#
Prof. Jian Wang’s group and collaborators discovered the emergence and evolution of high-temperature anomalous metal states in FeSe/SrTiO3

Recently, Prof. Jian Wang’s group at International Center of Quantum Materials, School of Physics, Peking University, in collaboration with Prof. Xincheng Xie from Peking University, Prof. Qi-Kun Xue and Prof. Lili Wang from Tsinghua University, Prof. Haiwen Liu from Beijing Normal University, Prof. Yi Liu from Renmin University of China, Prof. Nitin Samarth from Pennsylvania State University, and Prof. Minghu Pan from Shaanxi Normal University, observed the high-temperature bosonic anomalous metal states near 20 K in the two-dimensional interfacial high-temperature superconductor FeSe/SrTiO_{3}, representing the highest characteristic temperature of bosonic anomalous metal states reported to date. Over a decade of systematic experimental research, Prof Jian Wang’s group discovered that the two-dimensional superconducting states of FeSe thin films could be effectively controlled by tuning the normal-state resistance, which is achieved by controlling the growth conditions of the samples or fabricating periodic nanohole arrays. By these modulations, the research group discovered the emergence and evolution of the high-temperature bosonic metal states, and the characteristics of bosonic strange metal states in FeSe thin films. Based on the experimental results, this work proposed a microscopic model of the bosonic anomalous metal states (i.e., the quantum tunneling of vortices influenced by Ohmic dissipation), which significantly promotes the understanding of the universal mechanism of the bosonic metal states. This article, entitled “High-Temperature Anomalous Metal States in Iron-Based Interface Superconductors,” was published in *Physical Review Letters* on May 31, 2024 (*Physical Review Letters* 132, 226003 (2024))。

The superconductor-insulator transition is a paradigm of quantum phase transition, which represents an important topic in condensed matter physics and has been a research highlight over the last three decades. The discovery and pioneering investigations of the SIT have previously received the 2015 Oliver E. Buckley Condensed Matter Physics Prize. During the superconductor-insulator transitions, the early experimental studies have indicated the possible existence of another quantum ground state beyond the superconducting state and insulating state, namely the bosonic anomalous metal state (also known as the quantum metal state). However, the origin of the two-dimensional anomalous metal states remains a mystery.

Prof. Jian Wang’ s group and collaborators have made a series of important contributions to the study of anomalous metal states in two-dimensional superconducting systems. In collaboration with Prof. Yanrong Li *et al.*, they confirmed the existence of the two-dimensional anomalous metal state in nanopatterned high-temperature superconductor YBa_{2}Cu_{3}O_{7-x} films, and demonstrated that it is a novel quantum ground state dominated by bosons (Science 366, 1505-1509(2019)). In collaboration with Prof. Qi-Kun Xue *et al.*, they utilized high-quality filters to eliminate the external high-frequency noise during the ultralow-temperature transport measurements, and provided the solid experimental evidence of intrinsic anomalous metal states in high-quality PdTe_{2} superconducting films grown by molecular beam epitaxy (MBE) (Nano Letters 20, 5728-5734(2020)). Furthermore, in collaboration with Prof. Xi Lin and Prof. Xing Ying *et al.*, they directly observed the extrinsic anomalous metal states caused by external high-frequency noise, and the intrinsic anomalous metal states at lower temperatures and higher magnetic fields after using the effective filters in few-layer transition-metal dichalcogenide 4Ha-TaSe_{2} superconducting devices (Nano Letters 21, 7486-7494(2021)).

In this work, Prof. Jian Wang’s group and collaborators prepared high-quality crystalline FeSe films by MBE with the thickness down to one unit cell on SrTiO_{3} (STO) substrates, and performed the systematic transport measurements with ultralow temperature and strong magnetic field. The FeSe/STO is a two-dimensional interfacial high-temperature superconducting system with an onset transition temperature (*T*_{c}^{onset}) exceeding 40 K, and a zero-resistance temperature (*T*_{c}^{zero}) typically around 20 K. It was found that in FeSe/STO systems with relatively large normal-state resistances, as the temperature decreases, the resistance of the system first decreases and then gradually saturates at a finite value (Fig. 1a). Meanwhile, the Hall coefficient of the system is zero in temperature regime of the resistance saturation (Fig. 1b), revealing the existence of a bosonic anomalous metal states in the FeSe/STO system with the particle-hole symmetry similar to the superconducting states. It is noteworthy that the characteristic temperature of this anomalous metal state (*T*^{AM}) is close to 20 K, exceeding the characteristic temperatures of all previous results (Fig. 1c).

Figure 1. (a) Arrhenius plots of the sheet resistance versus temperature curves of the two-dimensional interfacial high-temperature superconducting FeSe/STO system, showing an anomalous metal state with a characteristic temperature *T*^{AM} up to 19.7 K. (b) Temperature-dependence of the sheet resistance and the Hall coefficient. (c) Overview of *T*^{AM} and the ratio *T*^{AM}/*T*_{c}^{onset} of various 2D superconducting systems.

To further investigate the behavior of the bosonic metal states in the FeSe/STO systems, the research group fabricated the periodic nanohole arrays on the system through reactive ion etching, forming a two-dimensional Josephson junction array structure. By increasing the etching time, the superconducting islands gradually shrink and the junction resistances between superconducting islands increase in the FeSe/STO Josephson junction array, and consequently the normal-state resistance of the system increases as well. In the 210 s-etched FeSe/STO films, the *T*^{AM} of the anomalous metal state is approximately 0.4 K, significantly lower than the *T*^{AM} of the unpatterned films. Meanwhile, in the temperature regime of the anomalous metal state in the nanopatterned FeSe/STO films, the magnetoresistance exhibits quantum oscillations corresponding to charge-2*e* quantum oscillations, revealing the bosonic nature of the anomalous metal states.

Additionally, in both unpatterned and nanopatterned FeSe/STO films, a linear-in-temperature (*T*-linear) resistance below *T*_{c}^{onset} was detected (Fig. 2), similar to the characteristics of the strange metal state exhibiting non-Fermi liquid behavior. In the FeSe/STO films, the slopes of this *T*-linear resistance are significantly larger than the fermionic strange metal state above *T*_{c}^{onset}, and the charge-2*e* quantum oscillations and significantly suppressed Hall coefficient are simultaneously observed within the temperature regime of the linear *T*-linear resistance behavior. Therefore, the *T*-linear resistance behavior below *T*_{c}^{onset} indicates the presence of a bosonic strange metal state in the FeSe/STO films.

Figure 2. Linear-in-temperature (*T*-linear) resistance behaviors in crystalline unpatterned (a) and nanopatterned (b) FeSe/STO systems.

Based on the experimental observations, the research group proposed a microscopic theoretical model for the anomalous metal state under zero magnetic field. The model is mainly based on the quantum tunneling of vortices in two-dimensional superconductors with the Ohmic dissipation effect generated by the coupling between bosonic modes and fermionic modes, which could give rise to the electrical transport characteristics of the bosonic anomalous metal states. In this picture, the average Ohmic dissipation strength is inversely proportional to the average link resistance , and is also inversely proportional to the normal-state resistance of the sample, *R*_{N}. This theoretical model can quantitatively characterize the resistance-temperature curves of the bosonic metal states (Fig. 3b), and qualitatively describe the evolution of the bosonic metal states tuned by *R*_{N} of the samples (Figure 3c). Therefore, this work not only reveals the high-temperature anomalous metal state in the FeSe/STO systems, which offers a promising platform for further experimental investigations on the anomalous metal state, but also succeeds in characterizing the evolution of bosonic metal states under zero magnetic field, shedding new light on the understanding of the origin of anomalous metal states.

Figure 3. (a) Schematic diagram of vortex dynamics. (b) Resistance-temperature curve of the high-temperature anomalous metal state (orange line) and the fitting results based on our theoretical model (purple lines). (c) *T*^{AM}/*T*_{c}^{onset} as a function of *R*_{N} for both unpatterned and nanopatterned films. (d) Quantitative simulation of the resistance-temperature behavior from our theoretical model considering different Ohmic dissipation strength.

In this work, Dr. Yanan Li (a former joint graduate student at Peking University and The Pennsylvania State University), Prof. Haiwen Liu and Dr. Haoran Ji from Peking University contributed equally to this work. Prof. Jian Wang and Prof. Yi Liu are the corresponding authors. This work was financially supported by the National Natural Science Foundation of China, the National Key Research and Development Program of China, Beijing Natural Science Foundation, the Basic and Applied Basic Research Major Programme of Guangdong Province, China, Jihua Laboratory, Beijing National Laboratory for Condensed Matter Physics, Young Elite Scientists Sponsorship Program by BAST, the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China.

Link to the paper：https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.226003