Quantum materials and quantum phase transitions have become research highlights in the field of condensed matter physics and materials science of the century. Different from thermal phase transitions, the quantum phase transitions occur at zero temperature adjusted by non-thermal parameters of the system and the quantum fluctuation rather than thermal fluctuation plays a key role around the quantum critical point. The 2015 Oliver E. Buckley prize (the most important prize in condensed matter physics) was awarded for the discovery and pioneer investigations of the superconductor-insulator transition, a paradigm of quantum phase transitions. During the quantum phase transition, besides the superconducting and insulating ground states, whether a quantum metallic state can exist in two-dimensional superconducting systems has been a core issue (Rev. Mod. Phys. 91, 11002 (2019)). According to the scaling theory of localization, the carriers in two-dimensional systems will be localized when approaching zero temperature due to the quantum interference and the divergence of phase coherence. Therefore, quantum metallic states are absent in two-dimensional systems. Although possible signature of quantum metallic state has been observed in various two-dimensional electron systems, the existence of quantum metallic state is still under intensive debate over the past 30 years due to the low critical temperature and the influence of external high frequency noise (Science Advances 5, 3826 (2019)).

Recently, Prof. Jian Wang and Boya Postdoc Yi Liu at Peking University and their collaborators for the first time demonstrated the existence of quantum metallic state in high temperature superconducting films patterned with an array of holes. The nanopatterned high temperature superconducting YBCO films undergo a superconductor-insulator transition with increasing etching time. The direct evidence of quantum metallic state is that the resistance drops and saturates with decreasing temperature in the low temperature regime. For high temperature superconducting YBCO films, the saturation of resistance occurs at around 5 K, 10 to 100 times higher than that observed in conventional superconducting systems, which makes the quantum metallic state in the YBCO films very stable and convincing. An ultralow temperature control experiment indicates that the resistance saturation behavior remains almost the same with or without the filters, which safely excludes the possible influence of external high frequency noise and provides undoubted experimental evidence of quantum metallic state. Furthermore, the measured zero Hall resistance of quantum metallic state reveals that the quantum metallic state preserves particle-hole symmetry similar to the superconducting state. Consistent with the theoretical expectation, the large magnetoresistance and linear voltage-current characteristic are also observed in the quantum metallic states in the nanopatterned YBCO films.

By performing systematic ultralow temperature transport measurement, they observed magnetoconductance quantum oscillations with a period corresponding to one superconducting flux quantum h/2e, indicating that the quantum metallic state is bosonic and the Cooper pairs (bosons) play a crucial role in quantum metallic state (the carriers of a conventional metallic system are electrons, i.e. fermions). For the films in the superconducting state, the oscillation amplitude monotonically grows and diverges with decreasing temperature. For the insulating films, the oscillation amplitude initially increases and then drops with decreasing temperature. In contrast, the oscillation amplitude for the films in quantum metallic state increases with decreasing temperature and then saturates in the low temperature regime. Further analysis reveals that the saturation of quantum oscillation amplitude gives rise to the saturation of Cooper pair phase coherence and thus may lead to the formation of quantum metallic state. Interestingly, with increasing disorder, the oscillation amplitude varies by at least nine orders of magnitude from the superconducting films to most insulating films in the zero temperature limit, whereas the normal resistance only changes by two orders of magnitude. This finding demonstrates that the Cooper pair phase coherence can be controlled over a wide range in the two-dimensional nanopatterned high temperature superconducting systems.

The paper was published online by Science on Thursday, November 14, 2019 (DOI: 10.1126/science.aax5798):https://science.sciencemag.org/content/early/2019/11/13/science.aax5798. Prof. Jian Wang at Peking University, Prof. James M. Valles Jr at Brown University and Prof. Jie Xiong at University of Electronic Science and Technology of China are corresponding authors of this paper. Chao Yang at University of Electronic Science and Technology of China and Yi Liu at Peking University contributed equally to this work. Other collaborators include Prof. Jimmy Xu at Brown University, Prof. Xi Lin at Peking University, Prof. Haiwen Liu at Beijing Normal University, Prof. Hong Yao at Tsinghua University and Prof. Yanrong Li at University of Electronic Science and Technology of China etc. This work was supported by the National Natural Science Foundation of China, the National Key R&D Program of China, Fundamental Research Funds for the Central Universities, Collaborative Innovation Center of Quantum Matter, the Strategic Priority Research Program of Chinese Academy of Sciences, the Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing Natural Science Foundation, Beijing Municipal Science and Technology Commission and China Postdoctoral Science Foundation.

Jian Wang group and collaborators have made a series of achievements in the field of quantum phase transition in two-dimensional superconductors. For example, they ever discovered quantum Griffiths singularity (Science 350, 509 (2015); Nature Communications 10, 3633 (2019)), a new quantum phase transition behavior. The detection of quantum bosonic metallic state in two-dimensional high temperature superconducting systems represents a new significant breakthrough in this field. This work not only provides solid evidence of quantum metallic state, which is under intensive debate for over thirty years around the world, but also paves a new way for further investigating the origin of quantum metallic state. Prof. Steven A. Kivelson at Stanford University gave high evaluation on this work and wrote a commentary in Journal Club for Condensed Matter Physics. In the commentary, Prof. Kivelson pointed out that 隆掳this conclusion (the demonstration of quantum metallic state) is of fundamental importance for our understanding of quantum materials.隆卤