Two-dimensional (2D) crystalline superconductors are research frontiers of condensed matter physics and materials science. In 2016, Prof. Iwasa at Tokyo university pointed out that quantum Griffiths singularity, anomalous metallic state and superconductivity surviving a large in-plane magnetic field (e.g. Ising superconductivity) are most important topics in the field of 2D crystalline superconductors (Nat. Rev. Mater.2, 16094 (2016)). Ising superconductor is a kind of superconducting system with strong spin-orbit coupling (SOC). It is reported that in transition metal dichalcogenides, such as gated MoS₂and one monolayer (ML) NbSe₂flake, the broken in-plane inversion symmetry gives rise to Zeeman-type SOC, which polarizes the spins of the electrons to the out-of-plane direction and leads to a huge in-plane critical magnetic field much larger than Pauli limit. The Pauli limit is defined as the magnetic field required to destroy the Cooper pairs via the spin pair breaking effect in conventional superconductors. This special superconductivity with strong Zeeman-type SOC is called Ising superconductivity. Because of Zeeman-type SOC and spin polarizations, Ising superconductors exhibit large in-plane critical field up to several times of the Pauli limit, normally corresponding to dozens of Tesla. For the first time, Prof. Jian Wang and collaborators reported the observation of Ising superconductivity inmacro-size monolayer NbSe₂films grown by molecular beam epitaxy (MBE) (Nano Lett.17, 6802 (2017)) and the interface induced Ising superconductivity in ultrathin crystalline Pb films (Phys. Rev. X8, 021002 (2018)).

Moreover, the existence of 2D anomalous metallic state is one of major questions in condensed matter physics. The possible signature of anomalous metallic state has been reported experimentally in various 2D superconducting systems over the past thirty years (Rev. Mod. Phys.91, 11002 (2019)). However, the emergence of anomalous metallic is still under intensive and wide debate due to the external high frequency noise in the measurements (Sci. Adv.5, 3826 (2019)). By performing ultralow temperature transport measurement with high-quality filters, Prof. Jian Wang and collaborators demonstrated the existence of anomalous metallic state in high temperature superconducting YBCO films with triangular array of holes (Science366, 1505(2019)). However, the solid evidence of anomalous metallic state has not been reported in high-quality crystalline films grown by MBE.

Recently, Prof. Jian Wang and Prof. Xi Lin at Peking University, in collaboration with Prof. Qi-Kun Xue, Prof. Lili Wang, Prof. Yong Xu, Prof. Hong Yao at Tsinghua University, Prof. Haiwen Liu at Beijing Normal University detected anomalous metallic state and a new kind of Ising superconductivity in 2D crystalline PdTe₂films grown by MBE. The systematic ultralow temperature transport measurement shows that 6-ML (around 3 nm) PdTe₂film exhibits a large in-plane critical field more than 7 times of the Pauli limit, which is the characteristic of Ising superconductivity. Different from the previously reported Ising superconductors, the PdTe₂film keeps the in-plane inversion symmetry, which indicates that there exists a new mechanism of Ising superconductivity (named type-II Ising superconductivity by Prof. Jian Wang in discussion with Prof. Yong Xu). Band structure calculation and theoretical analysis reveal that the 3-fold rotational symmetry in the PdTe₂films makes the effective magnetic field of SOC along the out-of-plane direction and leads to the out-of-plane spin polarization. The superconducting Cooper pairs formed by the electrons with out-of-plane spin polarization can survive under very large magnetic field parallel to the 2D system, which gives rise to the type-II Ising superconductivity with large in-plane critical field. Theoretical calculations indicate that for 2D superconducting systems with in-plane inversion symmetry, 4 and 6-fold rotational symmetry can also make the orientation of the effective SOC field to out-of-plane. Thus, the type-II Ising superconductivity can be generalized to various 2D systems with 3, 4 and 6-fold rotational symmetry. Therefore, the discovery of type-II Ising superconductivity is promising to stimulate a new research direction in the condensed matter physics.

Interestingly, under perpendicular magnetic field, the resistance of PdTe₂films drops and then saturates to a temperature-independent constant with decreasing temperature via ultralow temperature transport measurements with high-quality filters. It is the first solid experimental evidence of anomalous metallic states in high-quality 2D crystalline films grown by MBE, which further reveals that besides superconducting and insulating ground states, anomalous metallic state is another quantum ground state for 2D Bosonic systems. Moreover, most 2D superconducting systems are very sensitive to the atmosphere and easy to lose superconductivity. The superconductivity of PdTe₂films remains almost the same for more than 20 months without any protection layer. This macro-size ambient-stable superconducting system with strong SOC shows great potentials in superconducting electronic and spintronic applications.

Figure (a) The temperature dependence of in-plane critical fields of PdTe₂film, which is consistent with the theoretical formula of Ising superconductivity. The inset on the bottom left: the lattice structure of PdTe₂, indicating that it is a centrosymmetric system, different from the previously reported Ising superconductors. The inset on the top right: the schematic of type-II Ising pairing. (b) The lgR_S-1/T curves of PdTe₂film at different magnetic fields. The resistance drops and then saturates with decreasing temperature, which is the hallmark of anomalous metallic states. High quality filters are used in the measurements to well exclude the influence of high-frequency noise.

The paper was published online byNano Letterson June 25, 2020. (DOI: 10.1021/acs.nanolett.0c01356):https://pubs.acs.org/doi/full/10.1021/acs.nanolett.0c01356

Prof. Jian Wang at Peking University, Prof. Lili Wang at Tsinghua University and Prof. Xi Lin at Peking University are corresponding authors of this paper. Dr. Yi Liu at Peking University, Prof. Yong Xu at Tsinghua University, Jian Sun at Peking University and Dr. Chong Liu at Tsinghua University contributed equally to this work. Other collaborators include Prof. Qi-Kun Xue and Prof. Hong Yao at Tsinghua University, Prof. Haiwen Liu at Beijing Normal University etc.

This work was financially supported by the National Key Research and Development Program of China, the National Natural Science Foundation of China, the Strategic Priority Research Program of Chinese Academy of Sciences, the Beijing Natural Science Foundation, the Beijing Advanced Innovation Center for Future Chip and the China Postdoctoral Science Foundation.