KEYWORDS: NbSe 2 , transition-metal dichalcogenides, macro-size monolayer film, ultralow temperature and high magnetic field electrical transport, Ising superconductivity, quantum phase transition 2 ABSTRACT Two-dimensional (2D) transition metal dichalcogenides (TMDs) have a range of unique physics properties and could be used in the development of electronics, photonics, spintronics and quantum computing devices. The mechanical exfoliation technique of micro-size TMD flakes has attracted particular interest due to its simplicity and cost effectiveness. However, for most applications, large area and high quality films are preferred. Furthermore, when the thickness of crystalline films is down to the 2D limit (monolayer), exotic properties can be expected due to the quantum confinement and symmetry breaking. In this paper, we have successfully prepared macro-size atomically flat monolayer NbSe 2 films on bilayer graphene terminated surface of 6H-SiC(0001) substrates by molecular beam epitaxy (MBE) method. The films exhibit an onset superconducting critical transition temperature (T c onset ) above 6 K, 2 times higher than that of mechanical exfoliated NbSe 2 flakes. Simultaneously, the transport measurements at high magnetic fields reveal that the parallel characteristic field B c// is at least 4.5 times higher than the paramagnetic limiting field, consistent with Zeeman-protected Ising superconductivity mechanism. Besides, by ultralow temperature electrical transport measurements, the monolayer NbSe 2 film shows the signature of quantum Griffiths singularity when approaching the zero-temperature quantum critical point. TEXTQuasi-2D superconductors such as ultrathin films with thickness down to monolayer [1][2][3][4][5][6][7] 10, 11,13 , the coexistence of charge density wave (CDW) and the superconducting phase was observed down to the monolayer limit but the T c of monolayer NbSe 2 got significantly suppressed (less than 3.1 K) compared with its bulk value (7.2 K).Superconductor-insulator (metal) transition (SIT/SMT), a paradigm of quantum phase transition, is an important topic in condensed matter physics. In the 2D limit regime, the orbital effect is restricted in parallel magnetic field. Calculations show that in anisotropic superconductors, the FFLO state might lead to an enhancement of the upper critical field between 1.5 and 2.5 times of the Pauli paramagnetic limit field 32,35 . In perpendicular magnetic field cases, the characteristic field B c (0) of NbSe 2 film is estimated to be 2.87 T, smaller than the Pauli paramagnetic limit field (8.21 T). Besides, the 8 Maki parameter α⊥ = 0.44 is smaller than 1.8. In parallel magnetic field cases, the characteristic field B c// (0) ~ 37.22 T is at least 4.5 times of Pauli paramagnetic limit field, which exceeds the theoretical predictions of 1.5 ~ 2.5 times 32,35 . Therefore, the chance of the existence of FFLO state in monolayer NbSe 2 is little.The sample 3 (with T c onset ~ 6 K, Figure S5 For SIT, the sample critical resistance on phase transition is th...

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