Evidence for a nodal-line superconducting state in LaFePO

Observation of the non-linear Meissner effect

A long-standing theoretical prediction is that in clean, nodal unconventional superconductors the magnetic penetration depth λ, at zero temperature, varies linearly with magnetic field. This non-linear Meissner effect is an equally important manifestation of the nodal state as the well studied linear-in-T dependence of λ, but has never been convincingly experimentally observed. Here we present measurements of the nodal superconductors CeCoIn5 and LaFePO which clearly show this non-linear Meissner effect. We further show how the effect of a small dc magnetic field on λ(T) can be used to distinguish gap nodes from non-nodal deep gap minima. Our measurements of KFe2As2 suggest that this material has such a non-nodal state.

Prediction of topological nontrivial semimetals and pressure-induced Lifshitz transition in 1T'-MoS2 layered bulk polytypes

Recently, bulk MoS2 crystals stacked by 1T'-MoS2 monolayers have been synthesized successfully, but little is known about their stacking sequences and topological properties. Based on first-principles calculations and symmetry-based indicator theory, we discovered that three predicted bulk structures of MoS2 (named 2M-, 1T'- and β-MoS2) stacked by 1T' monolayers are topological insulators and nodal line semimetals with and without spin-orbit coupling. Their stacking stability, electronic structure and the topology origin were systematically investigated. Further research proves that in the absence of SOC the open- and closed-type nodal lines can coexist in the momentum space of 2M-MoS2, which also possesses drumhead-like surface state. Moreover, we predicted a pressure-induced Lifshitz transition at about 1.3 GPa in 2M-MoS2. Our findings greatly enrich the topological phases of MoS2 and probably bring MoS2 to the rapidly growing family of layered topological semimetals.

p-wave superconductivity in iron-based superconductors

The possibility of p-wave pairing in superconductors has been proposed more than five decades ago, but has not yet been convincingly demonstrated. One difficulty is that some p-wave states are thermodynamically indistinguishable from s-wave, while others are very similar to d-wave states. Here we studied the self-field critical current of NdFeAs(O,F) thin films in order to extract absolute values of the London penetration depth, the superconducting energy gap, and the relative jump in specific heat at the superconducting transition temperature, and find that all the deduced physical parameters strongly indicate that NdFeAs(O,F) is a bulk p-wave superconductor. Further investigation revealed that single atomic layer FeSe also shows p-wave pairing. In an attempt to generalize these findings, we re-examined the whole inventory of superfluid density measurements in iron-based superconductors and show quite generally that single-band weak-coupling p-wave superconductivity is exhibited in iron-based superconductors.

High-energy spin fluctuation in low-Tc iron-based superconductor LaFePO0.9

Spin fluctuations are widely believed to play an important role in the superconducting mechanisms of unconventional high temperature superconductors. Spin fluctuations have been observed in iron-based superconductors as well. However, in some iron-based superconductors such as LaFePO_0.9, they have not been observed by inelastic neutron scattering (INS). LaFePO_0.9 is an iron-based superconductor with a low superconducting transition temperature (T_c = 5 K), where line nodes are observed in the superconducting gap function. The line-node symmetry typically originates from sign reversal of the order parameter in spin-fluctuation-mediated superconductivity. This contradiction has been a long-standing mystery of this superconductor. Herein, spin fluctuations were found at high energies such as 30–50 meV with comparable intensities to an optimally doped LaFeAs(O, F). Based on this finding, the line-node symmetry can be explained naturally as spin-fluctuation-mediated superconductivity.

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.

Direct evidence for a pressure-induced nodal superconducting gap in the Ba0.65Rb0.35Fe2As2 superconductor

The superconducting gap structure in iron-based high-temperature superconductors (Fe-HTSs) is non-universal. In contrast to other unconventional superconductors, in the Fe-HTSs both d-wave and extended s-wave pairing symmetries are close in energy. Probing the proximity between these very different superconducting states and identifying experimental parameters that can tune them is of central interest. Here we report high-pressure muon spin rotation experiments on the temperature-dependent magnetic penetration depth in the optimally doped nodeless s-wave Fe-HTS Ba0.65Rb0.35Fe2As2. Upon pressure, a strong decrease of the penetration depth in the zero-temperature limit is observed, while the superconducting transition temperature remains nearly constant. More importantly, the low-temperature behaviour of the inverse-squared magnetic penetration depth, which is a direct measure of the superfluid density, changes qualitatively from an exponential saturation at zero pressure to a linear-in-temperature behaviour at higher pressures, indicating that hydrostatic pressure promotes the appearance of nodes in the superconducting gap.

Absence of strong magnetic fluctuations in FeP-based systems LaFePO and Sr₂ScO₃FeP

We report neutron inelastic scattering measurements on polycrystalline LaFePO and Sr2ScO3FeP, two members of the iron phosphide families of superconductors. No evidence is found for any magnetic fluctuations in the spectrum of either material in the energy and wavevector ranges probed. Special attention is paid to the wavevector at which spin-density-wave-like fluctuations are seen in other iron-based superconductors. We estimate that the magnetic signal, if present, is at least a factor of four (Sr2ScO3FeP) or seven (LaFePO) smaller than in the related iron arsenide and chalcogenide superconductors. These results suggest that magnetic fluctuations are not as influential on the electronic properties of the iron phosphide systems as they are in other iron-based superconductors.

Fermi surface topology of LaFePO and LiFeP

We perform charge self-consistent density functional theory combined with dynamical mean field theory calculations to study correlation effects on the Fermi surfaces of the iron pnictide superconductors LaFePO and LiFeP. We find a distinctive change in the topology of the Fermi surface in both compounds where a hole pocket with Fe d(z(2)) orbital character changes its geometry from a closed shape in the local-density approximation to an open shape upon inclusion of correlations. The opening of the pocket occurs in the vicinity of the Γ (Z) point in LaFePO (LiFeP). We discuss the relevance of these findings for the low superconducting transition temperature and the nodal gap observed in these materials.

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.

The electron-pairing mechanism of iron-based superconductors

The past three years have witnessed the discovery of a series of novel high-temperature superconductors. Trailing behind the cuprates, these iron-based compounds are the second-highest-temperature superconducting material family known to date. Despite the marked differences in the chemical composition, these materials share many properties with the cuprates and offer the hope of finally unveiling the secret of high-temperature superconductivity. The main theme of this review is the electron-pairing mechanism responsible for their superconductivity. We discuss the progress in this young field and point out the open issues.

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.

Nodes versus minima in the energy gap of iron pnictide superconductors from field-induced anisotropy

We develop the formalism for computing the oscillations of the specific heat and thermal transport under rotated magnetic field in multiband superconductors with anisotropic gap and apply it to iron-based materials. We show that these oscillations change sign at low temperatures and fields, which strongly influences the experimental conclusions about the gap structure. We find that recent measurements of the specific heat oscillations indicate that the iron-based superconductors possess an anisotropic gap with deep minima or nodes close to the line connecting electron and hole pockets. We predict the behavior of the thermal conductivity that will help distinguish between these cases.

Quantum oscillations probe the normal electronic states of novel superconductors

In 2008, new classes of high-temperature superconductors containing iron have been discovered. These iron pnictides offer a new area of exploration and understanding of superconductivity. Quantum oscillations is a bulk probe that allows us to map out the full Fermi surface of a superconducting system in its normal metallic state. These oscillations are determined by the Landau quantization in high magnetic fields and are usually observed at very low temperatures and in very clean samples. By knowing the exact nature of the quasi-particles in the normal state and the degree of electronic correlations, one can simplify and restrict theoretical models required to understand the pairing mechanism in superconductors. I will discuss the current understanding of the Fermi surface studies in iron-based superconductors as determined from quantum oscillations.

A perspective on the Fe-based superconductors

FeSe is employed as reference material to elucidate the observed high T(c) superconducting behaviour of the related layered iron pnictides. The structural and ensuing semimetallic band structural forms are here rather unusual, with the resulting ground state details extremely sensitive to the precise shape of the Fe-X coordination unit. The superconductivity is presented as coming from a combination of resonant valence bond and excitonic insulator physics, and incorporating boson-fermion degeneracy. Although sourced in a very different fashion, the latter leads to some similarities with the high temperature superconducting (HTSC) cuprates. The excitonic insulator behaviour sees spin density wave, charge density wave/periodic structural distortion, and superconductive instabilities all vie for ground state status. The conflict leads to a very sensitive and complex set of properties, frequently mirroring HTSC cuprate behaviour. The delicate balance between ground states is made particularly difficult to unravel by the micro-inhomogeneity of structural form which it can engender. It is pointed out that several other notable superconductors, layered in form, semimetallic with indirect overlap and possessing homopolar bonding, would look to fall into the same general category, β-ZrNCl and MgB(2) and the high pressure forms of several elements, like sulfur, phosphorus, lithium and calcium, being cases in point.

Self-energy effects and electron-phonon coupling in Fe-As superconductors

Doping and temperature dependent studies of optical phonon modes in Fe-122 pnictides are performed using Raman scattering experiments and compared with model calculations to elucidate the role of electron-phonon and spin-phonon interaction in this family of compounds. The frequency and linewidth of the B(1g) mode at around 210 cm(-1) is highlighted as appreciable anomalies at the superconducting and spin density wave transitions are observed that strongly depend on composition. We give estimates of the electron-phonon coupling related to this renormalization and calculate the phonon self-energy on the basis of a four-band model comparing different symmetries of the order parameters. In addition, we observe a pronounced quasi-elastic Raman response for the undoped compound, suggesting persisting magnetic fluctuations in the spin density wave state.

Quantum criticality and nodal superconductivity in the FeAs-based superconductor KFe2As2

The in-plane resistivity rho and thermal conductivity kappa of the FeAs-based superconductor KFe2As2 single crystal were measured down to 50 mK. We observe non-Fermi-liquid behavior rho(T) approximately T{1.5} at H{c{2}}=5 T, and the development of a Fermi liquid state with rho(T) approximately T{2} when further increasing the field. This suggests a field-induced quantum critical point, occurring at the superconducting upper critical field H{c{2}}. In zero field, there is a large residual linear term kappa{0}/T, and the field dependence of kappa_{0}/T mimics that in d-wave cuprate superconductors. This indicates that the superconducting gaps in KFe2As2 have nodes, likely d-wave symmetry. Such a nodal superconductivity is attributed to the antiferromagnetic spin fluctuations near the quantum critical point.

Doping dependence of heat transport in the iron-arsenide superconductor Ba(Fe(1-x)Co(x))2As2: from isotropic to a strongly k-dependent gap structure

The temperature and magnetic field dependence of the in-plane thermal conductivity kappa of the iron-arsenide superconductor Ba(Fe(1-x)Co(x))2As2 was measured down to T approximately 50 mK and up to H = 15 T as a function of Co concentration x in the range 0.048 < or = x < or = 0.114. At H = 0, a negligible residual linear term in kappa/T as T-->0 at all x shows that the superconducting gap has no nodes in the ab plane anywhere in the phase diagram. However, while the slow H dependence of kappa(H) at T-->0 in the underdoped regime is consistent with a superconducting gap that is large everywhere on the Fermi surface, the rapid increase in kappa(H) observed in the overdoped regime shows that the gap acquires a deep minimum somewhere on the Fermi surface. Outside the antiferromagnetic-orthorhombic phase, the superconducting gap structure has a strongly k-dependent amplitude.

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.

Theory of multiband superconductivity in iron pnictides

The precise nature of unconventional superconductivity (SC) in iron pnictides is presently a hotly debated issue. Here, using insights from normal state electronic structure and symmetry arguments, we show how an unconventional SC emerges from the bad metal "normal" state. Short-ranged, multiband spin and charge correlations generate nodeless SC in the active planar dxz,yz bands, and an interband proximity effect induces out-of-plane gap nodes in the passive d3z2-r2 band. While very good quantitative agreement with various key observations in the SC state and reconciliation with NMR and penetration depth data in the same picture are particularly attractive features of our proposal, clinching evidence would be an experimental confirmation of c-axis nodes in future work.

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.