. This discovery not only confirms TaAs as a 3D TWS, but also provides an ideal platform for realizing exotic physical phenomena (for example, negative magnetoresistance, chiral magnetic e ects and the quantum anomalous Hall e ect) which may also lead to novel future applications.

Weyl semimetals are crystalline solids that host emergent relativistic Weyl fermions and have characteristic surface Fermi-arcs in their electronic structure. Weyl semimetals with broken time reversal symmetry are difficult to identify unambiguously. In this work, using angle-resolved photoemission spectroscopy, we visualized the electronic structure of the ferromagnetic crystal Co3Sn2S2 and discovered its characteristic surface Fermi-arcs and linear bulk band dispersions across the Weyl points. These results establish Co3Sn2S2 as a magnetic Weyl semimetal that may serve as a platform for realizing phenomena such as chiral magnetic effects, unusually large anomalous Hall effect and quantum anomalous Hall effect.

Pairing symmetry is a fundamental property that characterizes a superconductor. For the iron-based high-temperature superconductors, an s(±)-wave pairing symmetry has received increasing experimental and theoretical support. More specifically, the superconducting order parameter is an isotropic s-wave type around a particular Fermi surface, but it has opposite signs between the hole Fermi surfaces at the zone centre and the electron Fermi surfaces at the zone corners. Here we report the low-energy electronic structure of the newly discovered superconductors, A(x)Fe(2)Se(2) (A=K,Cs) with a superconducting transition temperature (Tc) of about 30 K. We found A(x)Fe(2)Se(2) (A=K,Cs) is the most heavily electron-doped among all iron-based superconductors. Large electron Fermi surfaces are observed around the zone corners, with an almost isotropic superconducting gap of ~10.3 meV, whereas there is no hole Fermi surface near the zone centre, which demonstrates that interband scattering or Fermi surface nesting is not a necessary ingredient for the unconventional superconductivity in iron-based superconductors. Thus, the sign change in the s(±) pairing symmetry driven by the interband scattering as suggested in many weak coupling theories becomes conceptually irrelevant in describing the superconducting state here. A more conventional s-wave pairing is probably a better description.

Topological Weyl semimetal (TWS), a new state of quantum matter, has sparked enormous research interest recently. Possessing unique Weyl fermions in the bulk and Fermi arcs on the surface, TWSs offer a rare platform for realizing many exotic physical phenomena. TWSs can be classified into type-I that respect Lorentz symmetry and type-II that do not. Here, we directly visualize the electronic structure of MoTe2, a recently proposed type-II TWS. Using angle-resolved photoemission spectroscopy (ARPES), we unravel the unique surface Fermi arcs, in good agreement with our ab initio calculations that have nontrivial topological nature. Our work not only leads to new understandings of the unusual properties discovered in this family of compounds, but also allows for the further exploration of exotic properties and practical applications of type-II TWSs, as well as the interplay between superconductivity (MoTe2 was discovered to be superconducting recently) and their topological order.

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The nature of the parent compound of a high-temperature superconductor (HTS) often plays a pivotal role in determining its superconductivity. The parent compounds of the cuprate HTSs are antiferromagnetically ordered Mott insulators, while those of the iron-pnictide HTSs are metals with spin-density-wave order. Here we report the electronic identification of two insulating parental phases and one semiconducting parental phase of the newly discovered family of K x Fe 2Ày Se 2 superconductors. The two insulating phases exhibit Mott-insulator-like signatures, and one of the insulating phases is even present in the superconducting and semiconducting K x Fe 2Ày Se 2 compounds. However, it is mesoscopically phaseseparated from the superconducting or semiconducting phase. Moreover, we find that both the superconducting and semiconducting phases are free of the magnetic and vacancy orders present in the insulating phases, and that the electronic structure of the superconducting phase could be developed by doping the semiconducting phase with electrons. The rich electronic properties discovered in these parental phases of the K x Fe 2Ày Se 2 superconductors provide the foundation for studying the anomalous behavior in this new class of iron-based superconductors.

Topological quantum materials represent a new class of matter with both exotic physical phenomena and novel application potentials. Many Heusler compounds, which exhibit rich emergent properties such as unusual magnetism, superconductivity and heavy fermion behaviour, have been predicted to host non-trivial topological electronic structures. The coexistence of topological order and other unusual properties makes Heusler materials ideal platform to search for new topological quantum phases (such as quantum anomalous Hall insulator and topological superconductor). By carrying out angle-resolved photoemission spectroscopy and ab initio calculations on rare-earth half-Heusler compounds LnPtBi (Ln=Lu, Y), we directly observe the unusual topological surface states on these materials, establishing them as first members with non-trivial topological electronic structure in this class of materials. Moreover, as LnPtBi compounds are non-centrosymmetric superconductors, our discovery further highlights them as promising candidates of topological superconductors.

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