The Griffiths singularity in a phase transition, caused by disorder effects, was predicted more than 40 years ago. Its signature, the divergence of the dynamical critical exponent, is challenging to observe experimentally. We report the experimental observation of the quantum Griffiths singularity in a two-dimensional superconducting system. We measured the transport properties of atomically thin gallium films and found that the films undergo superconductor-metal transitions with increasing magnetic field. Approaching the zero-temperature quantum critical point, we observed divergence of the dynamical critical exponent, which is consistent with the Griffiths singularity behavior. We interpret the observed superconductor-metal quantum phase transition as the infinite-randomness critical point, where the properties of the system are controlled by rare large superconducting regions.

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...

We report on the observation of a helical Luttinger liquid in the edge of an InAs=GaSb quantum spin Hall insulator, which shows characteristic suppression of conductance at low temperature and low bias voltage. Moreover, the conductance shows power-law behavior as a function of temperature and bias voltage. The results underscore the strong electron-electron interaction effect in transport of InAs=GaSb edge states. Because of the fact that the Fermi velocity of the edge modes is controlled by gates, the Luttinger parameter can be fine tuned. Realization of a tunable Luttinger liquid offers a one-dimensional model system for future studies of predicted correlation effects. DOI: 10.1103/PhysRevLett.115.136804 PACS numbers: 71.10.Pm, 73.23.-b, 73.63.-b It is well known that electron-electron interactions play a more important role in one-dimensional (1D) electronic systems than in higher dimensional systems. In a 1D system, interactions cause electrons to behave in a strongly correlated way; so, under very general circumstances, 1D electron systems can be described by the TomonagaLuttinger liquid (LL) theory [1,2] instead of the meanfield Fermi liquid theory. A Luttinger parameter K characterizes the sign and the strength of the interactions: K < 1 for repulsion, K > 1 for attraction, and K ¼ 1 for the noninteracting case. Confirmations of LL have been examined in various materials, such as carbon nanotubes [3][4][5], semiconductor nanowires [6], and cleaved-edgeovergrowth 1D channels [7], as well as fractional quantum Hall edge states [8], respectively, for spinful or chiral Luttinger liquids. The experimental hallmarks of LL are a strongly suppressed tunneling conductance and a powerlaw dependence of the tunneling conductance on temperature and bias voltage [3][4][5]8]. In a weakly disordered spinful LL, transport experiments showed that the conductance reduces from the quantized value as the temperature is being decreased [6,7].The quantum spin Hall insulator (QSHI), also known as a two-dimensional (2D) topological insulator, is a topological state of matter supporting the helical edge states, which are counterpropagating, spin-momentum locked 1D modes protected by time reversal symmetry. It has recently attracted a lot of interest due to the peculiar helical edge properties and potential applications for quantum computation [9][10][11][12][13][14][15][16][17][18]. Experimentally, QSHI has been realized in HgTe quantum wells (QWs) [14] and in InAs=GaSb QWs [16][17][18]. In both cases, quantized conductance plateaus have been observed in devices with an edge length of several micrometers [14,18], implying ballistic transport in the edges. On the other hand, devices with longer edges have lower values of conductance [14,17,18], indicating certain backscattering processes occurred inside helical edges. In principle, single-particle elastic backscattering is forbidden in helical edges due to the protection of time reversal symmetry. Therefore, inelastic and/or multiparticle scattering should be the dominating sc...