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Recently, 2D Mo2C, a new member of the MXene family, has attracted much attention due to the exotic superconducting properties discovered in 2D α-Mo2C. Here, not only 2D α-Mo2C but also 2D β-Mo2C crystal sheets with distinct disordered carbon distributions were successfully grown. 2D β-Mo2C shows a much stronger superconductivity than 2D α-Mo2C, and their superconductivities have different hydrostatic pressure responses. The superconducting transition temperature Tc of 2D α-Mo2C shows a dome-shaped profile under pressure, implying the existence of two competing effects arising from phononic and electronic properties, while for 2D β-Mo2C, Tc decreases monotonically with increasing pressure, possibly due to phonon stiffening. These results indicate that the electronic properties have a more important influence on the superconductivity in 2D α-Mo2C compared to 2D β-Mo2C. The ordered and disordered carbon distributions in 2D α-Mo2C and β-Mo2C, respectively, may be the underlying origin for their different electronic and superconducting properties. It is still a mystery whether disorders could be beneficial for the superconductivity or not. In this work, it is surprising to find out that the carbon disordered 2D β-Mo2C crystal sheet shows a much stronger superconductivity than the carbon ordered 2D α-Mo2C crystal sheet, and the in-situ order-disorder transition from α-Mo2C to β-Mo2C induced by e-beam irradiation results in an enhanced superconductivity. Especially, the Tc variation trends of α-Mo2C and β-Mo2C are different under hydrostatic pressures. These results highlight the important role of disorders in the superconducting properties owing to the carbon distributions in Mo2C. Superconductors: 2D nanomaterials thrive under pressure and e-beam irradiation Two-dimensional (2D) molybdenum carbide (Mo2C) sheets, an ultrathin crystal system, have attracted much attention due to the exotic superconducting properties. Now, Li's group from the University of Science and Technology of China in Hefei and colleagues report that 2D Mo2C can be synthesized into two crystal forms that exhibit distinctly different superconducting behaviors when compressed in a pressure cell. The team demonstrated that the disordered 'beta' crystal phase of Mo2C becomes superconductive at higher temperatures than the more ordered 'alpha' form. The in-situ order-disorder transition from 'alpha' to 'beta' Mo2C induced by e-beam irradiation results in an enhanced superconductivity. Additionally, the superconductivities of the two forms of 2D crystals showed different responses to thickness changes. These experiments suggest that the positioning of carbon atoms plays a crucial role in the superconductivity in related 2D crystals. [ABSTRACT FROM AUTHOR]