Unconventional superconductivity often emerges in quantum materials which host strong interactions between electrons, especially when a magnetic transition can be tuned to zero-temperature at a quantum critical point. This association between magnetism and superconductivity motivated the long-standing view that magnetic fluctuations function as the “glue” that binds electrons into pairs, giving rise to superconductivity. However, the microscopic origin of this type of unconventional superconductivity remains one of the central unsolved problems in physics. Discovering new superconductors and comparing their phase diagrams is essential for identifying the universal features and underlying mechanisms that drive them.
In many families of unconventional superconductors, including many heavy-fermion superconductors, as well as the high-temperature copper-oxide and iron-based superconductors, the superconductivity develops in close proximity to an antiferromagnetic phase. In some heavy-fermion materials however, superconductivity is well-separated from antiferromagnetic quantum criticality in the phase diagram. A notable example is CeCu 2 Si 2 , where two superconducting regions emerge when pressure is applied: a low-pressure superconducting phase near an antiferromagnetic quantum critical point and a high-pressure phase that has been linked to fluctuations of the valence state of the cerium 4f electrons (Science 302, 2104 (2003)).
Superconductivity associated with ferromagnetism is much less common. In many clean metallic ferromagnets, applying pressure does not continuously suppress a ferromagnetic transition to a quantum critical point, but instead, there is either a change from ferromagnetism to another magnetic ground state (such as antiferromagnetism) or the ferromagnetism disappears abruptly at a first-order transition. In a few uranium-based heavy-fermion compounds, superconductivity can coexist with weak ferromagnetism near such first-order boundaries. In 2020, Prof. Huiqiu Yuan’s team at Zhejiang University reported a pressure-induced ferromagnetic quantum critical point in the clean ferromagnetic heavy-fermion compound CeRh 6 Ge 4 , which occurs together with strange-metal behavior (Nature 579, 51 (2020)). However, superconductivity has not yet been observed near ferromagnetic quantum criticality, but it is possible that a ferromagnetic quantum critical superconductor, potentially with spin-triplet pairing, could still be found.
Recently, Prof. Yuan’s group at the Center for Correlated Matter at Zhejiang University have made new strides towards that goal by uncovering an unexpected scenario for superconductivity in the heavy-fermion ferromagnet Ce 5 CoGe 2 . Ce 5 CoGe 2 exhibits ferromagnetic order at ambient pressure below the Curie temperature T c = 10.9 K, which occurs together with cluster spin-glass behavior (Phys. Rev. B 110, 144432 (2024)).
By tracking the low-temperature resistivity, specific heat, and magnetization under pressure, the team mapped out a pressure–temperature phase diagram that exhibits multiple electronic phases in a single material. As the applied pressure is increased, the ground state changes from ferromagnetic to antiferromagnetic when around 1.2 GPa of pressure is applied. The antiferromagnetic order is then further suppressed, reaching an antiferromagnetic quantum critical point near 3.2 GPa. Around this critical pressure, the electrical resistivity shows a nearly linear temperature dependence, which is a signature of strange metal behavior that has been observed in various classes of strongly correlated materials.
The most striking finding appears at higher pressures, where superconductivity emerges above about 5 GPa, and is therefore clearly separated from the antiferromagnetic quantum critical point. This separation contrasts with the typical scenario for heavy-fermion superconductors, where superconductivity is generally most robust in region near to where magnetism is suppressed, which establishes Ce 5 CoGe 2 as hosting a particularly unusual phase diagram.
Additional measurements support an unconventional superconducting state. The upper critical field, which is the magnetic field that must to applied to suppress superconductivity, exceeds the weak-coupling Pauli limit, and analysis indicates that the superconductivity emerges from a strongly correlated normal state in which the charge carriers have an enhanced effective mass. Notably, even though the effective mass decreases rapidly with increasing pressure, at lower pressures where superconductivity first emerges it remains comparable to that of established heavy-fermion superconductors.
Taken together, these results suggest that superconductivity in Ce 5 CoGe 2 may not be driven primarily by magnetic fluctuations at a quantum critical point. Other ingredients may also be relevant; for example, the authors note that Ce 4f valence fluctuations are one possible route discussed for the high-pressure superconducting region of CeCu 2 Si 2 . The team emphasize that further experiments will be needed to determine the superconducting order parameter and to identify the dominant pairing mechanism.
Overall, Ce 5 CoGe 2 provides a new experimental platform for exploring how superconductivity can emerge in the phase diagrams of strongly correlated materials, in which ferromagnetism gives way to antiferromagnetism before magnetic order disappears at a quantum critical point, while superconductivity develops only at higher pressures. Such a distinct phase diagram offers fresh opportunities to test competing ideas about unconventional superconductivity and the microscopic mechanisms that may enable it.
About Zhejiang University Center for Correlated Matter
The Center for Correlated Matter (CCM) was established in 2012 by Zhejiang University. Prof. Frank Steglich, the discoverer of heavy fermion superconductivity and an Emeritus Director of the Max-Planck Institute for Chemical Physics of Solids in Germany, was appointed as the founding director of the CCM. Its mission is to become a competitive center both nationally and internationally for performing fundamental research into the physics of correlated matter. The CCM is dedicated to scientific research at the frontiers of correlated matter. Special attention is paid to the emergent quantum phases and concomitant phenomena, arising from tunable many body electron interactions. Current research interests at the center include heavy fermion physics, unconventional superconductivity, quantum phase transitions, Kondo-lattice and mixed-valence behavior, spin liquids and Mott transitions. We synthesize and search for new correlated systems, and measure various physical quantities under multiple extreme conditions of low temperatures, high pressure and high magnetic fields. We also employ a variety of state-of-the-art techniques, including a range of spectroscopic methods such as ARPES, neutron and x-ray scattering, PCS and STM. The experimental findings are complemented by the exploration of their complex properties via theoretical models and numerical simulations. At the center, experimentalists and theorists work closely together to identify, probe and unravel the challenges of correlated matter.
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