| Summary: | The antiferromagnetic Ruddlesden-Popper ruthenate Ca_{3}Ru_{2}O_{7} is a model polar metal, combining inversion symmetry breaking with metallic conductivity; however, its low-temperature (T<48K) crystal structure and Fermi-surface topology remain ambiguous despite numerous measurements and theoretical studies. Here we perform both first-principles calculations with static correlations and angle-resolved photoelectron spectroscopy experiments to construct a complete model of Ca_{3}Ru_{2}O_{7}, reconciling inconsistencies among interpretations of electrical transport, thermopower measurements, and momentum- and energy-resolved band dispersions. The solution relies on treating the interplay among Coulomb repulsion, magnetic ordering, spin-orbit interactions, and the RuO_{6} octahedral degrees of freedom on equal footing. For temperatures 30<T<48K, we propose weak electron-electron interactions produce a symmetry-preserving metal-semimetal transition with Weyl nodes in proximity to the Fermi level, whereas an orthorhombic Pn2_{1}a structure emerges for T<30K, exhibiting charge- and spin-density waves from enhanced Coulombic interactions.
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