In this review article, we show our recent results relating to the undoped (Ce-free) superconductivity in the electron-doped high-Tc cuprates with the so-called T structure. For an introduction, we briefly mention the characteristics of the electron-doped T-cuprates, including the reduction annealing, conventional phase diagram and undoped superconductivity. Then, our transport and magnetic results and results relating to the superconducting pairing symmetry of the undoped and underdoped T-cuprates are shown. Collaborating spectroscopic and nuclear magnetic resonance results are also shown briefly. It has been found that, through the reduction annealing, a strongly localized state of carriers accompanied by an antiferromagnetic pseudogap in the as-grown samples changes to a metallic and superconducting state with a short-range magnetic order in the reduced superconducting samples. The formation of the short-range magnetic order due to a very small amount of excess oxygen in the reduced superconducting samples suggests that the T-cuprates exhibiting the undoped superconductivity in the parent compounds are regarded as strongly correlated electron systems, as well as the hole-doped high-Tc cuprates. We show our proposed electronic structure model to understand the undoped superconductivity. Finally, unsolved future issues of the T-cuprates are discussed.
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