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The dc breakdown characteristics in the gap with the thin dielectric sheet under atmospheric air were investigated experimentally. The breakdown phenomena were divided into three patterns by current and discharge light (photon) waveforms. The first pattern consisted of a single waveform as a primary pulse. The second pattern consisted of multiple secondary pulses as the successors of the primary pulse. The third pattern was a developing process from the second pattern to the breakdown of the sheet as a final stage. The breakdown voltage of the sheet was irregular even under the same experimental conditions, and its value increased with the sheet thickness. On the other hand, the breakdown voltage in the complex gap consisting of the thin sheet and air gap became higher than that of the thin sheet, and its maximum value reached the breakdown voltage in the air gap. These phenomena and the breakdown mechanism for each pattern were analyzed by the electric field distribution between the electrodes. The breakdown models in the gap with the thin sheet and the complex gap were proposed by comparing the experimental results with the breakdown mechanisms.