Angle-resolved photoemission spectroscopy (ARPES) has played an important role in determining the band structure and the superconducting gap structure of iron-based superconductors. In this paper, from the ARPES perspective, we briefly review the main results from our group in recent years on the iron-based superconductors and their parent compounds, and depict our current understanding on the antiferromagnetism and superconductivity in these materials.

Our recent scanning tunneling microscopy (STM) studies of the NaFe_1-xCo_xAs phase diagram over a wide range of dopings and temperatures are reviewed. Similar to the high-T_c cuprates, the iron-based superconductors lie in close proximity to a magnetically ordered phase. Therefore, it is widely believed that magnetic interactions or fluctuations play an important role in triggering their Cooper pairings. Among the key issues regarding the electronic phase diagram are the properties of the parent spin density wave (SDW) phase and the superconducting (SC) phase, as well as the interplay between them. The NaFe_1-xCo_xAs is an ideal system for resolving these issues due to its rich electronic phases and the charge-neutral cleaved surface. In our recent work, we directly observed the SDW gap in the parent state, and it exhibits unconventional features that are incompatible with the simple Fermi surface nesting picture. The optimally doped sample has a single SC gap, but in the underdoped regime we directly viewed the microscopic coexistence of the SDW and SC orders, which compete with each other. In the overdoped regime we observed a novel pseudogap-like feature that coexists with superconductivity in the ground state, persists well into the normal state, and shows great spatial variations.The rich electronic structures across the phase diagram of NaFe_1-xCo_xAs revealed here shed important new light for defining microscopic models of the iron-based superconductors. In particular, we argue that both the itinerant electrons and local moments should be considered on an equal footing in a realistic model.

The newly discovered iron-based superconductors have triggered renewed enormous research interest in the condensed matter physics community. Nuclear magnetic resonance (NMR) is a low-energy local probe for studying strongly correlated electrons, and particularly important for high-T_C superconductors. In this paper, we review NMR studies on the structural transition, antiferromagnetic order, spin fluctuations, and superconducting properties of several iron-based high-T_C superconductors, including LaFeAsO_1-xF_x, LaFeAsO_1-x, BaFe₂As₂, Ba_1-xK_xFe₂As₂, Ca_0.23Na_0.67Fe₂As₂, BaFe₂(As_1-xP_x)₂, Ba(Fe_1-xRu_x)₂As₂, Ba(Fe_1-xCo_x)₂As₂, Li_1+xFeAs, LiFe_1-xCo_xAs, NaFeAs, NaFe_1-xCo_xAs, K_yFe_2-xSe₂, and (Tl,Rb)_yFe_2-xSe₂.

Crystal structures and microstructural features, such as structural phase transitions, defect structures, and chemical and structural inhomogeneities, are known to have profound effects on the physical properties of superconducting materials. Recently, many studies on the structural properties of Fe-based high-T_c superconductors have been published. This review article will mainly focus on the typical microstructural features in samples that have been well characterized by physical measurements. (i) Certain common structural features are discussed, in particular, the crystal structural features for different superconducting families, the local structural distortions in the Fe₂Pn₂ (Pn=P, As, Sb) or Fe₂Ch₂ (Ch=S, Se, Te) blocks, and the structural transformations in the 122 system. (ii) In FeTe(Se) (11 family), the superconductivity, chemical and structural inhomogeneities are investigated and discussed in correlation with superconductivity. (iii) In the K_0.8Fe_1,6+xSe₂ system, we focus on the typical compounds with emphasis on the Fe-vacancy order and phase separations. The microstructural features in other superconducting materials are also briefly discussed.

The recent discovery of high-temperature superconductivity in iron-based pnictides (chalcogenides) not only triggers tremendous enthusiasm in searching for new superconducting materials, but also opens a new avenue to the study of the Kondo physics. CeFeAsO is a parent compound of the 1111-type iron-based superconductors. It shows 3d-antiferromagnetic (AFM) ordering below ～139 K and 4f-AFM ordering below ～4 K. On the other hand, the phosphide CeFePO is a ferromagnetically correlated heavy-fermion (HF) metal with Kondo scale T_K～10 K. These properties set up a new platform for research of the interplay among magnetism, Kondo effect, and superconductivity (SC). In this review, we present the recent progress in the study of chemical pressure effect in CeFeAsO_1-yF_y (y=0 and 0.05). This P/As-doping in CeFeAsO serves as an effective controlling parameter which leads to two magnetic critical points, x_c1≈0.4 and x_c2≈0.92, associated with suppression of 3d and 4f magnetism, respectively. We also observe a turning point of AFM-FM ordering of Ce³⁺ moment at x_c3≈0.37. The SC is absent in the phase diagram, which is attributed to the destruction to Cooper pair by Ce-FM fluctuations in the vicinity of x_c1. We continue to investigate CeFeAs_1-xP_xO_0.95F_0.05. With the separation of x_c1 and x_c3, this chemical pressure results in a broad SC region 0≤x≤q 0.53, while the original HF behavior is driven away by 5% F^- doping. Different roles of P and F dopings are addressed, and the interplay between SC and Ce-4f magnetism is also discussed.

Neutron scattering, with its ability to measure the crystal structure, the magnetic order, and the structural and magnetic excitations, plays an active role in investigating various families of Fe-based high-T_c superconductors. Three different types of antiferromagnetic orders have been discovered in the Fe plane, but two of them cannot be explained by the spin-densitywave (SDW) mechanism of nesting Fermi surfaces. Noticing the close relation between antiferromagnetic order and lattice distortion in orbital ordering from previous studies on manganites and other oxides, we have advocated orbital ordering as the underlying common mechanism for the structural and antiferromagnetic transitions in the 1111, 122, and 11 parent compounds. We observe the coexistence of antiferromagnetic order and superconductivity in the (Ba,K)Fe₂As₂ system, when its phase separation is generally accepted. Optimal T_c is proposed to be controlled by the local FeAs₄ tetrahedron from our investigation on the 1111 materials. The Bloch phase coherence of the Fermi liquid is found crucial to the occurrence of bulk superconductivity in iron chalcogenides of both the 11 and the 245 families. Iron chalcogenides carry a larger staggered magnetic moment (> 2 μ_B/Fe) than that in iron pnictides (< 1μ_B/Fe) in the antiferromagnetic order. Normal state magnetic excitations in the 11 superconductor are of the itinerant nature while in the 245 superconductor the spin-waves of localized moments. The observation of superconducting resonance peak provides a crucial piece of information in current deliberation of the pairing symmetry in Fe-based superconductors.

The iron-based superconductivity (IBSC) is a great challenge in correlated system. Angle-resolved photoemission spectroscopy (ARPES) provides electronic structure of the IBSCs, the pairing strength, and the order parameter symmetry. Here, we briefly review the recent progress in IBSCs and focus on the results from ARPES. The ARPES study shows the electronic structure of "122", "111", "11", and "122^*" families of IBSCs. It has been agreed that the IBSCs are unconventional superconductors in strong coupling region. The order parameter symmetry basically follows s_± form with considerable out-of-plane contribution.

In this article, we review the recent theoretical works on the spin fluctuations and superconductivity in iron-based superconductors. Using the fluctuation exchange approximation and multi-orbital tight-binding models, we study the characteristics of the spin fluctuations and the symmetries of the superconducting gaps for different iron-based superconductors. We explore the systems with both electron-like and hole-like Fermi surfaces (FS) and the systems with only the electron-like FS. We argue that the spin-fluctuation theories are successful in explaining at least the essential part of the problems, indicating that the spin fluctuation is the common origin of superconductivity in iron-based superconductors.

Our recent progress on the preparation of a series of new FeSe-based superconductors and the clarification of SC phases in potassium-intercalated iron selenides are reviewed here. By the liquid ammonia method, metals Li, Na, Ca, Sr, Ba, Eu, and Yb are intercalated in between FeSe layers and form superconductors with transition temperatures of 30 K～46 K, which cannot be obtained by high-temperature routes. In the potassium-intercalated iron selenides, we demonstrate that at least two SC phases exist, K_xFe₂Se₂(NH₃)_y (x ≈ 0.3 and 0.6), determined mainly by the concentration of potassium. NH₃ has little, if any, effect on superconductivity, but plays an important role in stabilizing the structures. All these results provide a new starting point for studying the intrinsic properties of this family of superconductors, especially for their particular electronic structures.

In this short overview, we summarize the optical spectroscopy studies on iron selenide superconducting systems FeTe_1-xSe_x and A_xFe_2-ySe₂. We elaborate that optical spectroscopy measurements yield fruitful information about the band structure evolution across the AFM phase transition temperature, the electronic correlation effect, the superconducting pairing energy gap, the condensed carrier density or penetration depth, the inhomogeneity and the nanoscale phase separation between superconductivity and antiferromagnetism in those systems.

The second class of high-temperature superconductors (HTSCs), iron-based pnictides and chalcogenides, necessarily contain Fe₂X₂ ("X" refers to a pnictogen or a chalcogen element) layers, just like the first class of HTSCs which possess the essential CuO₂ sheets. So far, dozens of iron-based HTSCs, classified into nine groups, have been discovered. In this article, the crystal-chemistry aspects of the known iron-based superconductors are reviewed and summarized by employing "hard and soft acids and bases (HSAB)" concept. Based on these understandings, we propose an alternative route to exploring new iron-based superconductors via rational structural design.

Our recent progress in the fabrication of FeSe and K_xFe_2-ySe₂ ultra thin films and the understanding of their superconductivity properties is reviewed. The growth of high-quality FeSe and K_xFe_2-ySe₂ films is achieved in a well controlled manner by molecular beam epitaxy. The high-quality stoichiometric and superconducting crystalline thin films allow us to investigate the intrinsic superconductivity properties and the interplay between the superconductivity and the film thickness, the local structure, the substrate, and magnetism. In situ low-temperature scanning tunneling spectra reveal the nodes and the twofold symmetry in FeSe, high-temperature superconductivity at the FeSe/SrTiO₃ interface, phase separation and magnetic order in K_xFe_2-ySe₂, and the suppression of superconductivity by twin boundaries and Fe vacancies. Our findings not only provide fundamental information for understanding the mechanism of unconventional superconductivity, but also demonstrate a powerful way of engineering superconductors and raising the transition temperature.

In this article, we briefly review spin, charge, and orbital orderings in iron-based superconductors, as well as the multi-orbital models. The interplay of spin, charge, and orbital orderings is a key to understand the high temperature superconductivity. As an illustration, we use the two-orbital model to show the spin and charge orderings in iron-based superconductors based on the mean-field approximation in real space. The typical spin and charge orderings are shown by choosing appropriate parameters, which are in good agreement with experiments. We also show the effect of Fe vacancies, which can introduce the nematic phase and interesting magnetic ground states. The orbital ordering is also discussed in iron-based superconductors. It is found that disorder may play a role to produce the superconductivity.

Electron-phonon coupling (EPC) in cuprate and iron-based superconducting systems, as revealed by Raman scattering, is briefly reviewed. We introduce how to extract the coupling information through phonon lineshape. Then we discuss the strength of EPC in different high-temperature superconductor (HTSC) systems and possible factors affecting the strength. A comparative study between Raman phonon theories and experiments allows us to gain insight into some crucial electronic properties, especially superconductivity. Finally, we summarize and compare EPC in the two existing HTSC systems, and discuss what role it may play in the HTSC.

Iron-chalcogenide compounds with FeSe(Te, S) layers did not attract much attention until the discovery of high-T_c superconductivity (SC) in the iron-pnictide compounds at the begining of 2008. Compared with FeAs-based superconductors, iron-chalcogenide superconductors have aroused enormous enthusiasm to study the relationship between SC and magnetisms with several distinct features, such as different antiferromagnetic ground states with relatively large moments in the parents, indicating possibly different superconducting mechanisms, the existence of the excess Fe atoms or Fe vacancies in the crystal lattice. Another reason is that the large single crystals are easily grown for the iron-chalcogenide compounds. This review will focus on our exploration for the iron-chalcogenide superconductors and discussion on several issues, including the crystal structure, magnetic properties, superconductivity, and phase separation. Some of them reach a consensus but some important questions still remain to be answered.