Recently, Prof. Jian Wang’s group at International Center of Quantum Materials, Peking University, in collaboration with Prof. Liang Qiao at University of Electronic Science and Technology of China, Prof. Yi Liu at Renmin University of China, Prof. Guang-Ming Zhang at Tsinghua University, Prof. Yi-feng Yang at Chinese Academy of Sciences, Prof. Peng Gao at Peking University, observed the unconventional superconducting states with broken rotational symmetries in the infinite-layer nickelate superconductor Nd_0.8Sr_0.2NiO₂ thin films. The experimental results reveal that, as the external in-plane magnetic field increases, the in-plane azimuthal angular dependent magnetoresistance of the Nd_0.8Sr_0.2NiO₂ thin films manifests a rotational symmetry-breaking transition from isotropic to four-fold rotational symmetric (C₄) and then to a combination of four-fold and two-fold rotational symmetric (C₄+C₂). Within the magnetic field regime corresponding to the two-fold symmetric (C₂) anisotropy, the temperature dependence of the in-plane superconducting critical field of the Nd_0.8Sr_0.2NiO₂ film exhibits an anomalous upturn behavior. This work uncovers the evolution of various symmetry-breaking quantum states in nickelate superconducting films, providing a new perspective for a deeper understanding of the superconducting pairing symmetry, unconventional superconductivity, and the competition among different ordered states in the nickelate superconductors. This work, entitled “Rotational symmetry breaking in superconducting nickelate Nd_0.8Sr_0.2NiO₂ films”, was published online by Nature Communications on November 7, 2023 (Nature Communications 14, 7155 (2023)). Link to the paper: https://www.nature.com/articles/s41467-023-42988-8.

Since the discovery of high-temperature cuprate superconductors in 1986, the exploration of unconventional high-temperature superconducting systems and the understanding of the underlying superconducting mechanisms have become one of the most important research frontiers of condensed matter physics. In 2019, superconductivity was observed in the infinite-layer nickelate thin films with a superconducting transition temperature T_c of 15 K. Infinite-layer nickelates are isostructural to the high- T_c cuprate superconductors, and the Ni⁺ elements in the nickelates are in the same 3d⁹ electronic configuration as the Cu²⁺ in cuprates. Therefore, the emergence of the nickelate superconductors is of significant importance for investigating the physical mechanisms of unconventional high- T_c superconductivity.

According to the Bardeen-Cooper-Schrieffer (BCS) theory, two electrons with anti-parallel spins and time-reversed momenta form Cooper pairs through electron-phonon coupling, whose condensation gives rise to the emergence of superconductivity. The order parameter of the conventional superconductivity exhibits isotropic s-wave symmetry. However, the high- T_c cuprate superconductors (T_c > 40 K) show novel characteristics beyond the BCS theory, such as that the pairing of the electrons is driven by the antiferromagnetic spin fluctuations, and the superconducting order parameter is of nodal d-wave symmetry. Multiple theoretical works have suggested that nickelate superconductors may also exhibit d-wave pairing symmetry, similar to that of cuprate superconductors. However, the experimental results on the pairing symmetry of the nickelate superconductors are still under debate. Additionally, previous studies have reported the presence of charge order and antiferromagnetic interactions in the parent compound of nickelate superconductors. Therefore, revealing the mechanisms of the superconductivity in nickelates and exploring the interplay between superconductivity and other ordered states, such as charge order and antiferromagnetism, have become an important issue in this field.

In this work, Prof. Jian Wang’s group systematically studied the angular dependent transport behaviors of the superconducting state in infinite-layer nickelate Nd_0.8Sr_0.2NiO₂ films with the Corbino-disk configuration (Fig. 1a). The circular Corbino-disk electrode guarantees that the electric current flows radially from the center to the outermost electrode, ensuring that the measured anisotropy is the intrinsic properties of the Nd_0.8Sr_0.2NiO₂ thin films. The research group found that at small magnetic fields, the in-plane azimuthal angular dependent magnetoresistance R(φ) of the Nd_0.8Sr_0.2NiO₂ superconducting film is isotropic. However, as the applied in-plane magnetic field increases, the in-plane magnetoresistance R(φ) undergoes a transition from isotropy to four-fold rotational symmetry (C₄), which may correspond to the transition of the superconducting pairing symmetry from isotropic s-wave pairing to four-fold symmetric d-wave pairing. Further experiments reveal that the four-fold rotational symmetry (C₄) in the in-plane magnetoresistance R(φ) disappears simultaneously with the suppression of superconductivity at higher temperatures, indicating that this four-fold rotational symmetry (C₄) originates from the superconducting state in the Nd_0.8Sr_0.2NiO₂ film (Fig. 1b, 1c). The in-depth analysis of the in-plane magnetoresistance R(φ) also rules out the possibility that the four-fold rotational symmetry (C₄) arises from the magnetic moments of the Nd³⁺ in this material.

Approaching the low-temperature and large-magnetic-field regime, an additional two-fold rotational symmetry (C₂) component superimposed on the primary four-fold rotational symmetry (C₄) in the in-plane magnetoresistance R(φ) is observed, indicating further rotational symmetry breaking of the superconducting state in the Nd_0.8Sr_0.2NiO₂ thin films (Fig. 1d, 1e). The quantitative analysis of the anisotropies in the in-plane magnetoresistance R(φ) indicates that the four-fold rotational symmetry (C₄) and two-fold rotational symmetry (C₂) exhibit different temperature-dependence and opposite magnetic field-dependence, indicating that these two types of anisotropy should have different origins and a competitive relationship modulated by the magnetic field (Fig. 1f, 1g). This result suggests that the two-fold rotational symmetry (C₂) may originate from the stripe charge order fluctuation in the Nd_0.8Sr_0.2NiO₂ films after the suppression of superconductivity by the magnetic field.

Figure 1 (a) Schematic of the Corbino-disk device for in-plane azimuthal (φ) angular dependent magnetoresistance measurements. (b), (c) Azimuthal angular dependent magnetoresistance R(φ) at different temperatures under B = 8 T, showing four-fold rotational symmetry (C₄). (d), (e), Azimuthal angular dependent magnetoresistance R(φ) under B = 16 T, showing an additional two-fold rotational symmetry (C₂) component superimposed on the primary four-fold rotational symmetry (C₄). The light blue area in (d) is a guide to the eye, representing the C₂ anisotropy. (f), (g), Four-fold components ΔR_C4 (f) and two-fold components ΔR_C2 (g) versus the ratio between the averaged magnetoresistance and the normal state resistance (R_avg/ R_N) under different magnetic fields. Here, the values of the C₂ and C₄ components are extracted by the trigonometric function fitting.

Based on the experimental results of in-plane magnetoresistance R(φ) and temperature-dependent in-plane critical field B_c(T), the research group constructed the phase diagram of the infinite-layer nickelate Nd_0.8Sr_0.2NiO₂ thin films (Fig. 2a). This phase diagram reveals two phase transitions characterized by the spontaneous rotational symmetry breakings under the applied in-plane magnetic field. The phase diagram depicts the subtle balance and the intriguing interplay between superconductivity, charge order, antiferromagnetic correlation, and Kondo effect in the system. The first phase transition corresponds to the transition from isotropic superconductivity to four-fold anisotropic (C₄) superconductivity. This transition may be associated with the s-wave superconductivity arising from local spin fluctuations of the Kondo coupling, changing into the d-wave superconductivity favored by the antiferromagnetic coupling enhanced by the magnetic field. The second phase transition involves a further breakdown of the four-fold rotational symmetry (C₄), giving rise to the emergence of two-fold rotational symmetry (C₂). This transition may imply the emergence of stripe charge order fluctuation after the suppression of superconductivity by the magnetic field. Moreover, this phase transition is accompanied by an anomalous upturn of the temperature dependent in-plane critical field, implying the formation of finite momenta Cooper pairs due to the electron pairing in the periodic potential of the charge order, and the consequent secondary pair density wave (PDW) state (or the Fulde-Ferrell-Larkin-Ovchinnikov, FFLO state with broken time-reversal symmetry). This physical scenario has important implications on the general understanding of unconventional superconductivity, multiple competing orders, and novel quantum states in the Nd_0.8Sr_0.2NiO₂ thin films, and provides new insights for investigating the underlying mechanism of unconventional high- T_c superconductivity.

Figure 2 (a) B versus T phase diagram, summarizing the anisotropy of the in-plane magnetoresistance R(φ) and the temperature-dependent in-plane critical magnetic field B_c(T) results. (b)-(e) The representative in-plane magnetoresistance R(φ) at different temperatures and magnetic fields. With increasing magnetic fields, the in-plane magnetoresistance R(φ) manifests a rotational symmetry breaking from isotropy (e), to four-fold rotational symmetry (e), and to a combination of four-fold and two-fold rotational symmetry (b, c). The black arrows in this figure approximately mark the temperature and magnetic field where the R(φ) curves in (b)-(e) are measured.

    Prof. Jian Wang and Prof. Liang Qiao are the corresponding authors. Haoran Ji (graduate student at Peking University), Prof. Yi Liu, Yanan Li (a former joint graduate student at Peking University and The Pennsylvania State University) contributed equally to this work. This work was supported by National Natural Science Foundation of China, National Key Research and Development Program of China, the Strategic Priority Research Program of Chinese Academy of Sciences, Beijing Natural Science Foundation, Young Elite Scientists Sponsorship Program by BAST, the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China, Science and Technology Department of Sichuan Province.