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Nature Communications reports Jian Wang group and collaborators’ work on the observation of anomalous quantum Griffiths singularity

Recently, Jian Wang group at Peking university epitaxially grew high quality ultrathin lead films on the Si(111) substrate. They observed anomalous quantum Griffiths singularity at ultralow temperatures and theoretically explain this phenomenon in collaboration with Prof. X. C. Xie, Prof. Xi Lin at Peking University and Prof. Haiwen Liu at Beijing Normal University. This finding reveals the remarkable influence of the superconducting fluctuation and spin-orbit interaction on the quantum phase transitions in two-dimensional (2D) superconducting systems, and justify the universality of quantum Griffiths singularity in superconductor-metal transition including this system with anomalous phase boundary.

As a paradigm of quantum phase transition, superconductor-insulator/metal transition (SIT/SMT) has been widely investigated in 2D superconductors over the past 30 years. The quantum phase transition is a continuous transition at absolute zero temperature from one ground state to another tuned by a non-thermal parameter. With the development of film growth and device fabrication technique, 2D crystalline superconductors have become an idea platform to investigate the quantum phase transition. In previous studies, Jian Wang group in collaboration with Prof. X. C. Xie, Prof. Xucun Ma, Prof. Xi Lin, Prof. Qi-Kun Xue and others have discovered the quantum Griffiths singularity of SMT in 2D superconducting Ga films (Science 350, 542(2015) with a perspective paper Science 350, 509 (2015)). This intriguing phenomenon was regarded as one of the three important topics in 2D crystalline superconductors by Prof. Iwasa at Tokyo university (Nature Reviews Materials 2, 16094 (2016)). The main characteristic of quantum Griffiths singularity is the divergence of dynamic critical exponent when approaching the quantum critical point, indicating that the disorder can qualitatively change the critical behavior of the quantum phase transition.

Recently, Jian Wang group has successfully grown high quality crystalline lead film in the macroscopic scale on Si(111) substrate by molecular beam epitaxy technique and realized sub-nanometer scale control of layer-by-layer epitaxial growth. Then Prof. Jian Wang, in collaboration with Prof. Xincheng Xie, Prof. Xi Lin at Peking University and Prof. Haiwen Liu at Beijing Normal University, observed an anomalous SMT, as well as the anomalous quantum Griffiths singularity in 4-monolayer (ML) crystalline lead film (around 1 nanometer thick). According to the mean field theory, the upper critical field Bc2 of conventional superconductors increases with decreasing temperature. However, systematic ultralow temperature transport measurements reveal that the SMT of 4-ML lead film has an anomalous phase boundary in low temperature regime: the onset upper critical field gradually decreases with decreasing temperature. Scaling analysis on the magnetoresistance along the anomalous phase boundary indicates that the critical exponent increases rapidly and then diverges with decreasing magnetic field when approaching the quantum critical point, which is distinct from the characteristic of quantum Griffiths singularity that the critical exponent diverges with increasing field. Therefore, this phenomenon with anomalous phase boundary is named as anomalous quantum Griffiths singularity. To understand this anomalous behavior, the researchers developed a new phenomenological model based on the superconducting fluctuation theory including the effect of large spin-orbit coupling, and give quantitative explanation for the experimental phase boundary. To be specific, under the influence of spin-orbit interaction and superconducting fluctuation, the phase boundary of SMT deviates from the expectation of the mean field theory and buckles outward, which gives rise to the anomalous phase boundary with anomalous quantum Griffiths singularity. The discovery of this novel quantum phase transition not only demonstrates the universality of quantum Griffiths singularity along different phase boundary, but also reveals the profound influence of spin-orbit interaction and superconducting fluctuation on SMT, which sheds a new light on the understanding of the quantum phase transitions in 2D crystalline superconductors.

The paper was published in Nature Communications on August 12, 2019. (Nature Communications 10, 363 (2019) DOI: 10.1038/s41467-019-11607-w): https://www.nature.com/articles/s41467-019-11607-w

Prof. Jian Wang at Peking University and Prof. Haiwen Liu at Beijing Normal University are corresponding authors of this paper. Yi Liu and Ziqiao Wang at Peking University contributed equally to this work. Other collaborators include Prof. X. C. Xie, Prof. Xi Lin, and Yue Tang, Chaofei Liu, Cheng Chen, Ying Xing, Qingyan Wang in Jian Wang group, as well as Pujia Shan in Xi Lin group.

This work was financially supported by the National Key Research and Development Program of China, the National Natural Science Foundation of China, Collaborative Innovation Center of Quantum Matter, Strategic Priority Research Program of Chinese Academy of Sciences, Beijing Natural Science Foundation, China Postdoctoral Science Foundation and the Fundamental Research Funds for the Central Universities.

Figure 1 Anomalous quantum Griffiths singularity in a crystalline lead film with 4 atomic layer thickness. (a) Superconducting transition at zero field in the lead film. The inset is a schematic for four-probe transport measurements. (b) Temperature dependent resistance at out-of-plane magnetic fields from 0 to 5 T. (c) The lead film exhibits an anomalous phase boundary at low temperature regime, which is in good agreement with the phenomenological model based on superconducting fluctuations. (d) The critical exponent increases rapidly with decreasing field and has a trend to diverge when approaching zero temperature, indicating the occurrence of anomalous quantum Griffiths singularity.

Figure 2 Schematic of the phase boundary of anomalous superconductor to metal transition. Under the influence of spin-orbit interaction and superconducting fluctuations, the normal phase boundary described by mean field theory (dashed blue curve) buckles outward to the solid red curve. The critical field decreases with decreasing temperature when the temperature is below T’, representing the anomalous phase boundary. Anomalous quantum Griffiths singularity can be observed when approaching infinite randomness quantum critical point (IRQCP) along this anomalous phase boundary.