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Electron-doped cuprates consistently exhibit strong antiferromagnetic correlations, leading to the prevalent belief that antiferromagnetic spin fluctuations mediate Cooper pairing in these unconventional superconductors. However, early investigations showed that although antiferromagnetic spin fluctuations create the largest pseudogap at hot spots in momentum space, the superconducting gap is also maximized at these locations. This presented a paradox for spin-fluctuation-mediated pairing: Cooper pairing is strongest at momenta where the normal-state low-energy spectral weight is most suppressed. Here we investigate this paradox and find evidence that a gossamer—meaning very faint—Fermi surface can provide an explanation for these observations. We study Nd2–xCexCuO4 using angle-resolved photoemission spectroscopy and directly observe the Bogoliubov quasiparticles. First, we resolve the previously observed reconstructed main band and the states gapped by the antiferromagnetic pseudogap around the hot spots. Within the antiferromagnetic pseudogap, we also observe gossamer states with distinct dispersion, from which coherence peaks of Bogoliubov quasiparticles emerge below the superconducting critical temperature. Moreover, the direct observation of a Bogoliubov quasiparticle permits an accurate determination of the superconducting gap, yielding a maximum value an order of magnitude smaller than the pseudogap, establishing the distinct nature of these two gaps. We propose that orientation fluctuations in the antiferromagnetic order parameter are responsible for the gossamer states. 

Abstract The spin- $$\frac{1}{2}$$ 1 2 kagome antiferromagnet is considered an ideal host for a quantum spin liquid (QSL) ground state. We find that when the bonds of the kagome lattice are modulated with a periodic pattern, new quantum ground states emerge. Newly synthesized crystalline barlowite (Cu 4 (OH) 6 FBr) and Zn-substituted barlowite demonstrate the delicate interplay between singlet states and spin order on the spin- $$\frac{1}{2}$$ 1 2 kagome lattice. Comprehensive structural measurements demonstrate that our new variant of barlowite maintains hexagonal symmetry at low temperatures with an arrangement of distorted and undistorted kagome triangles, for which numerical simulations predict a pinwheel valence bond crystal (VBC) state instead of a QSL. The presence of interlayer spins eventually leads to an interesting pinwheel q  = 0 magnetic order. Partially Zn-substituted barlowite (Cu 3.44 Zn 0.56 (OH) 6 FBr) has an ideal kagome lattice and shows QSL behavior, indicating a surprising robustness of the QSL against interlayer impurities. The magnetic susceptibility is similar to that of herbertsmithite, even though the Cu 2+ impurities are above the percolation threshold for the interlayer lattice and they couple more strongly to the nearest kagome moment. This system is a unique playground displaying QSL, VBC, and spin order, furthering our understanding of these highly competitive quantum states.