The most essential feature of the superconducting state is the existence of pairs between electrons, and the pairing characteristic of pairing is an important window for understanding the microscopic mechanism of superconductivity. According to the different symmetries, the superconducting state can be divided into s-wave, p-wave, d-wave and so on. In the traditional theory, the p-wave paired superconducting state becomes a well-known topological superconductor due to its non-mediocre topology, but if the electron pairing inside a superconductor is an isotropic s-wave, the traditional theory holds that the superconducting state will not have non-mediocre topological properties.
Since the discovery of iron-based high-temperature superconductors in 2008, their electronic pairing characteristics have been controversial. Although there is strong experimental evidence to support that pairing is isotropic swave, due to the strong electron association in iron-based high-temperature superconductors, the theory predicts that different types of s waves can exist, and the symbolic distribution of their superconducting sequence parameters in the momentum space can be different.
Taking the monolayer FeSe/STiO as an example, although the system has the simplest lattice and electronic structure among iron-based superconductors, according to the symbols of the superconducting sequence parameters on its Fermi surface, it is considered that there are three possibilities for pairing symmetry (Figure 1): a nodeless d-wave superconducting state, a signed inverted wave superconducting state, and an unsigned inverted S-wave superconducting state. For the d wave state and the s wave state, because their superconducting sequence parameters have different transformation properties under symmetry operation, they can be distinguished by the Josephson junction experiment similar to that in copper-based superconductors; the wave state and the s wave state have exactly the same symmetry, which poses a huge challenge to how to distinguish these two superconducting states experimentally.
Figure 1: The Fermi surface of a monolayer FeSe/STiO and its possible superconductivity pairing symmetry, taking into account spin orbit coupling. where (a) corresponds to d-wave symmetry (the state is nodeless only if the superconducting sequence parameter is much greater than the coupling intensity of the system's spin orbit), (b) corresponds to wave symmetry, and (c) is ordinary s-wave symmetry. The blue and red symbols representing the superconducting order parameters on the Fermi surface are different.
Recently, Researchers Hu Jiangping and Fang Chen of the Laboratory of Condensed Matter Theory and Materials Calculation of the Institute of Physics of the Chinese Academy of Sciences/Beijing National Research Center for Condensed Matter Physics, together with Professor Zhang Fuchun and Postdoctoral Fellow Qin Shengshan of the Caffrey Institute of Theoretical Sciences of the University of Chinese Academy of Sciences (formerly doctoral students of the Institute of Physics), proposed that topological properties can be used to conclusively identify the symmetry of different s-wave pairs of iron-based superconductors.
As early as 2014, Hu Jiangping's research group theoretically predicted the existence of non-mediocre topological energy bands in iron-based superconductors, and this prediction has been confirmed by a large number of experiments in recent years, but in these past studies, the topological properties of iron-based superconductors have been limited to the surface state caused by their non-mediocre topological energy bands, and cannot be associated with the pairing properties of iron-based superconductors. In addition, Hu Jiangping's research group pointed out in a 2012 study that nonsymmorphic lattice structures of iron-based superconductors can trigger non-traditional superconductive pairing symmetry.
Recent work has further found that due to the non-point lattice structure, there is a special band degeneracy at the boundary of the Brillouin region, resulting in different s-wave superconductor pairing symmetries of iron-based superconductors having completely different topological properties. Specifically, the s wave state in Figure 1 is topologically mediocre, while the wave state is a second-order topological superconducting state protected by lattice symmetry. This is the first proposed intrinsic high-order topological superconductivity in an actual material system. They predict that if the monolayer FeSe/STiO is a wave state, then there will be two symmetry-protected Dirac cones on its (10) boundary (the boundary is composed of the nearest neighbor's Fe-Se-Fe), and a pair of Majorana zero-energy modules on its angles of (11) and (11) (right angles composed of the nearest neighbor Fe-Fe), as shown in Figure 2. The above conclusions also apply to other iron-based superconductors. The boundary state of the Dirac cone and the Majorana zero-energy mode located on the angle can be directly observed by methods such as STM.
Figure 2: (a) a schematic of the lattice structure of a monolayer FeSe, and (b) an electronic structure of a monolayer FeSe when considering spin orbit coupling. When the symmetry of a monolayer FeSe pair is a wave, there are two Dirac cones on the boundary formed by the nearest neighbor Fe-Se-Fe, as shown in (c); and a pair of Majorana zero energy modules at the right angle formed by the nearest neighbor Fe-Fe, as shown in (d).
The work provides a conclusive experimental observational measurement to distinguish between paired symmetries of iron-based superconductors, and lays the theoretical basis for future searches for inversion symmetry (inversion symmetric) topological superconductors: if the paired symmetry of topological superconductors is swave, then its lattice structure must be non-point, and iron-based superconductors are just one such example.
After the work was submitted to arXiv last year, it received special attention from international peers, and Postdoc Qin Shengshan received an invitation from the American Physical Society in November last year to make an invitation to report on the work at the upcoming annual meeting in March this year.
This research was funded by the Ministry of Science and Technology, the National Natural Science Foundation of China, and the Pilot Project of the Chinese Academy of Sciences. Article published in Physical Review X 12, 011030 (2022).
Edit: Fun Superman