The origin of anomalous Hall effect (AHE) in magnetic materials is one of the most intriguing aspects in condensed matter physics and has been a controversial topic for a long time. Recent studies indicate that the intrinsic AHE is closely related to the Berry curvature of occupied electronic states. In a magnetic Weyl semimetal with broken time-reversal symmetry, there are significant contributions to Berry curvature around Weyl nodes, possibly leading to a large intrinsic AHE. Here, we report the quite large AHE in the half-metallic ferromagnet Co₃Sn₂S₂ single crystal. By systematically mapping out the electronic structure of Co₃Sn₂S₂ both theoretically and experimentally, we demonstrate that the intrinsic AHE from the Weyl fermions near the Fermi energy is dominating. The intrinsic anomalous Hall conductivity depends linearly on the magnetization and can be reproduced by theoretical simulation, in which the Weyl nodes monotonically move with the constrained magnetic moment on Co atom.

${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ is a newly discovered $Z_2$ topological kagome metal showing the coexistence of a charge-density-wave (CDW)-like order at $T^{*}=94\mathrm{K}$ and superconductivity (SC) at $T_c=2.5\mathrm{K}$ at ambient pressure. Here, we study the interplay between CDW and SC in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6 GPa. We find that the CDW transition decreases with pressure and experience a subtle modification at $P_{c1}\approx 0.6–0.9\mathrm{GPa}$ before it vanishes completely at $P_{c2}\approx 2\mathrm{GPa}$. Correspondingly, $T_c(P)$ displays an unusual $M$-shaped double dome with two maxima around $P_{c1}$ and $P_{c2}$, respectively, leading to a tripled enhancement of $T_c$ to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range $P_{c1}\le P\le P_{c2}$ as evidenced by the broad superconducting transition and reduced superconducting volume fraction. The modification of CDW order around $P_{c1}$ has been discussed based on the band structure calculations. This work not only demonstrates the potential to raise $T_c$ of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electron correlations in this novel family of topological kagome metals.

Electronic systems with flat bands are predicted to be a fertile ground for hosting emergent phenomena including unconventional magnetism and superconductivity^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}, but materials that manifest this feature are rare. Here, we use scanning tunnelling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet Co₃Sn₂S₂ (refs. ^{16,17,18,19,20}). We observe a pronounced peak at the Fermi level, which we identify as arising from the kinetically frustrated kagome flat band. On increasing the magnetic field up to ±8 T, this state exhibits an anomalous magnetization-polarized many-body Zeeman shift, dominated by an orbital moment that is opposite to the field direction. Such negative magnetism is induced by spin–orbit-coupling quantum phase effects^{21,22,23,24,25} tied to non-trivial flat band systems. We image the flat band peak, resolve the associated negative magnetism and provide its connection to the Berry curvature field, showing that Co₃Sn₂S₂ is a rare example of a kagome magnet where the low-energy physics can be dominated by the spin–orbit-coupled flat band.

The combination of nontrivial band topology and symmetry-breaking phases gives rise to novel quantum states and phenomena such as topological superconductivity, quantum anomalous Hall effect, and axion electrodynamics. Evidence of intertwined charge density wave (CDW) and superconducting order parameters has recently been observed in a novel kagome material ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, Cs) that features a ${\mathbb{Z}}_2$ topological invariant in the electronic structure. However, the origin of the CDW and its intricate interplay with the topological state has yet to be determined. Here, using hard-x-ray scattering, we demonstrate a three-dimensional CDW with $2\times 2\times 2$ superstructure in $(\mathrm{Rb},\mathrm{Cs}){\mathrm{V}}_3{\mathrm{Sb}}_5$. Unexpectedly, we find that the CDW fails to induce acoustic phonon anomalies at the CDW wave vector but yields a novel Raman mode that quickly damps into a broad continuum below the CDW transition temperature. Our observations exclude strong electron-phonon-coupling-driven CDW in ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ and support an unconventional CDW that was proposed in the kagome lattice at van Hove filling.