Kagome lattices stand at the forefront of research due to their fascinating interplay of topology, correlations, and magnetism [1-3]. Their special geometry enables various quantum phenomena, such as frustration and correlated orders, and features an electronic structure with flat bands, van Hove singularities, and Dirac cones. This makes them a prime subject for both experimental and theoretical research, offering insights into complex physical properties and potential technological applications.

In my lecture, I aim to shed light on the latest experimental developments concerning superconductivity and the magnetic aspects of charge order in various kagome-lattice systems, studied from the perspective of local magnetic probe. This involves the use of muon-spin rotation (µSR) as a function of depth from the sample surface and under extreme conditions like hydrostatic pressure, uniaxial strain, ultra-low temperatures, and high magnetic fields. µSR is complemented by magnetoresistance and X-ray diffraction techniques. Key systems under discussion will include: (1) The AV3Sb5 (A = K, Rb, Cs) compound series with V kagome lattice, notable for displaying a range of symmetry-breaking electronic orders, such as charge order and superconductivity. Here, we have identified a depth-tunable time-reversal symmetry-breaking state associated with charge order, as well as unconventional superconductivity [4-7]. (2) The bilayer kagome material ScV6Sn6, where hidden magnetism within the charge-ordered state was observed [8]. (3) The LaRu3Si2 system with Ru kagome layers, in which we identified two distinct types of charge order (bond order), with one manifesting above room temperature [9,10]. This finding marks the first instance of observing a charge-ordered state at or above room temperature in a correlated kagome lattice.

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