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Register a new userDirac fermions and flat bands in the ideal kagome metal FeSn
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The kagome lattice based on 3d transition metals is a versatile platform for novel topological phases hosting symmetry-protected electronic excitations and exotic magnetic ground states. However, the paradigmatic states of the idealized two-dimensional (2D) kagome lattice - Dirac fermions and topological flat bands - have not been simultaneously observed, partly owing to the complex stacking structure of the kagome compounds studied to date. Here, we take the approach of examining FeSn, an antiferromagnetic single-layer kagome metal with spatially-decoupled kagome planes. Using polarization- and termination-dependent angle-resolved photoemission spectroscopy (ARPES), we detect the momentum-space signatures of coexisting flat bands and Dirac fermions in the vicinity of the Fermi energy. Intriguingly, when complemented with bulk-sensitive de Haas-van Alphen (dHvA) measurements, our data reveal an even richer electronic structure that exhibits robust surface Dirac fermions on specific crystalline terminations. Through band structure calculations and matrix element simulations, we demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals under kagome symmetry, while the surface state realizes a rare example of fully spin-polarized 2D Dirac fermions when combined with spin-layer locking in FeSn. These results highlight FeSn as a prototypical host for the emergent excitations of the kagome lattice. The prospect to harness these excitations for novel topological phases and spintronic devices is a frontier of great promise at the confluence of topology, magnetism, and strongly-correlated electron physics.
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Layered kagome-lattice 3d transition metals are emerging as an exciting platform to explore the frustrated lattice geometry and quantum topology. However, the typical kagome electronic bands, characterized by sets of the Dirac-like band capped by a phase-destructive flat band, have not been clearly observed, and their orbital physics are even less well investigated. Here, we present close-to-textbook kagome bands with orbital differentiation physics in CoSn, which can be well described by a minimal tight-binding model with single-orbital hopping in Co kagome lattice. The capping flat bands with bandwidth less than 0.2 eV run through the whole Brillouin zone, especially the bandwidth of the flat band of out-of-plane orbitals is less than 0.02 eV along G-M. The energy gap induced by spin-orbit interaction at the Dirac cone of out-of-plane orbitals is much smaller than that of in-plane orbitals, suggesting orbital-selective character of the Dirac fermions.
The kagome lattice is a fertile platform to explore topological excitations with both Fermi-Dirac and Bose-Einstein statistics. While relativistic Dirac Fermions and flat-bands have been discovered in the electronic structure of kagome metals, the spin excitations have received less attention. Here we report inelastic neutron scattering studies of the prototypical kagome magnetic metal FeSn. The spectra display well-defined spin waves extending up to 120 meV. Above this energy, the spin waves become progressively broadened, reflecting interactions with the Stoner continuum. Using linear spin wave theory, we determine an effective spin Hamiltonian that reproduces the measured dispersion. This analysis indicates that the Dirac magnon at the K-point remarkably occurs on the brink of a region where well-defined spin waves become unobservable. Our results emphasize the influential role of itinerant carriers on the topological spin excitations of metallic kagome magnets.
CoSn is a Pauli paramagnet with relatively flat d-bands centered about 100 meV below the Fermi energy Ef. Single crystals of CoSn lightly doped with Fe, In, or Ni are investigated using x-ray and neutron scattering, magnetic susceptibility and magnetization, ac susceptibility, specific heat and resistivity measurements. Within the rigid band approximation, hole doping with a few percent of Fe or In should move the flat bands closer to Ef, whereas electron doping with Ni should move the flat bands further away from Ef. We provide evidence that this indeed occurs. Fe and In doping drive CoSn toward magnetism, while Ni doping suppresses CoSns already weak magnetic response. The resulting ground state is different for Fe versus In doping. For Fe-doped crystals, Co1-xFexSn, with 0.02 < x < 0.27, the magnetic and specific heat data are consistent with the formation of a spin glass, with a glass transition temperature, Tg, ranging from 1 K for x=0.02 to 10 K for x= 0.27. Powder and single crystal neutron diffraction found no evidence of long-range magnetic order below Tg with x = 0.17. For In-doped crystals, CoSn1-yIny, both the magnetic susceptibility and the Sommerfeld coefficient, gamma, increase substantially relative to pure CoSn, but with no clear indication of a magnetic transition for 0.05 < y < 0.2. CoSn crystals doped with Ni (Co0.93Ni0.07Sn) have a significantly smaller magnetic susceptibility and gamma than pure CoSn, consistent with the flat bands further from Ef.
The energy spectra for the tight-binding models on the Lieb and kagome lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band spectrum for the Lieb lattice is distorted, generating two pairs of Dirac points. While the upper pair evolves into graphene-like Dirac cones in the kagome limit, the low energy pair evolves until it merges producing the band-bottom flat band. The topological characterization of the Dirac points is achieved by projecting the Hamiltonian on the two relevant bands in order to obtain an effective Dirac Hamiltonian. The low energy pair of Dirac points is particularly interesting in this respect: when they emerge, they have opposite winding numbers, but as they merge, they have the same winding number. This apparent paradox is due to a continuous rotation of their states in pseudo-spin space, characterized by a winding vector. This simple, but quite rich model, suggests a way to a systematic characterization of two-band contact points in multiband systems.
Symmetry principles play a critical role in formulating the fundamental laws of nature, with a large number of symmetry-protected topological states identified in recent studies of quantum materials. As compelling examples, massless Dirac fermions are jointly protected by the space inversion symmetry $P$ and time reversal symmetry $T$ supplemented by additional crystalline symmetry, while evolving into Weyl fermions when either $P$ or $T$ is broken. Here, based on first-principles calculations, we reveal that massless Dirac fermions are present in a layered FeSn crystal containing antiferromagnetically coupled ferromagnetic Fe kagome layers, where each of the $P$ and $T$ symmetries is individually broken but the combined $PT$ symmetry is preserved. These stable Dirac fermions protected by the combined $PT$ symmetry with additional non-symmorphic $S_{rm{2z}}$ symmetry can be transformed to either massless/massive Weyl or massive Dirac fermions by breaking the $PT$ or $S_{rm{2z}}$ symmetry. Our angle-resolved photoemission spectroscopy experiments indeed observed the Dirac states in the bulk and two-dimensional Weyl-like states at the surface. The present study substantially enriches our fundamental understanding of the intricate connections between symmetries and topologies of matter, especially with the spin degree of freedom playing a vital role.
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