulting physical properties including superconductivity and magnetism.