Family Of Iron-based Superconductors Research Articles

Orbital nematic order and interplay with magnetism in the two-orbital Hubbard model

Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturing symmetry broken magnetic and orbitally ordered phases. Both approaches show that the electron and hole doping affect the two orders differently. While hole doping tends to suppress both magnetism and orbital ordering, the electron doping suppresses magnetism faster. Crucially, we find a realistic parameter regime for moderate electron doping that stabilizes orbital nematicity in the absence of long-range antiferromagnetic order. This is reminiscent of the non-magnetic orbital nematic phase observed recently in FeSe and a number of iron pnictide materials and raises the possibility that at least in some cases, the observed electronic nematicity may be primarily due to orbital rather than magnetic fluctuations.

Electronic structure of (Ca0.85La0.15)FeAs2

We report a comprehensive study of orbital character and tridimensional nature of the electronic structure of (Ca0.85La0.15)FeAs2 from recently discovered “112” family of Iron-based superconductors (IBS), with angle-resolved photoemission spectroscopy. We observed that the band structure is similar to that of “122” family, namely, there are three hole-like bands at the Brillouin zone (BZ) center and two electron-like bands at the BZ corner. The bands near the Fermi level (EF) are mainly derived from the Fe t2g orbitals. On the basis of our present and earlier studies, we classify IBS into the three types according to their crystal structures. We show that although the bands near EF mainly originate from Fe 3d electrons, they are significantly modified by the interaction between the superconducting slabs and the intermediate atoms.

Superconductivity in K- and Na-doped BaFe2As2: What can we learn from heat capacity and pressure dependence of Tc

A brief overview of changes in the superconducting transition temperature under pressure and evolution of specific heat capacity jump at Tc for two related families of iron-based superconductors, Ba 1-x K x Fe 2 As 2 (0.2 ≤ x ≤ 1.0) and Ba 1-x Na x Fe 2 As 2 (0.2 ≤ x ≤ 0.9) will be given. For Ba 1-x K x Fe 2 As 2 the specific heat capacity jump at Tc measured over the whole extent of the superconducting dome shows clear deviation from the empirical, [Formula: see text], scaling (known as the BNC scaling) for x > 0.7. At the same concentrations range apparent equivalence of effects of pressure and K -substitution on Tc fails. These observations suggests a significant change of the superconducting state for x > 0.7. In contrast, the data for the large portion of Ba 1-x Na x Fe 2 As 2 (0.2 ≤ x ≤ 0.9) series follow the BNC scaling. However, the pressure dependence of Tc (measured up to ~12 kbar) have clear nonlinearities for Na concentration in 0.2–0.25 region, that may be consistent with Tc crossing the phase boundaries of the emergent, narrow, antiferromagnetic/tetragonal phase. Results will be discussed in context other studies of these two related families of iron-based superconductors.

Framework structures of interconnected layers in calcium iron arsenides.

The new calcium iron arsenide compounds Ca(n(n+1)/2)(Fe(1-x)M(x))(2+3n)M'(n(n-1)/2)As((n+1)(n+2)/2) (n = 1-3; M = Nb, Pd, Pt; M' = □, Pd, Pt) were synthesized and their crystal structures determined by single-crystal X-ray diffraction. The series demonstrates the structural flexibility of iron arsenide materials, which otherwise prefer layered structures, as is known from the family of iron-based superconductors. In the new compounds, iron arsenide tetrahedral layers are bridged by iron-centered pyramids, giving rise to so far unknown frameworks of interconnected FeAs layers. Channels within the structures are occupied with calcium and palladium or platinum, respectively. Common basic building blocks are identified that lead to a better understanding of the building principles of these structures and their relation to CaFe4As3.

Comparison of the pinning energy in Fe(Se1−xTex) compound between single crystals and thin films

Among the families of iron-based superconductors, we investigate flux pinning mechanisms in the Fe(Se1−xTex) compound. We perform magneto-resistance and current-voltage measurements on single-crystals, as well as on several epitaxial thin films grown on different substrates (CaF2, LaAlO3). The activation energy is derived as a function of magnetic field, U(H). The influence of magnetic field orientation on the pinning energy activation mechanism is also studied, leading to the anisotropy analysis which reveals low anisotropy in thin films grown on CaF2 substrate with respect to single crystals and films grown on LaAlO3. Concerning the dominant pinning regime, the exponents of the power law dependence U0(H) ∝ H−α have been evaluated, confirm that weak pinning is a general characteristic of this compound. The single exponent feature, generally noticed on thin films grown on SrTiO3 substrate and associated to a strong single vortex regime, has been observed in thin films grown on LaAlO3, only in the parallel configuration. At the end, this overall comparison can be useful to develop a technological material able to compete with high temperature superconductors.

Segregation of antiferromagnetism and high-temperature superconductivity inCa1−xLaxFe2As2

We report the effect of applied pressures on magnetic and superconducting order in single crystals of the aliovalent La-doped iron pnictide material Ca$_{1-x}$La$_{x}$Fe$_{2}$As$_{2}$. Using electrical transport, elastic neutron scattering and resonant tunnel diode oscillator measurements on samples under both quasi-hydrostatic and hydrostatic pressure conditions, we report a series of phase diagrams spanning the range of substitution concentrations for both antiferromagnetic and superconducting ground states that include pressure-tuning through the antiferromagnetic (AFM) quantum critical point. Our results indicate that the observed superconducting phase with maximum transition temperature of $T_{c}$=47 K is intrinsic to these materials, appearing only upon suppression of magnetic order by pressure tuning through the AFM critical point. In contrast to all other intermetallic iron-pnictide superconductors with the ThCr$_2$Si$_2$ structure, this superconducting phase appears to exist only exclusively from the antiferromagnetic phase in a manner similar to the oxygen- and fluorine-based iron-pnictide superconductors with the highest transition temperatures reported to date. The unusual dichotomy between lower-$T_{c}$ systems with coexistent superconductivity and magnetism and the tendency for the highest-$T_{c}$ systems to show non-coexistence provides an important insight into the distinct transition temperature limits in different members of the iron-based superconductor family.

Heat capacity jump atTcand pressure derivatives of superconducting transition temperature in the Ba1−xNaxFe2As2(0.1≤x≤0.9) series

We present the evolution of the initial (up to $\ensuremath{\sim}10$ kbar) hydrostatic pressure dependencies of ${T}_{c}$ and of the ambient pressure, and the jump in the heat capacity associated with the superconducting transition as a function of Na doping in the Ba${}_{1\ensuremath{-}x}$Na${}_{x}$Fe${}_{2}$As${}_{2}$ family of iron-based superconductors. For Na concentrations $0.15\ensuremath{\le}x\ensuremath{\le}0.9$, the jump in specific heat at ${T}_{c}$, $\ensuremath{\Delta}{C}_{p}{|}_{{T}_{c}}$, follows the $\ensuremath{\Delta}{C}_{p}\ensuremath{\propto}{T}^{3}$ (the so-called BNC scaling) found for most BaFe${}_{2}$As${}_{2}$-based superconductors. This finding suggests that, unlike the related Ba${}_{1\ensuremath{-}x}$K${}_{x}$Fe${}_{2}$As${}_{2}$ series, there is no significant modification of the superconducting state (e.g., change in superconducting gap symmetry) in the Ba${}_{1\ensuremath{-}x}$Na${}_{x}$Fe${}_{2}$As${}_{2}$ series over the whole studied Na concentration range. Pressure dependencies are nonmonotonic for $x=0.2$ and $0.24$. For other Na concentrations, ${T}_{c}$ decreases under pressure in an almost linear fashion. The anomalous behavior of the $x=0.2$ and $0.24$ samples under pressure is possibly due to the crossing of the phase boundaries of the narrow antiferromagnetic tetragonal phase, unique for the Ba${}_{1\ensuremath{-}x}$Na${}_{x}$Fe${}_{2}$As${}_{2}$ series, with the application of pressure. The negative sign of the pressure derivatives of ${T}_{c}$ across the whole superconducting dome (except for $x=0.2$) is a clear indication of the nonequivalence of substitution and pressure for the Ba${}_{1\ensuremath{-}x}$Na${}_{x}$Fe${}_{2}$As${}_{2}$ series.

A Short Review of the S4 Symmetric Microscopic Model for Iron-Based High Temperature Superconductors

We briefly review the recently constructed two orbital microscopic model for iron-based superconductors based on S4 symmetry[1]. With this faithful representation of the kinematics of the tri-layer FeAs or FeSe structure, the model provides answers and physical pictures to fundamental questions related to the robustness of superconductivity and pairing symmetry, unifies different families of iron-based superconductors, casts new insight into the connections to the other high Tc superconductors, cuprates, and reveals why an s-wave pairing can be stabilized by repulsive interactions. Further progresses include that the model provides a clean understanding of band reconstruction observed in magnetically ordered states, which is a strong support to the kinematics of the S4 model, and captures the essential low energy physics of iron-based superconductors based on numerical results from unbiased quantum Monte Carlo simulation.

Iron-Based Superconductors as Odd-Parity Superconductors

Parity is a fundamental quantum number used to classify a state of matter. Materials rarely possess ground states with odd parity. We show that the superconducting state in iron-based superconductors is classified as an odd-parity s-wave spin-singlet pairing state in a single trilayer FeAs=Se, the building block of the materials. In a low-energy effective model constructed on the Fe square bipartite lattice, the superconducting order parameter in this state is a combination of an s-wave normal pairing between two sublattices and an s-wavepairing within the sublattices. The state has a fingerprint with a real-space sign inversion between the top and bottom As=Se layers. The results suggest that iron-based super- conductors are a new quantum state of matter, and the measurement of the odd parity can help to establish high-temperature superconducting mechanisms. DOI: 10.1103/PhysRevX.3.031004 Subject Areas: Condensed Matter Physics, Superconductivity Symmetry plays the central role in the search for beauty in physics. It controls the structure of matter and allows us to simplify a complicated problem. The gauge principle is a fundamental principle in physics. Models formulated in different gauge settings are equivalent. Symmetry and gauge principles together provide the foundations of mod- ern physics that allow us to solve complicated problems. The recently discovered iron-based high-temperature superconductors (high T c )( 1-3) are layered materials with complicated electronic structures. Their complexity causes a major difficulty in understanding pairing symme- try, which arguably is the most important property and clue to determine the pairing mechanism (4,5). In a strongly correlated electron system, major physics is determined locally in real space. Important properties, such as pairing symmetry in a superconducting state, are ex- pected to be robust against small variations of Fermi surfaces in reciprocal space. Although the superconducting mechanism related to high-temperature superconductors (high Tc) has not yet been determined, the robust d-wave pairing symmetry in cuprates (6) can be understood under this principle. Does this principle still hold for iron-based supercon- ductors? Namely, do all iron-based superconductors pos- sess one universal pairing state? Unlike cuprates, the answer to this question is highly controversial because different theoretical approaches have provided different answers and no universal state has been identified (5). Nevertheless, as local electronic structures in all families of iron-based superconductors are almost identical and phase diagrams are smooth against doping (4,5), it is hard to argue that the materials can approach many differ- ent superconducting ground states.

Nanoscale surface element identification and dopant homogeneity in the high-Tcsuperconductor PrxCa1−xFe2As2

We use scanning tunneling microscopy to determine the surface structure and dopant distribution in Pr${}_{x}$Ca${}_{1\ensuremath{-}x}$Fe${}_{2}$As${}_{2}$, the highest-${T}_{c}$ member of the 122 family of iron-based superconductors. We identify the cleaved surface termination by mapping the local tunneling barrier height, related to the work function. We image the individual Pr dopants responsible for superconductivity, and show that they do not cluster, but in fact repel each other at short length scales. We therefore suggest that the low volume fraction high-${T}_{c}$ superconducting phase is unlikely to originate from Pr inhomogeneity.

Heat capacity jump atTcand pressure derivatives of superconducting transition temperature in the Ba1−xKxFe2As2(0.2≤x≤1.0) series

We present the evolution of the initial (up to $\ensuremath{\sim}$10 kbar) hydrostatic pressure dependencies of ${T}_{c}$ and of the ambient pressure jump in the heat capacity associated with the superconducting transition as a function of K doping in the Ba${}_{1\ensuremath{-}x}$K${}_{x}$Fe${}_{2}$As${}_{2}$ family of iron-based superconductors. The pressure derivatives show a weak but distinct anomaly near $x\ensuremath{\sim}0.7$. In the same concentration region, $\ensuremath{\Delta}{C}_{p}{|}_{{T}_{c}}$ deviates from the $\ensuremath{\Delta}{C}_{p}\ensuremath{\propto}{T}^{3}$ scaling found for most BaFe${}_{2}$As${}_{2}$-based superconductors. These results are consistent with a possible significant modification of the superconducting state, occurring near $x\ensuremath{\sim}0.7$.

Superconductivity induced by U doping in the SmFeAsO system

Through partial substitution of Sm by U in SmFeAsO, a different member of the family of iron-based superconductors was successfully synthesized. X-ray diffraction measurements show that the lattice constants along the a and c axes are both squeezed through U doping, indicating a successful substitution of U at the Sm site. The parent compound shows a strong resistivity anomaly near 150 K, associated with spin-density-wave instability.U doping suppresses this instability and leads to a transition to the superconducting state at temperatures up to 49 K. Magnetic measurements confirm the bulk superconductivity in this system. For the sample with a doping level of x = 0.2, the external magnetic field suppresses the onset temperature very slowly, indicating a rather high upper critical field. In addition, the Hall effect measurements show that U clearly dopes electrons into the material.

Universal pair-breaking in transition-metal-substituted iron-pnictide superconductors

The experimental transport scattering rate was determined for a wide range of optimally doped transition-metal-substituted FeAs-based compounds with the ThCr${}_{2}$Si${}_{2}$ (122) crystal structure. The maximum transition temperature ${T}_{c}$ for several Ba-, Sr-, and Ca-based 122 systems follows a universal rate of suppression with increasing scattering rate indicative of a common pair-breaking mechanism. Extraction of standard pair-breaking parameters puts a limit of $\ensuremath{\sim}$26 K on the maximum ${T}_{c}$ for all transition-metal-substituted 122 systems, in agreement with experimental observations, and sets a critical scattering rate of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ s${}^{\ensuremath{-}1}$ for the suppression of the superconducting phase. The observed critical scattering rate is much weaker than that expected for a sign-changing order parameter with strong interband scattering, providing important constraints on the nature of the superconducting gap in the 122 family of iron-based superconductors.

Spin Hall effect in iron-based superconductors: A Dirac-point effect

We have theoretically explored the intrinsic spin Hall effect (SHE) in the iron-based superconductor family with a variety of materials. The study is motivated by an observation that, in addition to an appreciable spin-orbit coupling in the Fe 3d states, a character of the band structure in which Dirac cones appear below the Fermi energy may play a crucial role in producing a large SHE. Our investigation does indeed predict a substantially large spin Hall conductivity in the heavily hole-doped regime such as KFe$_2$As$_2$. The magnitude of the SHE has turned out to be comparable with that for Pt despite a relatively small spin-orbit coupling, which we identify to come from a huge contribution from the gap opening induced by the spin-orbit coupling at the Dirac point, which can become close to the Fermi energy for the heavy hole doping.

Divergent Nematic Susceptibility in an Iron Arsenide Superconductor

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition can be complicated by coupling between distinct order parameters. We show how measurement of the divergent nematic susceptibility of the iron pnictide superconductor Ba(Fe(1-x)Co(x))(2)As(2) distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also indicate an electronic nematic quantum phase transition near the composition with optimal superconducting transition temperature.

Electronic structure and Fermi surface of iron-based superconductors R2Fe3Si5 (R = Lu;Y;Sc) from first principles

Electronic structures of three superconducting rare-earth iron silicides (Lu;Y;Sc)2Fe3Si5 and non-superconducting Lu2Ru3Si5, adopting a tetragonal crystal structure (P4/mnc), have been calculated employing the full-potential local-orbital method within the density functional theory. The investigations were focused particularly on the band structures and Fermi surfaces, existing in four bands and containing rather three-dimensional electronlike and holelike sheets. They support an idea of unconventional multi-band superconductivity in these ternaries, proposed earlier by other authors for Lu2Fe3Si5, based on heat-capacity, resistivity, electromagnetic and muon spin rotation measurements. Finally, a discussion on differences in the electronic structures between the investigated here and other common families of iron-based superconductors is carried out.

Transport properties and electronic phase diagram of single-crystallineCa10(Pt3As8)((Fe1−xPtx)2As2)5

Sizable single-crystalline samples of ${\mathrm{Ca}}_{10}({\mathrm{Pt}}_{3}{\mathrm{As}}_{8}){({({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Pt}}_{x})}_{2}{\mathrm{As}}_{2})}_{5}$ (the 10-3-8 phase) with $0\ensuremath{\leqslant}x<0.1$ have been grown and have been systematically characterized via x-ray diffraction, magnetic, and transport measurements. The unsubstituted sample is a heavily doped semiconductor with no sign of magnetic order down to 2 K. With increasing Pt content, the metallic behavior appears, and superconductivity is realized for $x\ensuremath{\geqslant}0.023$. ${T}_{\mathrm{c}}$ rises to its maximum of approximately 13.6 K at the doping level of $x\ensuremath{\sim}0.06$ and then decreases for higher $x$ values. The electronic phase diagram of the 10-3-8 phase was mapped out based on the magnetic and transport measurements. The mass anisotropy parameter $\ensuremath{\Gamma}\ensuremath{\sim}10$, obtained from resistive measurements in magnetic fields, indicates a relatively large anisotropy in the iron-based superconductor family. This strong two-dimensional character may lead to the absence of magnetic order. A linear $T$ dependence of susceptibility at high temperatures is observed, indicating that spin fluctuations exist in the underdoped region as in most of the Fe-pnictide superconductors.

Structural analysis and superconductivity of CeFeAsO1−xHx

We performed the neutron powder diffraction (NPD) and synchrotron x-ray diffraction measurements on CeFeAsO${}_{1\ensuremath{-}x}$(D,H)${}_{x}$ ($x$ $=$ 0.0 \ensuremath{-} 0.48) as a representative of 1111-type family of iron-based superconductors $Ln$FeAsO${}_{1\ensuremath{-}x}$H${}_{x}$ ($Ln$ $=$ lanthanoid). Deuterated and hydrogenated samples (CeFeAsO${}_{1\ensuremath{-}x}$D${}_{x}$ and CeFeAsO${}_{1\ensuremath{-}x}$H${}_{x}$) were synthesized by the solid-state reaction of a metal oxide, arsenides, and a hydride and a deuteride source under an applied pressure of 2 GPa. No distinct differences were found between the structural and superconducting properties of the hydride and deuteride samples. Rietveld analyses of the NPD patterns demonstrated that deuterium exclusively substitutes on the oxygen sites in the 1111-type structures according to the nominal composition. Bulk superconductivity was observed over a wide $x$ region (0.1 $x$ 0.4) and the superconducting dome had a rather flat shape with a maximum ${T}_{\mathrm{c}}$ $=$ 47 K at around $x$ $=$ 0.25. It was concluded from density functional theory calculations and comparison with the superconducting dome of the fluorine-substituted system that the charge state of the hydrogen substituting the oxygen sites was \ensuremath{-}1. The relationship between the lattice parameter $a$ and ${T}_{\mathrm{c}}$ in our samples prepared from metal hydrides is almost the same as that reported previously for samples prepared from cerium hydroxide. These results strongly suggest that H${}^{\ensuremath{-}}$ ions exclusively occupy the oxygen sites in both samples, regardless of the hydrogen species in the starting material.

Pairing symmetries of several iron-based superconductor families and some similarities with cuprates and heavy-fermions

We show that, by using the unit-cell transformation between 1 Fe per unit cell to 2 Fe per unit cell, one can qualitatively understand the pairing symmetry of several families of iron-based superconductors. In iron-pnictides and iron-chalcogenides, the nodeless s±-pairing and the resulting magnetic resonance mode transform nicely between the two unit cells, while retaining all physical properties unchanged. However, when the electron-pocket disappears from the Fermi surface with complete doping in KFe2As2, we find that the unit-cell invariant requirement prohibits the occurrence of s±-pairing symmetry (caused by inter-hole-pocket nesting). However, the intra-pocket nesting is compatible here, which leads to a nodal d-wave pairing. The corresponding Fermi surface topology and the pairing symmetry are similar to Ce-based heavy-fermion superconductors. Furthermore, when the Fermi surface hosts only electron-pockets in KyFe2-xSe2, the inter-electron-pocket nesting induces a nodeless and isotropic d-wave pairing. This situation is analogous to the electron-doped cuprates, where the strong antiferromagnetic order creates similar disconnected electron-pocket Fermi surface, and hence nodeless d-wave pairing appears. The unit-cell transformation in KyFe2-xSe2 exhibits that the d-wave pairing breaks the translational symmetry of the 2 Fe unit cell, and thus cannot be realized unless a vacancy ordering forms to compensate for it. These results are consistent with the coexistence picture of a competing order and nodeless d-wave superconductivity in both cuprates and KyFe1.6Se2.

Spin fluctuations and unconventional pairing in KFe2As2

We study the relation between the spin fluctuation and superconductivity in an heavily hole doped end material KFe$_2$As$_2$. We construct a five orbital model by approximately unfolding the Brillouin zone of the three dimensional ten orbital model obtained from first principles calculation. By applying the random phase approximation, we obtain the spin susceptibility and solve the linearized Eliashberg equation. The incommensurate spin fluctuation observed experimentally is understood as originating from interband interactions, where the multiorbital nature of the band structure results in an electron-hole asymmetry of the incommensurability in the whole iron-based superconductor family. As for superconductivity, s-wave and d-wave pairings are found to be in close competition, where the sign change in the gap function in the former is driven by the incommensurate spin fluctuations. We raise several possible explanations for the nodes in the superconducting gap of KFe$_2$As$_2$ observed experimentally.