Jian Wang group and collaborators report the in-plane quantum Griffiths singularity in two-dimensional crystalline superconductors
News cover: In-plane quantum Griffiths singularity
As a paradigm of quantum phase transition, the superconductor–insulator/metal transition in two dimensional (2D) superconductors has been investigated for more than 30 years. Quantum Griffiths singularity (QGS), as a novel phenomenon of superconductor–metal transition, reveals the profound influence of quenched disorder. Characterized by a divergent critical exponent zν, the QGS was firstly observed in Ga films [1] by Jian Wang group and collaborators in 2015. Subsequently, the QGS was detected in other 2D superconductors [2-4] under perpendicular magnetic field. It is believed that the underlying mechanism of QGS strongly relates to the vortex effect. However, whether the QGS can exist in the vortex-free case remains a mystery.
Recently, Prof. Jian Wang, Prof. X. C. Xie and Prof. Xi Lin at Peking University, in collaboration with Prof. Yi Liu at Renmin University of China, Prof. Haiwen Liu at Beijing Normal University, Prof. Qi-Kun Xue and Prof. Lili Wang at Tsinghua University and Prof. Ying Xing at China University of Petroleum (Beijing), observed the QGS under parallel field in ultrathin crystalline PdTe2 films grown by molecular beam epitaxy. The superconductor–metal transition in the four-monolayer (about 2 nm) thick PdTe2 film was systematically observed and the magnetoresistance isotherms cross each other in a relatively large and well-defined transition region under both perpendicular and parallel magnetic fields. The critical exponent zν is proved to be divergent as the perpendicular and parallel magnetic fields increase through the scaling analysis, demonstrating the existence of QGS. It is reported by previous works that the formation of quantum Griffiths phase is accompanied by the evolution from vortex lattice to vortex glass-like phase. However, the vortex cannot form under parallel magnetic field. As a result, the observation of in-plane QGS uncovers a new mechanism of quantum phase transition where the effect of vortex can be negligible. When the thickness of PdTe2 film is increased to six monolayers, the QGS disappears under perpendicular field but persists under parallel field. This discordance further confirms the differences in microscopic processes under perpendicular and parallel magnetic fields.
The ultrathin crystalline PdTe2 films are type-II Ising superconductors with strong spin-orbit coupling (SOC) [5] and the in-plane critical field of PdTe2 films depends on the effective Zeeman-type SOC. Because of the different local disorder strength, the in-plane critical magnetic field varies with location. When the in-plane magnetic field is near the mean-field critical field, the regions with relatively large disorder are easier to lose superconductivity and form the normal state, while the others keep superconducting and form the rare regions. The formation of rare regions under parallel field may give rise to the in-plane QGS.
Moreover, the direct activated scaling analysis with a new irrelevant correction has been proposed where the effect of irrelevant parameters is taken into account. The irrelevant parameters should be considered when studying quantum phase transitions at finite temperatures. Based on the new method, the phase boundary of PdTe2 films is fitted and the magnetoresistance isotherms are corrected when considering the irrelevant parameters. Compared to the indirect activated scaling analysis in previous work, this new method is an important progress, and provides new evidence of QGS.
The discovery of in-plane QGS reveals a new microscopic mechanism in the absence of vortices, changes paradigm and understanding of the quantum phase transitions and paves a new way to study quantum phase transitions under parallel magnetic field. This work will stimulate more in-depth discussions on superconductor–metal quantum phase transitions under parallel magnetic fields, and further promote the establishment of new physical paradigm and models of quantum phase transitions.
The paper was published online by Physical Review Letters on September 24, 2021 (Phys. Rev. Lett. 127, 137001 (2021), DOI: 10.1103/PhysRevLett.127.137001). Prof. Jian Wang at Peking University and Prof. Haiwen Liu at Beijing Normal University are corresponding authors of this paper. Prof. Yi Liu at Renmin University of China and Shichao Qi at Peking University contributed equally to this work. Other collaborators include Prof. X. C. Xie and Prof. Xi Lin at Peking University, Prof. Qi-Kun Xue and Prof. Lili Wang at Tsinghua University, Prof. Ying Xing at China University of Petroleum (Beijing), etc. This work was financially supported by the National Key Research and Development Program of China, the National Natural Science Foundation of China, Beijing Natural Science Foundation, the Strategic Priority Research Program of Chinese Academy of Sciences and China Postdoctoral Science Foundation.
Figures: (a) The schematic for standard four-electrode transport measurements on the PdTe2 film under parallel magnetic field. (b) Parallel magnetic field dependence of the sheet resistance at different temperatures. (c)The major evidence of the in-plane quantum Griffith singularity: the divergence of the critical exponent. (d) The direct activated scaling analysis with irrelevant corrections, which confirms the existence of the QGS.
Reference：
[1] Y. Xing et al., Science 350, 542-545 (2015).
[2] S. C. Shen et al., Phys. Rev. B 94, 144517 (2016).
[3] Y. Xing et al., Nano Lett. 17, 6802-6807 (2017).
[4] Y. Liu et al., Nat. Commun. 10, 3633 (2019).
[5] Y. Liu et al., Nano Lett. 20, 5728-5734 (2020).
Paper link: Y. Liu, S. C. Qi, J. C. Fang, J. Sun, C. Liu, Y. Z. Liu, J. J. Qi, Y. Xing, H. W. Liu, X. Lin, L. L. Wang, Q.-K. Xue, X. C. Xie, J. Wang, Phys. Rev. Lett.127, 137001 (2021). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.137001