Microwave surface-impedance measurements of the magnetic penetration depth in single crystal Ba1-xKxFe2As2 superconductors: evidence for a disorder-dependent superfluid density

Emergence of superconductivity from fully incoherent normal state in an iron-based superconductor (Ba0.6K0.4)Fe2As2

In unconventional superconductors, it is generally believed that understanding the physical properties of the normal state is a pre-requisite for understanding the superconductivity mechanism. In conventional superconductors like niobium or lead, the normal state is a Fermi liquid with a well-defined Fermi surface and well-defined quasipartcles along the Fermi surface. Superconductivity is realized in this case by the Fermi surface instability in the superconducting state and the formation and condensation of the electron pairs (Cooper pairing). The high temperature cuprate superconductors, on the other hand, represent another extreme case that superconductivity can be realized in the underdoped region where there is neither well-defined Fermi surface due to the pseudogap formation nor quasiparticles near the antinodal regions in the normal state. Here we report a novel scenario that superconductivity is realized in a system with well-defined Fermi surface but without quasiparticles along the Fermi surface in the normal state. High resolution laser-based angle-resolved photoemission measurements have been performed on an optimally-doped iron-based superconductor (Ba_0.6K_0.4)Fe₂As₂. We find that, while sharp superconducting coherence peaks emerge in the superconducting state on the hole-like Fermi surface sheets, no quasiparticle peak is present in the normal state. Its electronic behaviours deviate strongly from a Fermi liquid system. The superconducting gap of such a system exhibits an unusual temperature dependence that it is nearly a constant in the superconducting state and abruptly closes at T_c. These observations have provided a new platform to study unconventional superconductivity in a non-Fermi liquid system.

Superconducting properties of thes±-wave state: Fe-based superconductors

Although the pairing mechanism of Fe-based superconductors (FeSCs) has not yet been settled with consensus with regard to the pairing symmetry and the superconducting (SC) gap function, the vast majority of experiments support the existence of spin-singlet sign-changings-wave SC gaps on multi-bands (s±-wave state). This multi-bands±-wave state is a very unique gap stateper seand displays numerous unexpected novel SC properties, such as a strong reduction of the coherence peak, non-trivial impurity effects, nodal-gap-like nuclear magnetic resonance signals, various Volovik effects in the specific heat (SH) and thermal conductivity, and anomalous scaling behaviors with a SH jump and condensation energy versusTc, etc. In particular, many of these non-trivial SC properties can easily be mistaken as evidence for a nodal-gap state such as ad-wave gap. In this review, we provide detailed explanations of the theoretical principles for the various non-trivial SC properties of thes±-wave pairing state, and then critically compare the theoretical predictions with experiments on FeSCs. This will provide a pedagogical overview of to what extent we can coherently understand the wide range of different experiments on FeSCs within thes±-wave gap model.

Collective mode at Lifshitz transition in iron-pnictide superconductors

We obtain the exact low-energy spectrum of two mobile holes in a t-J model for an isolated layer in an iron-pnictide superconductor. The minimum d xz and d yz orbitals per iron atom are included, with no hybridization between the two. After tuning the Hund coupling to a putative quantum critical point (QCP) that separates a commensurate spin-density wave from a hidden-order antiferromagnet at half filling, we find an s-wave hole-pair groundstate and a d-wave hole-pair excited state. Near the QCP, both alternate in sign between hole Fermi surface pockets at the Brillouin zone center and emergent electron Fermi surface pockets at momenta that correspond to commensurate spin-density waves (cSDW). The dependence of the energy splitting with increasing Hund coupling yields evidence for a true QCP in the thermodynamic limit near the putative one, at which the s-wave and d-wave Cooper pairs are degenerate. A collective s-to-d-wave oscillation of the macroscopic superconductor that couples to orthorhombic shear strain is also identified. Its resonant frequency is predicted to collapse to zero at the QCP in the limit of low hole concentration. This implies degeneracy of Cooper pairs with s, d and [Formula: see text] symmetry in the corresponding quantum critical state. We argue that the critical state describes Cooper pairs in hole-doped iron superconductors at the Lifshitz transition, where electron bands first rise above the Fermi level. We thereby predict that the s-to-d-wave collective mode observed by Raman spectroscopy in Ba1-x K x Fe2As2 at optimal doping should also be observed at higher doping near the Lifshitz transition.

Concealed d-wave pairs in the s± condensate of iron-based superconductors

A central question in iron-based superconductivity is the mechanism by which the paired electrons minimize their strong mutual Coulomb repulsion. In most unconventional superconductors, Coulomb repulsion is minimized through the formation of higher angular momentum Cooper pairs, with Fermi surface nodes in the pair wavefunction. The apparent absence of such nodes in the iron-based superconductors has led to a belief they form an s-wave ([Formula: see text]) singlet state, which changes sign between the electron and hole pockets. However, the multiorbital nature of these systems opens an alternative possibility. Here, we propose a new class of [Formula: see text] state containing a condensate of d-wave Cooper pairs, concealed by their entanglement with the iron orbitals. By combining the d-wave ([Formula: see text]) motion of the pairs with the internal angular momenta [Formula: see text] of the iron orbitals to make a singlet ([Formula: see text]), an [Formula: see text] superconductor with a nontrivial topology is formed. This scenario allows us to understand the development of octet nodes in potassium-doped Ba1-x KXFe2As2 as a reconfiguration of the orbital and internal angular momentum into a high spin ([Formula: see text]) state; the reverse transition under pressure into a fully gapped state can then be interpreted as a return to the low-spin singlet. The formation of orbitally entangled pairs is predicted to give rise to a shift in the orbital content at the Fermi surface, which can be tested via laser-based angle-resolved photoemission spectroscopy.

Tetrahedral and orbital pairing: a fully gapped pairing scenario for the iron-based superconductors

Motivated by the fully gapped superconductivity in iron-based superconductors with uncompensated electron pockets, we propose a spin singlet, but orbital triplet analogue of the superfluid phase of ^{3}He-B. We show that orbital triplets with a nominal d-wave symmetry at the iron sites can transform as s-wave pairs under rotations about the selenium sites. Linear combinations of such d(xy) and d(x2-y(2)) triplets form a fully gapped, topological superconductor. Raman-active excitations are predicted to develop below the superconducting transition temperature.

Superfluid density in the s±-wave state of clean iron-based superconductors

Based on a phenomenological model and the Kubo formula, we investigate the superfluid density ρ(s)(T) and then the penetration depth λ(T) of the iron-based superconductors in the coexistence region of the spin-density wave and superconductivity, and also in the overdoped region. Our calculations show a dramatic increase of λ(0) with the decrease of the doping concentration x below x = 0.1. This result is consistent with the experimental observations. At low temperatures, ρ(s)(T) shows an exponential-law behavior, while at higher temperatures, the linear-in-T behavior is dominant before it trends to vanish. It is in qualitative agreement with the direct measurement of superfluid density in films of Fe-pnictide superconductor at x = 0.08. The evolution of Δλ(T) can be roughly fitted by a power-law function with the exponent depending on the doping concentration. We show that the Uemura relation holds for the iron-based superconductors only at very low doping levels.

A sharp peak of the zero-temperature penetration depth at optimal composition in BaFe2(As(1-x)P(x))2

In a superconductor, the ratio of the carrier density, n, to its effective mass, m*, is a fundamental property directly reflecting the length scale of the superfluid flow, the London penetration depth, λ(L). In two-dimensional systems, this ratio n/m* (~1/λ(L)(2)) determines the effective Fermi temperature, T(F). We report a sharp peak in the x-dependence of λ(L) at zero temperature in clean samples of BaFe(2)(As(1)(-x)P(x))(2) at the optimum composition x = 0.30, where the superconducting transition temperature T(c) reaches a maximum of 30 kelvin. This structure may arise from quantum fluctuations associated with a quantum critical point. The ratio of T(c)/T(F) at x = 0.30 is enhanced, implying a possible crossover toward the Bose-Einstein condensate limit driven by quantum criticality.

Nodal versus nodeless behaviors of the order parameters of LiFeP and LiFeAs superconductors from magnetic penetration-depth measurements

High-precision measurements of magnetic penetration depth λ in clean single crystals of LiFeAs and LiFeP superconductors reveal contrasting behaviors. In LiFeAs the low-temperature λ(T) shows a flat dependence indicative of a fully gapped state, which is consistent with previous studies. In contrast, LiFeP exhibits a T-linear dependence of superfluid density infinity λ(-2), indicating a nodal superconducting order parameter. A systematic comparison of quasiparticle excitations in the 1111, 122, and 111 families of iron-pnictide superconductors implies that the nodal state is induced when the pnictogen height from the iron plane decreases below a threshold value of ~1.33 Å.

Doping dependent evolution of magnetism and superconductivity in Eu(1-x)K(x)Fe2As2 (x = 0-1) and temperature dependence of the lower critical field H(c1)

We have synthesized polycrystalline samples of Eu(1-x)K(x)Fe2As2 (x = 0-1) and carried out systematic characterization using x-ray diffraction, ac and dc magnetic susceptibility, and electrical resistivity measurements. A clear signature of the coexistence of a superconducting transition (T(c) = 5.5 K) with spin density wave (SDW) ordering is observed in our underdoped sample with x = 0.15. The SDW transition disappears completely for the x = 0.3 sample and superconductivity arises below 20 K. The superconducting transition temperature Tc increases with increase in the K content and a maximum Tc = 33 K is reached for x = 0.5, beyond which it decreases again. The doping dependent Tx phase diagram is extracted from the magnetic and electrical transport data. It is found that magnetic ordering of Eu moments coexists with the superconductivity up to x = 0.6. The isothermal magnetization data taken at 2 K for the doped samples suggest the 2+ valence state of the Eu ions. We also present the temperature dependence of the lower critical field H(c1) of the superconducting polycrystalline samples. The values of H(c1)(0) obtained for x = 0.3, 0.5, and 0.7 after taking the demagnetization factor into account are 202, 330, and 212 Oe, respectively. The London penetration depth λ(T) calculated from the lower critical field does not show exponential dependence at low temperature, as would be expected for a fully gapped clean s-wave superconductor. In contrast, it shows a T2 power law feature up to T = 0.3Tc, as observed in Ba(1-x)K(x)Fe2As2 and BaFe(2-x)Co(x)As2.

Exotic d-wave superconducting state of strongly hole-doped K(x)Ba(1-x)Fe2As2

We investigate the superconducting phase in the K(x)Ba(1-x)Fe2As2 122 compounds from moderate to strong hole-doping regimes. Using the functional renormalization group, we show that, while the system develops a nodeless anisotropic s(±) order parameter in the moderately doped regime, gapping out the electron pockets at strong hole doping drives the system into a nodal (cos k(x) + cos k(y))(cos k(x) - cos k(y)) d-wave superconducting state. This is in accordance with recent experimental evidence from measurements on KFe2As2 which observe a nodal order parameter in the extreme doping regime. The magnetic instability is strongly suppressed.

Mechanism for explaining differences in the order parameters of FeAs-based and FeP-based pnictide superconductors

We put forward a scenario that explains the difference between the order-parameter character in arsenide (As) and phosphorous (P) iron-based superconductors. Using functional renormalization group to analyze it in detail, we find that nodal superconductivity on the electron pockets (hole pocket gaps are always nodeless) can naturally appear when the hole pocket at (π,π) in the unfolded Brillouin zone is absent, as is the case in LaOFeP. There, electron-electron interactions render the gap on the electron pockets softly nodal (of s(±) form). When the pocket of d(xy) orbital character is present, intraorbital interactions with the d(xy) part of the electron Fermi surface drives the superconductivity nodeless.

Local measurement of the superfluid density in the pnictide superconductor Ba(Fe(1-x)Co(x))(2)As(2) across the superconducting dome

We measure the penetration depth λab(T) in Ba(Fe(1-x)Co(x))(2)As(2) using local techniques that do not average over the sample. The superfluid density ρs(T) ≡ 1/λab(T)2 has three main features. First, ρs (T = 0) falls sharply on the underdoped side of the dome. Second, λab(T) is flat at low T at optimal doping, indicating fully gapped superconductivity, but varies more strongly in underdoped and overdoped samples, consistent with either a power law or a small second gap. Third, ρs (T) varies steeply near Tc for optimal and underdoping. These observations are consistent with an interplay between magnetic and superconducting phases.

Quasiparticle scattering induced by charge doping of iron-pnictide superconductors probed by collective vortex pinning

Charge doping of iron-pnictide superconductors leads to collective pinning of flux vortices, whereas isovalent doping does not. Moreover, flux pinning in the charge-doped compounds is consistently described by the mean-free path fluctuations introduced by the dopant atoms, allowing for the extraction of the elastic quasiparticle scattering rate. The absence of scattering by dopant atoms in isovalently doped BaFe2(As(1-x)P(x))(2) is consistent with the observation of a linear temperature dependence of the low-temperature penetration depth in this material.

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.

Anisotropic structure of the order parameter in FeSe(0.45)Te(0.55) revealed by angle-resolved specific heat

The central issues for understanding iron (Fe)-based superconductors are the symmetry and structure of the superconducting gap. So far the experimental data and theoretical models have been highly controversial. Some experiments favor two or more constant or nearly constant gaps, others indicate strong anisotropy and yet others suggest gap zeros ('nodes'). A unique method for addressing this issue, and one of very few methods that are bulk and angle resolved, is measuring the electronic-specific heat in a rotating magnetic field. In this study, we present the first such measurement for an Fe-based high-T(c) superconductor. We observed a fourfold oscillation of the specific heat as a function of the in-plane magnetic field direction. Our results are consistent with the expectations for an extended s-wave model, with a significant gap anisotropy on the electron pockets and the gap minima along the ΓM (Fe-Fe bond) direction.

Volovik effect in the ±s-wave state for the iron-based superconductors

We studied the field dependencies of specific heat coefficient γ(H)=lim(T→0)C(T,H)/T and thermal conductivity coefficient lim(T→0)κ(T,H)/T of the ±s-wave state in the mixed state. It is a generic feature of the two band s-wave state with the unequal sizes of gaps, small ΔS and large ΔL, that Doppler shift of the quasiparticle excitations (Volovik effect) creates a finite density of states, on the extended states outside of vortex cores, proportional to H in contrast to the square root(H) dependence of the d-wave state. The impurity scattering effect makes this generic H-linear dependence sublinear approaching to the square root(H) behavior. Our calculations of lim(T→0)κ(T,H)/T successfully fit the experimental data of Ba(Fe1-xCox)2 As2 with different Co-doping x by systematically varying the gap size ratio R=|ΔS|/|ΔL|. We also resolve the dilemma of a substantial value of γ(H→0) but almost zero value of lim(T→0)κ(T,H→0)/T.

Violation of Anderson's theorem for the sign-reversing s-wave state of iron-pnictide superconductors

Based on the five-orbital model, we study the effect of local impurity in iron pnictides, and find that the interband impurity scattering is promoted by the d-orbital degree of freedom. This fact means that the fully gapped sign-reversing s-wave state, which is predicted by spin fluctuation theories, is very fragile against impurities. In the BCS theory, only 1% impurities with intermediate strength induce huge pair breaking, resulting in the large in-gap state and prominent reduction in Tc, contrary to the prediction based on simple orbital-less models. The present study provides a stringent constraint on the pairing symmetry and the electronic states in iron pnictides.

Evidence for a nodal energy gap in the iron-pnictide superconductor LaFePO from penetration depth measurements by scanning SQUID susceptometry

We measure changes in the penetration depth lambda of the T_{c} approximately 6 K superconductor LaFePO. In the process, scanning SQUID susceptometry is demonstrated as a technique for accurately measuring local temperature-dependent changes in lambda, ideal for studying early or difficult-to-grow materials. lambda is found to vary linearly with temperatures from 0.36 to approximately 2 K, with a slope of 143 +/- 15 A/K, suggesting line nodes in the superconducting order parameter. The linear dependence up to approximately T_{c}/3, similar to the cuprate superconductors, indicates well-developed nodes.

Nonexponential London penetration depth of FeAs-based superconducting RFeAsO(0.9)F(0.1) (R = La, Nd) single crystals

The superconducting penetration depth lambda(T) has been measured in RFeAsO(0.9)F(0.1) (R = La, Nd) single crystals (R-1111). In Nd-1111, we find an upturn in lambda(T) upon cooling and attribute it to the paramagnetism of the Nd ions, similar to the case of the electron-doped cuprate Nd-Ce-Cu-O. After the correction for paramagnetism, the London penetration depth variation is found to follow a power-law behavior, Deltalambda_{L}(T) proportional, variantT;{2} at low temperatures. The same T2 variation of lambda(T) was found in nonmagnetic La-1111 crystals. Analysis of the superfluid density and of penetration depth anisotropy over the full temperature range is consistent with two-gap superconductivity. Based on this and on our previous work, we conclude that both the RFeAsO (1111) and BaFe(2)As(2) (122) families of pnictide superconductors exhibit unconventional two-gap superconductivity.