Electronic Structure Investigation of 12442 Iron-Based Superconductors Based on Block-Layer Model

Superconducting transition temperature(Tc),as a crucial parameter,exploring its relationship with various macroscopic and microscopic factors helps to understand the mechanism of high-temperature superconductivity from multiple perspectives,aiding in a multidimensional comprehension of high-temperature superconductivity mechanisms.Drawing inspiration from the block-layer structure models of cuprate superconductors,we computationally investigated the interlayer interaction energies in the 12442-type iron-based superconducting materials AkCa_(2)Fe_(4)As_(4)F_(2)(Ak=K,Rb,Cs)systems based on the block-layer model and explored their relationship with Tc.We observed that an increase in interlayer combinative energy leads to a decrease in Tc,while conversely,a decrease in interlayer combination energy results in an increase in Tc.Further,we found that the contribution of the Fe 3d band structure,especially the 3dz2 orbital,to charge transfer is significant.

Crystal chemistry and structural design of iron-based superconductors

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.

Angle-resolved photoemission spectroscopy study on iron-based superconductors

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.

Common Electronic Features and Electronic Nematicity in Parent Compounds of Iron-Based Superconductors and FeSe/SrTiO_3 Films Revealed by Angle-Resolved Photoemission Spectroscopy

We report comprehensive angle-resolved photoemission investigations on the electronic structures and nematicity of the parent compounds of the iron-based superconductors including CeFeAsO, BaFe2As2, NaFeAs, FeSe and undoped FeSe/SrTiO3 films with 1, 2 and 20 layers. While the electronic structure near tile Brillouin zone center F varies dramatically among different materials, the electronic structure near the Brillouin zone corners （M points）, as well as their temperature dependence, are rather similar. The electronic structure near the zone corners is dominated by the electronic nematicity that gives rise to a band splitting of the dxz and dyz bands below the nematie transition temperature. A clear relation is observed between the band splitting magnitude arid the onset temperature of nematicity. Our results may shed light on the origin of nematicity, its effect on the electronic structures, and its relation with superconductivity in the iron-based superconductors.

Review of nuclear magnetic resonance studies on iron-based superconductors

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-Tc superconductors. In this paper, we review NMR studies on the structural transition, antiferromagnetic order, spin fluctuations, and superconducting properties of several iron-based high-Tc superconductors, including LaFeAsOl_xFx, LaFeAsOl_x, BaFe2As2, Bal_xKxFe2As2, Cao.23Nao.67Fe2As2, BaFe2（Asl_xPx）2, Ba（Fel_xRux）2As2, Ba（Fel_xCox）2As2, Lil＋xFeAs, LiFel_xCoxAs, NaFeAs, NaFel_xCoxAs, KyFe2_xSe2, and （T1,Rb）yFe2_xSe2.

Exploring Majorana zero modes in iron-based superconductors

Majorana zero modes(MZMs) are Majorana-fermion-like quasiparticles existing in crystals or hybrid platforms with topologically non-trivial electronic structures. They obey non-Abelian braiding statistics and are considered promising to realize topological quantum computing. Discovery of MZM in the vortices of the iron-based superconductors(IBSs)has recently fueled the Majorana research in a way which not only removes the material barrier requiring construction of complicated hybrid artificial structures, but also enables observation of pure MZMs under higher temperatures. So far,MZMs have been observed in iron-based superconductors including FeTe_(0.55)Se_(0.45),(Li_(0.84)Fe_(0.16))OHFe Se, Ca KFe_(4)As_(4),and Li Fe As. In this topical review, we present an overview of the recent STM studies on the MZMs in IBSs. We start with the observation of MZMs in the vortices in FeTe_(0.55)Se_(0.45)and discuss the pros and cons of FeTe_(0.55)Se_(0.45) compared with other platforms. We then review the following up discovery of MZMs in vortices of Ca KFe_(4)As_(4), impurity-assisted vortices of Li Fe As, and quantum anomalous vortices in FeTe_(0.55)Se_(0.45), illustrating the pathway of the developments of MZM research in IBSs. Finally, we give perspective on future experimental works in this field.

Doping Induced Gap Anisotropy in Iron-Based Superconductors:a Point-Contact Andreev Reflection Study of BaFe2-xNixAs2 Single Crystals

We report a systematic investigation on c-axis point-contact Andreev reflection （PCAR） in BaFe2-xNixAs2 superconducting single crystals from underdoped to overdoped regions （0.075≤ x ≤0.15）. At low temperatures, an in-gap sharp peak at low-bias voltage is observed in PCAR for overdoped samples, in contrast to the case of underdoped junctions, in which an in-gap plateau is observed. The variety of the conductance spectra with doping can be well described by using a generalized Blonder-Tinkham-Klapwijk formalism with an angle-dependent gap. This gap shows a clear crossover from a nodeless in the underdoped side to a nodal feature in the overdoped region. This result provides evidence of the doping-induced evolution of the superconducting order parameter when the inter-pocket and intra-pocket scattering are tuned through doping, as expected in the s± scenario.

Photoemission study of iron-based superconductor

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.

Spin, charge, and orbital orderings in iron-based superconductors

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.

Josephson vortices and intrinsic Josephson junctions in the layered iron-based superconductor Ca_(10)(Pt_(3)As_(8))((Fe_(0.9)Pt_(0.1))_(2)As_(2))_(5)

Modulated electronic state due to the layered crystal structures brings about moderate anisotropy of superconductivity in the iron-based superconductors and thus Abrikosov vortices are expected in the mixed state.However,based on the angular and temperature dependent transport measurements in iron-based superconductor Ca_(10)(Pt_(3)As_(8))((Fe_(0.9)Pt_(0.1))_(2)As_(2))_(5) with Tc(≌)12 K,we find clear evidences of a crossover from Abrikosov vortices to Josephson vortices at a crossover temperature T*(≌)7 K,when the applied magnetic field is parallel to the superconducting FeAs layers,i.e.,the angle between the magnetic field and the FeAs layers θ=0°.This crossover to Josephson vortices is demonstrated by an abnormal decrease(increase)of the critical current(flux-flow resistance)below T*,in contrast to the increase(decrease)of the critical current(flux-flow resistance)above T* expected for Abrikosov vortices.Furthermore,when θ is larger than 0.5°,the flux-flow resistance and critical current have no anomalous behaviors across T*.These anomalous behaviors can be understood in terms of the distinct transition from the well-pinned Abrikosov vortices to the weakly-pinned Josephson vortices upon cooling,when the coherent length perpendicular to the FeAs layers ξ⊥ becomes shorter than half of the interlayer distance d/2.These experimental findings indicate the existence of intrinsic Josephson junctions below T* and thus quasi-two-dimensional superconductivity in Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5,similar to those in the cuprate superconductors.

Hybrid crystals of cuprates and iron-based superconductors

We propose two possible new compounds, Ba2CuO2Fe2As2and K2CuO2Fe2Se2, which hybridize the building blocks of two high temperature superconductors, cuprates and iron-based superconductors. These compounds consist of square CuO2 layers and antifluorite-type Fe2X2（X = As, Se） layers separated by Ba/K. The calculations of binding energies and phonon spectra indicate that they are dynamically stable, which ensures that they may be experimentally synthesized. The Fermi surfaces and electronic structures of the two compounds inherit the characteristics of both cuprates and iron-based superconductors. These compounds can be superconductors with intriguing physical properties to help to determine the pairing mechanisms of high Tc superconductivity.

Thermal fluctuation conductivity and dimensionality in iron-based superconductors

The time-dependent Ginzburg–Landau Lawrence–Doniach model is used to investigate the superconducting fluctuation electrical conductivities.The theoretical result based on the self-consistent Gaussian approximation is used to fit the transport measurement data of iron-based superconductors F-doped La OFe As and Ba Fe_（2-x）Ni_xAs_2.We demonstrate that La OFe As shows layered behavior,while Ba Fe_（2-x）Ni_xAs_2 is more of a 3D feature.The conductivity in the region near Tc is well described by the theoretical formula.

Electronic structure and spatial inhomogeneity of iron-based superconductor FeS

Iron-based superconductor family FeX(X=S,Se,Te)has been one of the research foci in physics and material science due to their record-breaking superconducting temperature(FeSe film)and rich physical phenomena.Recently,FeS,the least studied Fe X compound(due to the difficulty in synthesizing high quality macroscopic crystals)attracted much attention because of its puzzling superconducting pairing symmetry.In this work,combining scanning tunneling microscopy and angle resolved photoemission spectroscopy(ARPES)with sub-micron spatial resolution,we investigate the intrinsic electronic structures of superconducting FeS from individual single crystalline domains.Unlike FeTe or FeSe,FeS remains identical tetragonal structure from room temperature down to 5 K,and the band structures observed can be well reproduced by our ab-initio calculations.Remarkably,mixed with the 1×1 tetragonal metallic phase,we also observe the coexistence of √5×√5 reconstructed insulating phase in the crystal,which not only helps explain the unusual properties of FeS,but also demonstrates the importance of using spatially resolved experimental tools in the study of this compound.

Microstructure and structural phase transitions in iron-based superconductors

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-Tc 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 FeeCh2 （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 Ko.sFe1.6＋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.

Spin fluctuations and unconventional superconducting pairing in iron-based superconductors

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 char- acteristics 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.

Electron-phonon coupling in cuprate and iron-based superconductors revealed by Raman scattering

Electron-phonon coupling （EPC） in cuprate and iron-based superconducting systems, as revealed by Raman scat- tering, 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.

Crystal structures and sign reversal Hall resistivities in iron-based superconductors Lix(C3H10N2)0.32FeSe（0.15

Heavy electron-doped FeSe-derived materials have attracted attention due to their uncommon electronic structures with only ‘electron pockets’, and they are different from other iron-based superconductors. Here, we report the crystal structures, superconductivities and normal state properties of two new Li-doped FeSe-based materials, i.e.,Li0.15(C3H10N2)0.32 FeSe(P-4) and Lix(C3H10N2)0.32 FeSe(P4/nmm, 0.25 < x < 0.4) with superconducting transition temperatures ranging from 40 K to 46 K. The determined crystal structures reveal a coupling between Li concentration and the orientation of 1,3-diaminopropane molecules within the largely expanded FeSe layers. Superconducting fluctuations appear in the resistivity of the two superconductors and are fitted in terms of the quasi two-dimensional(2 D) Lawrence–Doniach model. The existence of a crossing point and scaling behavior in the T-dependence of diamagnetic response also suggests that the two superconductors belong to the quasi-2 D system. Interestingly, with the increase of temperature, a sign of Hall coefficient(RH) reversing from negative to positive is observed at ~185 K in both phases, suggesting that‘hole pockets’ emerge in these electron-doped FeSe materials. First principle calculations indicate that the increase in FeSe layer distance will lift up a ‘hole band’ associated with dx2-y2 character and increase the hole carriers. Our findings suggest that the increase in two dimensionalities may lead to the sign-reversal Hall resistivity in Lix(C3H10N2)0.32 FeSe at high temperature.

Observation of mode-like features in tunneling spectra of iron-based superconductors

We report scanning tunneling microscopy/spectroscopy（STM/STS） studies on iron-based superconductors of Ba1-xKxFe2As2 and nearly optimally doped Fe（Te,Se）. Mode-like features were observed universally outside the superconducting gaps in the tunneling spectra, which are similar to our previous observations in other samples and can be ascribed to the interaction between electrons and spin excitations. Furthermore, an almost linear relationship between the superconducting gaps and the superconducting transition temperatures was noted and should also be taken into account in understanding the mechanism of iron-based superconductors.

Observation of Nearly Quantized Majorana Conductance Plateau in an Iron-based Superconductor

In 1937,Ettore Majorana,an Italian physicist,predicted an elementary particle called the Majorana Fermion,for which the particle is its own anti-particle.The Majorana Fermion in condensed matter physics is also known as the Majorana zero mode.Because Majorana zero modes obey non-Abel statistics,it holds a great promise for the realization of topological quantum computing,which has attracted widespread interest.

Polarized Neutron Scattering Reveals Preferred Spin Excitations in the Bilayer Iron-Based Superconductor CaK(Fe_(0.96)Ni_(0.04))_(4)As_(4)

In unconventional superconductors,the major challenge on the mechanism research is to reveal how the electrons form Cooper pairs and collectively condense to a superconducting state under both interactions from charge and spin.The ironbased superconductors are similar to those copper oxide and heavy fermion superconductors;they also exhibit strong spin fluctuations,which likely promote the superconducting pairing by acting as the bosonic“pairing glue”.Such argument is supported by a spin resonance mode with a peak energy universally linear scaling with Tc.However,it is still unknown whether in such multi-orbital systems the spin system may have some preferred fluctuating directions that is coupled to the orbital degree of freedom.