The bulk samples were made using the solid-state reaction method under high pressure and high temperature using the appropriate precursors BaCuO2.13 and Ca2CuO3. The precursor BaCuO2.13 was obtained by calcining BaO2 and CuO at 900°C in flowing oxygen gas for a total duration of 60 hours, intermittently grinding twice in the interests of homogeneity. The precursor Ca2CuO3 was prepared first by calcining a well-ground mixture of CaCO3 and CuO at 950°C in air for 20 hours, and then the obtained Ca2CuO3 powder was sintered in flowing oxygen gas at 950°C for 40 hours with one or two intermediate grinding. The process of making Ca2CuO3 was in an open environment; therefore, the carbon can escape, and the amount of carbon is not counted in the precursor Ca2CuO3. The carbon in the final sample is thus introduced only in the next step of high-pressure and high-temperature sintering process. After mixing and grinding different components with molar ratios of 1.8BaCuO2.13, 1.4Ca2CuO3, 0.2CaCO3, 0.2BaCO3, 1.2CuO, and appropriate amount of 0.8Ag2O (used as oxidizer), the mixture was pressed into a pellet with the nominal formula of (Cu0.4C0.4)Ba2Ca3Cu4O11+δ. This pellet was sealed into a gold capsule for the final step of high-pressure and high-temperature synthesis. For high-pressure synthesis, the sample enclosed by gold capsule was placed into a BN container, surrounded by graphite sleeve resistance heater and pressure transmitting MgO rods. The final reaction was carried out at 1100° to 1150°C under 3.5 GPa for 1 to 2 hours and then cooled down to room temperature in 5 minutes before the pressure was released. The chemical analysis was performed on some grains by using energy dispersive x-ray spectrum based on SEM (Phenom ProX), and the results are shown in fig. S5. The statistics show that the carbon exists in all grains with the molar ratio of 0.3 to 0.4 per formula of (Cu,C)-1234, being consistent with the stoichiometry of the pellet before the last step sintering. The compositions from the analysis are really close to the nominal ones of the pellet before the last step sintering under high pressure and high temperature.

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