The iron-based superconductors (FeSCs) were first discovered in 2008 with transition temperature (Tc) up to 55 K. Despite some resemblances to the high-Tc cuprates, these materials present a unique case where unconventional superconductivity and other ordering phenomena thrive in a multi-orbital setting.

While FeSCs can have multiple structures, they all share common building blocks of FeX layers (X = As, P, S, Se, Te). These layers are formed by edge-sharing tetrahedrons, with Fe atoms at the tetrahedron centers and X atoms at the corners. Consequently, the degeneracy of five 3d orbitals from iron is lifted under this tetrahedron crystal field and further hybridization. For the undoped case, the six valence electrons will occupy five 3d orbitals for high spin state or selectively occupy four of them with uppermost d_{xy} orbital unoccupied for low spin state. Therefore, under tight binding approximation, this orbital configuration will lead to a multi-Fermi surface, where multiple bands around Fermi level with different symmetries all play important roles. In such multi-orbital setting with onsite spin, more interactions need to be considered, such as the interorbital and intraorbital hopping and repulsion, on-site Hund’s coupling and off-site exchange interactions. With different tuning parameters, the strength of these interactions will vary relatively and the system will develop different long-range orders with a drastic change in electronic structure. Therefore, investigations in momentum and orbital dependency are essential to understand these long-range orders in FeSCs.

The FeSCs problem turned out to be another ideal platform for angle-resolved photoemission(ARPES) studies. Similar to cuprates, the stacked layered structure enables easy in-situ cleavage to expose large flat surfaces. Furthermore, governed by symmetry rules, different polarization states of incident photons will select bands with different orbital symmetry. This enables us to verify the orbital characteristic of bands and selectively trace part of them for evolutionary study. In addition, we also designed an instrument to apply anisotropic strain in-situ for the system, which is crucial for disentangling domain effect and nematic phase studies.

In the following, we summarize our experimental result that provides insights on many critical problems in FeSCs. Current projects include temperature and doping-dependent evolution of electronic structure and possible topological superconductivity and enhancement of Tc in monolayer FeSe. The main goal of these projects is to form a unified picture and explore the pairing mechanism in FeSCs.

## Previous Highlights

### Electron correlation effect in normal state

Normal state serves as a starting point for understanding FeSCs. Even though most FeSCs are generally metallic, the bad metal behavior in transport indicates non-negligible electron-electron correlation effect. This is confirmed by the strong renormalization of bandwidth from our ARPES measurement. After systematically investigating orbital-dependent correlation effect over a wide range of FeSCs, we come to the following summaries:

(1) The bandwidth of all bands systematically narrows from the phosphide to the arsenide to chalcogenide, corresponding to an increasing trend of the renormalization factor;

(2) The bandwidth of d_{xy} narrows at a much faster speed than that of d_{yz} from the phosphides to the chalcogenides;

(3) In iron-chalcogenide, where the electron correlation is much stronger, we find a temperature-induced crossover from the metallic state at low temperature to an orbital-selective Mott phase at high temperatures.

Our experimental observations shows that FeScs host an orbital selective Mott insulating phase, which provides critical information of theoretical modeling of FeSCs.

Reference

[1] D.H. Lu *et al.*, Nature **455**, 81 (2008)

[2] M. Yi *et al.*, PNAS **108**, 6878 (2011)

[3] M. Yi *et al.*, Phys. Rev. Lett. **110**, 067003(2013)

[4] Z.K. Liu *et al.*, Phys. Rev. B **92**, 235138(2015)

[5] M. Yi *et al.*, Npj Quantum Materials, 2:57(2017)

### Evolution of electronic structure across nematic phase transition

Hopping between different orbitals is present in multiple bands near Fermi level. This multiband structure becomes more complicated when symmetry is further broken at the nematic phase transition. In the nematic state, in-plane C4 symmetry degrades to C2 symmetry, leading to the lifting of degeneracy between d_{yz} and d_{xz} orbitals. In spin-density wave state (SDW), translation symmetry is further broken, leading to the folding of Brillouin zone. Therefore, clarifying the evolutions of different bands becomes an important but challenging task. By adopting polarization techniques, we use ARPES to study the complex evolutionary behavior of the system.

Unlike most FeSCs where nematic state arises in a narrow temperature region above the AFM state, undoped bulk FeSe, on the other hand, has a nematic state that remains stable over a wide temperature range in the absence of the AFM state. Therefore, undoped bulk FeSe serves as a great platform for investigating band evolution across the nematic transition. The figure below shows the latest schematic of nematic band reconstruction proposed by M. Yi et al. In tetragonal phase (fig (a)), the degeneracy of d_{xz} and d_{yz} orbitals are protected by C4 symmetry. In the orthomorphic phase, the degeneracy between d_{xz} and d_{yz} bands is lifted with respect to momentum. Near Γ, the d_{xz} hole band shifts up, while the d_{yz} hole band top shifts down to below Ef. However, d_{xz} band is observed to shift downward along the Γ_{1}- M_{Y} path while shifting upward along the M_{Y} - Γ_{2}. Such momentum dependent shift in band degeneracy further indicates the appearance of hybridization between the d_{xz} and d_{yz} orbitals, resulting in a band inversion. The final evolutionary picture is summarized in fig (d) and (e). For a detailed discussion, please refer to ref [1].

More detailed structure of the nematic order parameter is discovered by our group members recently. The nematic order parameter is defined as the energy difference between d_{xz} and d_{yz} bands in ARPES spectrum. H. Pfau et al. investigate bands along Γ-X in both FeSe and BaFe_{2}As_{2} and find the flip of sign of the nematic order parameter along Γ-X. The orbital dependent nature of the nematic order parameter puts strong constraint on the theoretical modeling of FeSCs.

Reference

[1] M. Yi *et al.*, Phys. Rev. X 9, 041049(2019)

[2] H. Pfau *et al.*, Phys. Rev. Lett. 123, 066402(2019)

[3] H. Pfau *et al.*, Phys. Rev. B 99, 035118(2019)

### Dynamical competition between spin-density wave order and superconducting order

One of the central problems for FeSCs is the unconventional pairing mechanism for high-temperature superconductivity. Understanding the relationship between different order parameters will provide clues for pairing symmetry. Therefore, the coexistence of spin-density-wave state and superconducting state in many iron pnictide attracted great interests.

M. Yi et al. carried out ARPES measurement on Ba_{1-x}K_{x}Fe_{2}As_{2}. They adopt the gap size induced by spin-density wave and superconductivity as a measure of the strength of coherent electronic excitations of the corresponding order. Below Neel temperature, the spin-density-wave gap opens and saturates. However, the size of the spin-density-wave gap decreases when the superconducting gap emerges. Therefore, they proposed a competing picture of spin-density wave state and superconducting state. This coexisting and competing mechanism of spin-density-wave state and superconducting state excludes the possibilities for a conventional s++ pairing mechanism.

Reference

[1] M. Yi *et al.*, Nat. Commun., 5:3711(2014)