Thermoelectric properties of (Ba,K)Cd2As2 crystallized in the CaAl2Si2-type structure.

As-Based Zintl compounds Ba1-xKxCd2As2 crystallized in the CaAl2Si2-type structure (space group P3[combining macron]m1) were prepared using solid-state reactions followed by hot-pressing. We have successfully substituted K for Ba up to x = 0.08, producing hole-carrier doping with concentrations up to 1.60 × 1020 cm-3. We have determined the band-gap value of non-doped BaCd2As2 to be 0.40 eV from the temperature dependence of the electrical resistivity. Both the electrical resistivity and the Seebeck coefficient decrease with hole doping, leading to a power factor value of 1.28 mW m-1 K-2 at 762 K for x = 0.04. A first-principles band calculation shows that the relatively large power factor mainly originates from the two-fold degeneracy of the bands comprising As px,y orbitals and from the anisotropic band structure at the valence-band maximum. The lattice thermal conductivity is suppressed by the K doping to 0.46 W m-1 K-1 at 773 K for x = 0.08, presumably due to randomness. The effect of randomness is compensated by an increase in the electronic thermal conductivity, which keeps the total thermal conductivity approximately constant. In consequence, the dimensionless figure-of-merit ZT reaches a maximum value of 0.81 at 762 K for x = 0.04.

Orbital-anisotropic electronic structure in the nonmagnetic state of BaFe2(As1-xP x )2 superconductors.

High-temperature superconductivity in iron-pnictides/chalcogenides arises in balance with several electronic and lattice instabilities. Beside the antiferromagnetic order, the orbital anisotropy between Fe 3d xz and 3d yz occurs near the orthorhombic structural transition in several parent compounds. However, the extent of the survival of orbital anisotropy against the ion-substitution remains to be established. Here we report the composition (x) and temperature (T) dependences of the orbital anisotropy in the electronic structure of a BaFe2(As1-xP x )2 system by using angle-resolved photoemission spectroscopy. In the low-x regime, the orbital anisotropy starts to evolve on cooling from high temperatures above both antiferromagnetic and orthorhombic transitions. By increasing x, it is gradually suppressed and survives in the optimally doped regime. We find that the in-plane orbital anisotropy persists in a large area of the nonmagnetic phase, including the superconducting dome. These results suggest that the rotational symmetry-broken electronic state acts as the stage for superconductivity in BaFe2(As1-xP x )2.

Anisotropic resonance modes emerging in an antiferromagnetic superconducting state.

Two strong arguments in favor of magnetically driven unconventional superconductivity arise from the coexistence and closeness of superconducting and magnetically ordered phases on the one hand, and from the emergence of magnetic spin-resonance modes at the superconducting transition on the other hand. Combining these two arguments one may ask about the nature of superconducting spin-resonance modes occurring in an antiferromagnetic state. This problem can be studied in underdoped BaFe2 As2, for which the local coexistence of large moment antiferromagnetism and superconductivity is well established by local probes. However, polarized neutron scattering experiments are required to identify the nature of the resonance modes. In the normal state of Co underdoped BaFe2 As2 the antiferromagnetic order results in broad magnetic gaps opening in all three spin directions that are reminiscent of the magnetic response in the parent compound. In the superconducting state two distinct anisotropic resonance excitations emerge, but in contrast to numerous studies on optimum and over-doped BaFe2 As2 there is no isotropic resonance excitation. The two anisotropic resonance modes appearing within the antiferromagnetic phase are attributed to a band selective superconducting state, in which longitudinal magnetic excitations are gapped by antiferromagnetic order with sizable moment.

Spin excitations in hole-overdoped iron-based superconductors.

Understanding the overall features of magnetic excitation is essential for clarifying the mechanism of Cooper pair formation in iron-based superconductors. In particular, clarifying the relationship between magnetism and superconductivity is a central challenge because magnetism may play a key role in their exotic superconductivity. BaFe2As2 is one of ideal systems for such investigation because its superconductivity can be induced in several ways, allowing a comparative examination. Here we report a study on the spin fluctuations of the hole-overdoped iron-based superconductors Ba1-xKxFe2As2 (x = 0.5 and 1.0; Tc = 36 K and 3.4 K, respectively) over the entire Brillouin zone using inelastic neutron scattering. We find that their spin spectra consist of spin wave and chimney-like dispersions. The chimney-like dispersion can be attributed to the itinerant character of magnetism. The band width of the spin wave-like dispersion is almost constant from the non-doped to optimum-doped region, which is followed by a large reduction in the overdoped region. This suggests that the superconductivity is suppressed by the reduction of magnetic exchange couplings, indicating a strong relationship between magnetism and superconductivity in iron-based superconductors.

Suppression of spin-exciton state in hole overdoped iron-based superconductors.

The mechanism of Cooper pair formation in iron-based superconductors remains a controversial topic. The main question is whether spin or orbital fluctuations are responsible for the pairing mechanism. To solve this problem, a crucial clue can be obtained by examining the remarkable enhancement of magnetic neutron scattering signals appearing in a superconducting phase. The enhancement is called spin resonance for a spin fluctuation model, in which their energy is restricted below twice the superconducting gap value (2Δs), whereas larger energies are possible in other models such as an orbital fluctuation model. Here we report the doping dependence of low-energy magnetic excitation spectra in Ba1-xKxFe2As2 for 0.5 < x < 0.84 studied by inelastic neutron scattering. We find that the behavior of the spin resonance dramatically changes from optimum to overdoped regions. Strong resonance peaks are observed clearly below 2Δs in the optimum doping region, while they are absent in the overdoped region. Instead, there is a transfer of spectral weight from energies below 2Δs to higher energies, peaking at values of 3Δs for x = 0.84. These results suggest a reduced impact of magnetism on Cooper pair formation in the overdoped region.

Anisotropy of the superconducting gap in the iron-based superconductor BaFe2(As(1-x)P(x))2.

We report peculiar momentum-dependent anisotropy in the superconducting gap observed by angle-resolved photoemission spectroscopy in BaFe2(As(1-x)P(x))2 (x = 0.30, Tc = 30 K). Strongly anisotropic gap has been found only in the electron Fermi surface while the gap on the entire hole Fermi surfaces are nearly isotropic. These results are inconsistent with horizontal nodes but are consistent with modified s ± gap with nodal loops. We have shown that the complicated gap modulation can be theoretically reproduced by considering both spin and orbital fluctuations.

Normal-state charge dynamics in doped BaFe2As2: roles of doping and necessary ingredients for superconductivity.

In high-transition-temperature superconducting cuprates and iron arsenides, chemical doping plays an important role in inducing superconductivity. Whereas in the cuprate case, the dominant role of doping is to inject charge carriers, the role for the iron arsenides is complex owing to carrier multiplicity and the diversity of doping. Here, we present a comparative study of the in-plane resistivity and the optical spectrum of doped BaFe2As2, which allows for separation of coherent (itinerant) and incoherent (highly dissipative) charge dynamics. The coherence of the system is controlled by doping, and the doping evolution of the charge dynamics exhibits a distinct difference between electron and hole doping. It is found in common with any type of doping that superconductivity with high transition temperature emerges when the normal-state charge dynamics maintains incoherence and when the resistivity associated with the coherent channel exhibits dominant temperature-linear dependence.

Universality of the dispersive spin-resonance mode in superconducting BaFe2As2.

Spin fluctuations in superconducting BaFe2(As(1-x)P(x))2 (x=0.34, T(c)=29.5 K) are studied using inelastic neutron scattering. Well-defined commensurate magnetic signals are observed at (π, 0), which is consistent with the nesting vector of the Fermi surface. Antiferromagnetic (AFM) spin fluctuations in the normal state exhibit a three-dimensional character reminiscent of the AFM order in nondoped BaFe2As2. A clear spin gap is observed in the superconducting phase forming a peak whose energy is significantly dispersed along the c axis. The bandwidth of dispersion becomes larger with approaching the AFM ordered phase universally in all superconducting BaFe2As2, indicating that the dispersive feature is attributed to three-dimensional AFM correlations. The results suggest a strong relationship between the magnetism and superconductivity.

Splitting of resonance excitations in nearly optimally doped Ba(Fe0.94Co0.06)2As2: an inelastic neutron scattering study with polarization analysis.

Magnetic excitations in Ba(Fe0.94Co0.06)2As2: are studied by polarized inelastic neutron scattering above and below the superconducting transition. In the superconducting state, we find clear evidence for two resonancelike excitations. At a higher energy of about 8 meV, there is an isotropic resonance mode with weak dispersion along the c direction. In addition, we find a lower excitation at 4 meV that appears only in the c-polarized channel and whose intensity strongly varies with the l component of the scattering vector. These resonance excitations behave remarkably similar to the gap modes in the antiferromagnetic phase of the parent compound BaFe2As2.

Dependence of carrier doping on the impurity potential in transition-metal-substituted FeAs-based superconductors.

In order to examine to what extent the rigid-band-like electron doping scenario is applicable to the transition metal-substituted Fe-based superconductors, we have performed angle-resolved photoemission spectroscopy studies of Ba(Fe(1-x)Ni(x))(2)As(2) (Ni-122) and Ba(Fe(1-x)Cu(x))(2)As(2) (Cu-122), and compared the results with Ba(Fe(1-x)Co(x))(2)As(2) (Co-122). We find that Ni 3d-derived features are formed below the Fe 3d band and that Cu 3d-derived ones further below it. The electron and hole Fermi surface (FS) volumes are found to increase and decrease with substitution, respectively, qualitatively consistent with the rigid-band model. However, the total extra electron number estimated from the FS volumes (the total electron FS volume minus the total hole FS volume) is found to decrease in going from Co-, Ni-, to Cu-122 for a fixed nominal extra electron number, that is, the number of electrons that participate in the formation of FS decreases with increasing impurity potential. We find that the Néel temperature T(N) and the critical temperature T(c) maximum are determined by the FS volumes rather than the nominal extra electron concentration or the substituted atom concentration.

Anisotropy of the in-plane resistivity of underdoped Ba(Fe(1-x)Co(x))2As2 superconductors induced by impurity scattering in the antiferromagnetic orthorhombic phase.

We investigated the in-plane resistivity anisotropy for underdoped Ba(Fe(1-x)Co(x))(2)As(2) single crystals with improved quality. We demonstrate that the anisotropy in resistivity in the magnetostructural ordered phase arises from the anisotropy in the residual component which increases in proportion to the Co concentration x. This gives evidence that the anisotropy originates from the impurity scattering by Co atoms substituted for the Fe sites, rather than the so far proposed mechanisms such as the anisotropy of Fermi velocities of reconstructed Fermi surface pockets. As doping proceeds to the paramagnetic-tetragonal phase, a Co impurity transforms to a weak and isotropic scattering center.

Effect of Co doping on the in-plane anisotropy in the optical spectrum of underdoped Ba(Fe(1-x)Co(x))2As2.

We investigate the anisotropy in the in-plane optical spectra of detwinned Ba(Fe(1-x)Co(x))(2)As(2). The optical conductivity spectrum of BaFe(2)As(2) shows appreciable anisotropy in the magnetostructural ordered phase, whereas the dc (ω = 0) resistivity is nearly isotropic at low temperatures. Upon Co doping, the resistivity becomes highly anisotropic, while the finite-energy intrinsic anisotropy is suppressed. It is found that anisotropy in resistivity arises from anisotropic impurity scattering due to the presence of doped Co atoms, and it is extrinsic in origin. The intensity of a specific optical phonon mode is also found to show striking anisotropy in the ordered phase. The anisotropy induced by the Co impurity and that observed in the optical phonon mode are hallmarks of the highly polarizable electronic state in the ordered phase.

Universal heat conduction in the iron arsenide superconductor KFe2As2: evidence of a d-wave state.

The thermal conductivity κ of the iron arsenide superconductor KFe2As2 was measured down to 50 mK for a heat current parallel and perpendicular to the tetragonal c axis. A residual linear term at T→0, κ(0)/T is observed for both current directions, confirming the presence of nodes in the superconducting gap. Our value of κ(0)/T in the plane is equal to that reported by Dong et al. [Phys. Rev. Lett. 104, 087005 (2010)] for a sample whose residual resistivity ρ(0) was 10 times larger. This independence of κ(0)/T on impurity scattering is the signature of universal heat transport, a property of superconducting states with symmetry-imposed line nodes. This argues against an s-wave state with accidental nodes. It favors instead a d-wave state, an assignment consistent with five additional properties: the magnitude of the critical scattering rate Γ(c) for suppressing T(c) to zero; the magnitude of κ(0)/T, and its dependence on current direction and on magnetic field; the temperature dependence of κ(T).

Octet-line node structure of superconducting order parameter in KFe2As2.

In iron-pnictide superconductivity, the interband interaction between the hole and electron Fermi surfaces (FSs) is believed to play an important role. However, KFe(2)As(2) has three zone-centered hole FSs and no electron FS but still exhibits superconductivity. Our ultrahigh-resolution laser angle-resolved photoemission spectroscopy unveils that KFe(2)As(2) is a nodal s-wave superconductor with highly unusual FS-selective multi-gap structure: a nodeless gap on the inner FS, an unconventional gap with "octet-line nodes" on the middle FS, and an almost-zero gap on the outer FS. This gap structure may arise from the frustration between competing pairing interactions on the hole FSs causing the eightfold sign reversal. Our results suggest that the A(1g) superconducting symmetry is universal in iron-pnictides, in spite of the variety of gap functions.

Anisotropic energy gaps of iron-based superconductivity from intraband quasiparticle interference in LiFeAs.

If strong electron-electron interactions between neighboring Fe atoms mediate the Cooper pairing in iron-pnictide superconductors, then specific and distinct anisotropic superconducting energy gaps Δ(i)(k) should appear on the different electronic bands i. Here, we introduce intraband Bogoliubov quasiparticle scattering interference (QPI) techniques for determination of Δ(i)(k) in such materials, focusing on lithium iron arsenide (LiFeAs). We identify the three hole-like bands assigned previously as γ, α(2), and α(1), and we determine the anisotropy, magnitude, and relative orientations of their Δ(i)(k). These measurements will advance quantitative theoretical analysis of the mechanism of Cooper pairing in iron-based superconductivity.

Unprecedented anisotropic metallic state in undoped iron arsenide BaFe2As2 revealed by optical spectroscopy.

An ordered phase showing remarkable electronic anisotropy in proximity to the superconducting phase is now a hot issue in the field of high-transition-temperature superconductivity. As in the case of copper oxides, superconductivity in iron arsenides competes or coexists with such an ordered phase. Undoped and underdoped iron arsenides have a magnetostructural ordered phase exhibiting stripe-like antiferromagnetic spin order accompanied by an orthorhombic lattice distortion; both the spin order and lattice distortion break the tetragonal symmetry of crystals of these compounds. In this ordered state, anisotropy of in-plane electrical resistivity is anomalous and difficult to attribute simply to the spin order and/or the lattice distortion. Here, we present the anisotropic optical spectra measured on detwinned BaFe(2)As(2) crystals with light polarization parallel to the Fe planes. Pronounced anisotropy is observed in the spectra, persisting up to an unexpectedly high photon energy of about 2 eV. Such anisotropy arises from an anisotropic energy gap opening below and slightly above the onset of the order. Detailed analysis of the optical spectra reveals an unprecedented electronic state in the ordered phase.

Incommensurate spin fluctuations in hole-overdoped superconductor KFe2As2.

A neutron scattering study of heavily hole-overdoped superconducting KFe2As2 revealed a well-defined low-energy incommensurate spin fluctuation at [π(1 ± 2 δ),0] with δ = 0.16. The incommensurate structure differs from the previously observed commensurate peaks in electron-doped AFe2As2 (A = Ba, Ca, or Sr) at low energies. The direction of the peak splitting is perpendicular to that observed in Fe(Te,Se) or in Ba(Fe,Co)2As2 at high energies. A band structure calculation suggests interband scattering between bands around the Γ and X points as an origin of this incommensurate peak. The perpendicular direction of the peak splitting can be understood within the framework of multiorbital band structure. The results suggest that spin fluctuation is more robust in hole-doped than in electron-doped samples, which can be responsible for the appearance of superconductivity in the heavily hole-doped samples.

Quasi-two-dimensional Fermi surfaces and coherent interlayer transport in KFe2As2.

We report the results of the angular-dependent magnetoresistance oscillations (AMROs), which can determine the shape of bulk Fermi surfaces (FSs) in quasi-two-dimensional (Q2D) systems, in a highly hole-doped Fe-based superconductor KFe2As2 with Tc ≈ 3.7 K. From the AMROs, we determined the two Q2D FSs with rounded-square cross sections, correspond to 12% and 17% of the first Brillouin zone. The rounded-squared shape of the FS cross section is also confirmed by the analyses of the interlayer transport under in-plane fields. From the obtained FS shape, we infer the character of the 3d orbitals that contribute to the FSs.