We present a clear case study on the occurrence of two successive X-class flares including a decade-class flare (X9.3) and two coronal mass ejections (CMEs) triggered by shearing motion and sunspot rotation in active region NOAA 12673 on 2017 September 6. A shearing motion between the main sunspots with opposite polarities started on September 5 and even lasted after the second X-class flare on September 6. Moreover, the main sunspot with negative polarity rotated around its umbral center and another main sunspot with positive polarity also exhibited a slow rotation. The sunspot with negative polarity at the northwest of active region also began to rotate counter-clockwise before the onset of the first X-class flare, which is related to the formation of the second S-shaped structure. The successive formation and eruption of two S-shaped structures were closely related to the counter-clockwise rotation of three sunspots. The existence of a flux rope is found prior to the onset of two flares by using non-linear force free field extrapolation based on the vector magnetograms observed by SDO/HMI. The first flux rope corresponds to the first S-shaped structures mentioned above. The second S-shaped structure was formed after the eruption of the first flux rope. These results suggest that shearing motion and sunspot rotation play an important role in the buildup of the free energy and the formation of flux ropes in the corona which produces solar flares and CMEs.

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