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Two-dimensional (2D) semiconductor of MoS2 has great potential for advanced electronics technologies beyond silicon1-9. So far, high-quality monolayer MoS2 wafers10-12 are already available and various demonstrations from individual transistors to integrated circuits have also been shown13-15. In addition to the monolayer, multilayers have narrower band gaps but improved carrier mobilities and current capacities over the monolayer5,16-18. However, achieving high-quality multilayer MoS2 wafers remains a challenge. Here we report the growth of high quality multilayer MoS2 4-inch wafers via the layer-by-layer epitaxy process. The epitaxy leads to well-defined stacking orders between adjacent epitaxial layers and offers a delicate control of layer numbers up to 6. Systematic evaluations on the atomic structures and electronic properties were carried out for achieved wafers with different layer numbers. Significant improvements on device performances were found in thicker-layer field effect transistors (FETs), as expected. For example, the average field-effect mobility ({\mu}FE) at room temperature (RT) can increase from ~80 cm2V-1s-1 for monolayer to ~110/145 cm2V-1s-1 for bilayer/trilayer devices. The highest RT {\mu}FE=234.7 cm2V-1s-1 and a record-high on-current densities of 1.704 mA{\mu}m-1 at Vds=2 V were also achieved in trilayer MoS2 FETs with a high on/off ratio exceeding 107. Our work hence moves a step closer to practical applications of 2D MoS2 in electronics., Comment: 13 pages,4 Figures

The success of modern civilization is built upon widespread cooperation in human society, deciphering the mechanisms behind has being a major goal for centuries. A crucial fact is, however, largely missing in most prior studies that games in the real world are typically played simultaneously and interactively rather than separately as assumed. Here we introduce the idea of interacting games that different games coevolve and influence each other's decision-making. We show that as the game-game interaction becomes important, the cooperation phase transition dramatically improves, a fairly high level of cooperation is reached for all involved games when interaction goes to be strong. A mean-field theory indicates that a new mechanism -- \emph{the dynamical reciprocity}, as a counterpart to the well-known network reciprocity, is at work to foster cooperation, which is confirmed by the detailed analysis. This revealed reciprocity is robust against variations in the game type, the population structure, and the updating rules etc, and more games generally yield a higher level of cooperation. Our findings point out the great potential towards high cooperation for many issues are interwoven with each other in the real world, and also the possibility of sustaining decent cooperation even in extremely adverse circumstances., Comment: 5 pages, 4 figures, 1 table, a companion long paper (arXiv:2102.00360) is also posted. Comments are welcomed

We study the evolution of two mutually interacting games with both pairwise games as well as the public goods game on different topologies. On 2d square lattices, we reveal that the game-game interaction can promote the cooperation prevalence in all cases, and the cooperation-defection phase transitions even become absent and fairly high cooperation is expected when the interaction goes to be very strong. A mean-field theory is developed that points out new dynamical routes arising therein. Detailed analysis shows indeed that there are rich categories of interactions in either individual or bulk scenario: invasion, neutral, and catalyzed types; their combination puts cooperators at a persistent advantage position, which boosts the cooperation. The robustness of the revealed reciprocity is strengthened by the studies of model variants, including asymmetrical or time-varying interactions, games of different types, games with time-scale separation, different updating rules etc. The structural complexities of the underlying population, such as Newman--Watts small world networks, Erd\H{o}s--R\'enyi random networks, and Barab\'asi--Albert networks, also do not alter the working of the dynamical reciprocity. In particular, as the number of games engaged increases, the cooperation level continuously improves in general. Our work thus uncovers a new class of cooperation mechanism and indicates the great potential for human cooperation where concurrent issues are so often seen in the real world., Comment: 22 pages, 19 figures, 2 tables, a companion short paper (arXiv:2101.00359) is also posted. Any comments are welcomed