Superconductivity without nesting in LiFeAs

Charge-Density-Wave-Induced Peak-Dip-Hump Structure and the Multiband Superconductivity in a Kagome Superconductor CsV_{3}Sb_{5}

The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal AV_{3}Sb_{5} (A=K, Rb, Cs) family. With high-resolution angle-resolved photoemission spectroscopy, we study the electronic properties of CDW and superconductivity in CsV_{3}Sb_{5}. The spectra around K[over ¯] is found to exhibit a peak-dip-hump structure associated with two separate branches of dispersion, demonstrating the isotropic CDW gap opening below E_{F}. The peak-dip-hump line shape is contributed by linearly dispersive Dirac bands in the lower branch and a dispersionless flat band close to E_{F} in the upper branch. The electronic instability via Fermi surface nesting could play a role in determining these CDW-related features. The superconducting gap of ∼0.4  meV is observed on both the electron band around Γ[over ¯] and the flat band around K[over ¯], implying the multiband superconductivity. The finite density of states at E_{F} in the CDW phase is most likely in favor of the emergence of multiband superconductivity, particularly the enhanced density of states associated with the flat band. Our results not only shed light on the controversial origin of the CDW, but also offer insights into the relationship between CDW and superconductivity.

Iron pnictides and chalcogenides: a new paradigm for superconductivity

Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen-Cooper-Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund's interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

Importance of [Formula: see text] orbital and electron correlation in iron-based superconductors revealed by phase diagram for 1111-system

The structural flexibility at three substitution sites in LaFeAsO enabled investigation of the relation between superconductivity and structural parameters over a wide range of crystal compositions. Substitutions of Nd for La, Sb or P for As, and F or H for O were performed. All these substitutions modify the local structural parameters, while the F/H-substitution also changes band filling. It was found that the superconducting transition temperature [Formula: see text] is strongly affected by the pnictogen height [Formula: see text] from the Fe-plane that controls the electron correlation strength and the size of the [Formula: see text] hole Fermi surface (FS). With increasing [Formula: see text], weak coupling BCS superconductivity switches to the strong coupling non-BCS one where electron correlations and the [Formula: see text] hole FS may be important.

Effect of Nonlocal Correlations on the Electronic Structure of LiFeAs

We investigate the role of nonlocal correlations in LiFeAs by exploring an ab initio-derived multiorbital Hubbard model for LiFeAs via the two-particle self-consistent (TPSC) approach. The multiorbital formulation of TPSC approximates the irreducible interaction vertex to be an orbital-dependent constant, which is self-consistently determined from local spin and charge sum rules. Within this approach, we disentangle the contribution of local and nonlocal correlations in LiFeAs and show that in the local approximation one recovers the dynamical mean field theory result. The comparison of our theoretical results to most recent angular-resolved photoemission spectroscopy and de Haas-van Alphen data shows that nonlocal correlations in LiFeAs are decisive to describe the measured spectral function A(k[over →],ω), Fermi surface, and scattering rates. These findings underline the importance of nonlocal correlations and benchmark different theoretical approaches for iron-based superconductors.

Quantum Phase Transition of Correlated Iron-Based Superconductivity in LiFe_{1-x}Co_{x}As

The interplay between unconventional Cooper pairing and quantum states associated with atomic scale defects is a frontier of research with many open questions. So far, only a few of the high-temperature superconductors allow this intricate physics to be studied in a widely tunable way. We use scanning tunneling microscopy to image the electronic impact of Co atoms on the ground state of the LiFe_{1-x}Co_{x}As system. We observe that impurities progressively suppress the global superconducting gap and introduce low energy states near the gap edge, with the superconductivity remaining in the strong-coupling limit. Unexpectedly, the fully opened gap evolves into a nodal state before the Cooper pair coherence is fully destroyed. Our systematic theoretical analysis shows that these new observations can be quantitatively understood by the nonmagnetic Born-limit scattering effect in an s±-wave superconductor, unveiling the driving force of the superconductor to metal quantum phase transition.

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.

Magnetic excitations in the normal and nematic phases of iron pnictides

In this paper, we theoretically study the behaviors of the magnetic excitations (MEs) in the normal and nematic phases of iron pnictides. The normal state MEs exhibit commensurability to diamond and square-like structure transition with the increase of energy. This structure transition persists in the spin and orbital scenarios of nematic phases, although the MEs show anisotropic behaviors due to the C ₄ symmetry breaking induced by the nematic orders. The MEs exhibit distinct energy evolution behaviors between the spin and orbital scenarios of nematicity. For the spin-nematic scenario, the anisotropy of the MEs persists up to the high energy region. In contrast, for the orbital-nematic scenario, it reduces dramatically in the low energy region and is negligible in the high energy region. These distinct behaviors of the MEs are attributed to the different origins between the spin and orbital scenarios of nematic orders.

Observation of the weak electronic correlations in KFeCoAs2 (3d 6): an isoelectronic to the parent compounds of 122 series of iron pnictides BaFe2As2

Using the angle-resolved photoemission spectroscopy and band structure calculations we study the electronic structure of KFeCoAs₂, which is isoelectronic to the parent material of 122 series of iron-based superconductors BaFe₂As₂. Although band structure calculations predict nearly identical dispersions of the electronic states in both compounds, experiment reveals drastic differences in both the global renormalization and Fermi surfaces. On the basis of the comparison of electronic structures of these two isoelectronic compounds, we demonstrate local magnetic correlations as a vital role for the peculiar low-energy electron dynamics of iron-based superconductors.

Correlation-Enhanced Odd-Parity Interorbital Singlet Pairing in the Iron-Pnictide Superconductor LiFeAs

The rich variety of iron-based superconductors and their complex electronic structure lead to a wide range of possibilities for gap symmetry and pairing components. Here we solve in the two-Fe Brillouin zone the full frequency-dependent linearized Eliashberg equations to investigate spin-fluctuations mediated Cooper pairing for LiFeAs. The magnetic excitations are calculated with the random phase approximation on a correlated electronic structure obtained with density functional theory and dynamical mean field theory. The interaction between electrons through Hund's coupling promotes both the intraorbital d_{xz(yz)} and the interorbital magnetic susceptibility. As a consequence, the leading pairing channel, conventional s^{+-}, acquires sizable interorbital d_{xy}-d_{xz(yz)} singlet pairing with odd parity under glide-plane symmetry. The combination of intra- and interorbital components makes the results consistent with available experiments on the angular dependence of the gaps observed on the different Fermi surfaces.

Orbital Selective Spin Excitations and their Impact on Superconductivity of LiFe_{1-x}Co_{x}As

We use neutron scattering to study spin excitations in single crystals of LiFe_{0.88}Co_{0.12}As, which is located near the boundary of the superconducting phase of LiFe_{1-x}Co_{x}As and exhibits non-Fermi-liquid behavior indicative of a quantum critical point. By comparing spin excitations of LiFe_{0.88}Co_{0.12}As with a combined density functional theory and dynamical mean field theory calculation, we conclude that wave-vector correlated low energy spin excitations are mostly from the d_{xy} orbitals, while high-energy spin excitations arise from the d_{yz} and d_{xz} orbitals. Unlike most iron pnictides, the strong orbital selective spin excitations in the LiFeAs family cannot be described by an anisotropic Heisenberg Hamiltonian. While the evolution of low-energy spin excitations of LiFe_{1-x}Co_{x}As is consistent with the electron-hole Fermi surface nesting conditions for the d_{xy} orbital, the reduced superconductivity in LiFe_{0.88}Co_{0.12}As suggests that Fermi surface nesting conditions for the d_{yz} and d_{xz} orbitals are also important for superconductivity in iron pnictides.

Two distinct superconducting phases in LiFeAs

A non-trivial temperature evolution of superconductivity including a temperature-induced phase transition between two superconducting phases or even a time-reversal symmetry breaking order parameter is in principle expected in multiband superconductors such as iron-pnictides. Here we present scanning tunnelling spectroscopy data of LiFeAs which reveal two distinct superconducting phases: at = 18 K a partial superconducting gap opens, evidenced by subtle, yet clear features in the tunnelling spectra, i.e. particle-hole symmetric coherence peak and dip-hump structures. At Tc = 16 K, these features substantiate dramatically and become characteristic of full superconductivity. Remarkably, the distance between the dip-hump structures and the coherence peaks remains practically constant in the whole temperature regimeT ≤ . This rules out the connection of the dip-hump structures to an antiferromagnetic spin resonance.

Theoretical approach to resonant inelastic x-ray scattering in iron-based superconductors at the energy scale of the superconducting gap

We develop a phenomenological theory to predict the characteristic features of the momentum-dependent scattering amplitude in resonant inelastic x-ray scattering (RIXS) at the energy scale of the superconducting gap in iron-based super-conductors. Taking into account all relevant orbital states as well as their specific content along the Fermi surface we evaluate the charge and spin dynamical structure factors for the compounds LaOFeAs and LiFeAs, based on tight-binding models which are fully consistent with recent angle-resolved photoemission spectroscopy (ARPES) data. We find a characteristic intensity redistribution between charge and spin dynamical structure factors which discriminates between sign-reversing and sign-preserving quasiparticle excitations. Consequently, our results show that RIXS spectra can distinguish between s± and s++ wave gap functions in the singlet pairing case. In addition, we find that an analogous intensity redistribution at small momenta can reveal the presence of a chiral p-wave triplet pairing.

ARPES measurements of the superconducting gap of Fe-based superconductors and their implications to the pairing mechanism

Its direct momentum sensitivity confers to angle-resolved photoemission spectroscopy (ARPES) a unique perspective in investigating the superconducting gap of multi-band systems. In this review we discuss ARPES studies on the superconducting gap of high-temperature Fe-based superconductors. We show that while Fermi-surface-driven pairing mechanisms fail to provide a universal scheme for the Fe-based superconductors, theoretical approaches based on short-range interactions lead to a more robust and universal description of superconductivity in these materials. Our findings are also discussed in the broader context of unconventional superconductivity.

Orbital characters and electronic correlations in KCo2Se2

We report a comprehensive study of the tridimensional nature and orbital characters of the low-energy electronic structure in KCo2Se2, using polarization- and photon energy-dependent angle-resolved photoemission spectroscopy. We observed one electron-like Fermi surface (FS) at the Brillouin zone (BZ) center, four electron-like FSs centered at the BZ corner, and one hole-like FS at the BZ boundary. The FSs show weak dispersion along the kz direction, indicating the near-two-dimensional nature of FSs in KCo2Se2. In combination with the local-density approximation calculations, we determined the orbital characters of the low-energy electronic bands, which are mainly derived from the Co 3d orbital, mixed with part of the Se 4p states. The [Formula: see text] orbital gives a significant contribution to the band crossing the Fermi level. A band renormalization of about 1.6 is needed to capture the essential dispersive features, which suggests that electronic correlations are much weaker than that in KyFe2-xSe2.

Interaction-induced singular Fermi surface in a high-temperature oxypnictide superconductor

In the family of iron-based superconductors, LaFeAsO-type materials possess the simplest electronic structure due to their pronounced two-dimensionality. And yet they host superconductivity with the highest transition temperature Tc ≈ 55K. Early theoretical predictions of their electronic structure revealed multiple large circular portions of the Fermi surface with a very good geometrical overlap (nesting), believed to enhance the pairing interaction and thus superconductivity. The prevalence of such large circular features in the Fermi surface has since been associated with many other iron-based compounds and has grown to be generally accepted in the field. In this work we show that a prototypical compound of the 1111-type, SmFe(0.92)Co(0.08)AsO , is at odds with this description and possesses a distinctly different Fermi surface, which consists of two singular constructs formed by the edges of several bands, pulled to the Fermi level from the depths of the theoretically predicted band structure by strong electronic interactions. Such singularities dramatically affect the low-energy electronic properties of the material, including superconductivity. We further argue that occurrence of these singularities correlates with the maximum superconducting transition temperature attainable in each material class over the entire family of iron-based superconductors.

Reconstruction of band structure induced by electronic nematicity in an FeSe superconductor

We have performed high-resolution angle-resolved photoemission spectroscopy on an FeSe superconductor (T_{c}∼8  K), which exhibits a tetragonal-to-orthorhombic structural transition at T_{s}∼90  K. At low temperature, we found splitting of the energy bands as large as 50 meV at the M point in the Brillouin zone, likely caused by the formation of electronically driven nematic states. This band splitting persists up to T∼110  K, slightly above T_{s}, suggesting that the structural transition is triggered by the electronic nematicity. We have also revealed that at low temperature the band splitting gives rise to a van Hove singularity within 5 meV of the Fermi energy. The present result strongly suggests that this unusual electronic state is responsible for the unconventional superconductivity in FeSe.

The anomaly Cu doping effects on LiFeAs superconductors

The Cu substitution effect on the superconductivity of LiFeAs has been studied in comparison with Co/Ni substitution. It is found that the shrinking rate of the lattice parameter c for Cu substitution is much smaller than that of Co/Ni substitution. This is in conjugation with the observation of ARPES that shows almost the same electron and hole Fermi surfaces (FSs) size for undoped and Cu substituted LiFeAs sample, except for a very small hole band sinking below Fermi level with doping. This indicates that there is little doping effect at Fermi surface by Cu substitution, in sharp contrast to the more effective carrier doping effect by Ni or Co.

Optical conductivity of iron-based superconductors

The new family of unconventional iron-based superconductors discovered in 2006 immediately relieved their copper-based high-temperature predecessors as the most actively studied superconducting compounds in the world. The experimental and theoretical effort made in order to unravel the mechanism of superconductivity in these materials has been overwhelming. Although our understanding of their microscopic properties has been improving steadily, the pairing mechanism giving rise to superconducting transition temperatures up to 55 K remains elusive. And yet the hope is strong that these materials, which possess a drastically different electronic structure but similarly high transition temperatures compared to the copper-based compounds, will shed essential new light onto the several-decade-old problem of unconventional superconductivity. In this work we review the current understanding of the itinerant-charge-carrier dynamics in the iron-based superconductors and parent compounds largely based on the optical conductivity data the community has gleaned over the past seven years using such experimental techniques as reflectivity, ellipsometry, and terahertz transmission measurements and analyze the implications of these studies for the microscopic properties of the iron-based materials as well as the mechanism of superconductivity therein.

Lifshitz transition and chemical instabilities in Ba(1-x)K(x)Fe2As2 superconductors

For solid-solution Ba1-xKxFe2As2 Fermi surface evolution is mapped via Bloch spectral functions calculated using density functional theory implemented in Korringa-Kohn-Rostoker multiple scattering theory with the coherent-potential approximation. Spectral functions reveal electronic dispersion, topology, orbital character, and broadening (electron-lifetime effects) due to chemical disorder. Dissolution of electron cylinders occurs near x∼0.9 with a nonuniform, topological (Lifshitz) transition, reducing the interband interactions; yet the dispersion maintains its dxz or dyz character. Formation energies indicate alloying at x=0.35, as observed, and a tendency for segregation on the K-rich (x>0.6) side, explaining the difficulty of controlling sample quality and the conflicting results between characterized electronic structures. Our results reveal Fermi surface transitions in alloyed samples that influence s± to nodal superconductivity and suggest the origin for deviations of common trends in Fe-based superconductors, such as Bud'ko-Ni-Canfield scaling.

Nature of the bad metallic behavior of Fe1.06Te inferred from its evolution in the magnetic state

We investigate with angle-resolved photoelectron spectroscopy the changes of the Fermi surface and the main bands from the paramagnetic state to the antiferromagnetic (AFM) state occurring below 72 K in Fe1.06Te. The evolution is completely different from that observed in Fe pnictides, as nesting is absent. The AFM state is a rather good metal, in agreement with our magnetic band structure calculation. On the other hand, the paramagnetic state is very anomalous with a large pseudogap of ~65 meV on the electron pocket that closes in the AFM state. We discuss this behavior in connection with spin fluctuations existing above the magnetic transition and the correlations predicted in the spin-freezing regime of the incoherent metallic state.

A phenomenological multiband Eliashberg model for LiFeAs

The phenomenology of a LiFeAs superconductor can be explained in the framework of four-band s±-wave Eliashberg theory. We have examined the experimental data available in the literature and we have found that it is possible to reproduce the experimental critical temperature, the gap values and the upper critical magnetic field within an effective model in a moderately strong coupling regime that must include both an intraband term λ11 ∼ 0.9 and an interband spin-fluctuation ([Formula: see text]) coupling. The presence of a nonnegligible intraband coupling can be a fictitious effect of the violation of Migdal's theorem.

A flat band at the chemical potential of a Fe1.03Te0.94S0.06 superconductor observed by angle-resolved photoemission spectroscopy

The electronic structure of superconducting Fe1.03Te0.94S0.06 has been studied by angle-resolved photoemission spectroscopy (ARPES). Experimental band topography is compared to the calculations using the methods of Korringa-Kohn-Rostoker (KKR) with the coherent potential approximation (CPA) and the linearized augmented plane wave with local orbitals (LAPW+LO) method. The region of the Γ point exhibits two hole pockets and a quasiparticle peak close to the chemical potential (μ) with undetectable dispersion. This flat band with mainly d(z)(2) orbital character is most likely formed by the top of the outer hole pocket or is evidence of a third hole band. It may cover up to 3% of the Brillouin zone volume and should give rise to a Van Hove singularity. Studies performed for various photon energies indicate that at least one of the hole pockets has a two-dimensional character. The apparently nondispersing peak at μ is clearly visible for 40 eV and higher photon energies, due to an effect of the photoionization cross-section rather than band dimensionality. Orbital characters calculated by LAPW+LO for stoichiometric FeTe do not reveal the flat dz(2) band but are in agreement with the experiment for the other dispersions around Γ in Fe1.03Te0.94S0.06.

Anomalous superconducting state in LiFeAs implied by the 75As Knight shift measurement

(75)As NMR investigation of a single crystal of superconducting LiFeAs is presented. The Knight shift and the in situ ac susceptibility measurements as a function of temperature and external field are indicative of two superconducting (SC) transition temperatures, each of which is associated with its own upper critical field. Strikingly, the Knight shift maintains its normal state value over a temperature range in the SC state before it drops abruptly, being consistent with spin-singlet pairing. Together with our previous NMR study, the anomalous SC state featuring the constant Knight shift is attributed to the extremely sensitive SC properties of LiFeAs, probably stemming from its proximity to a critical instability.

Interband quasiparticle scattering in superconducting LiFeAs reconciles photoemission and tunneling measurements

Several angle-resolved photoemission spectroscopy (ARPES) studies reveal a poorly nested Fermi surface of LiFeAs, far away from a spin density wave instability, and clear-cut superconducting gap anisotropies. On the other hand a very different, more nested Fermi surface and dissimilar gap anisotropies have been obtained from quasiparticle interference (QPI) data, which were interpreted as arising from intraband scattering within holelike bands. Here we show that this ARPES-QPI paradox is completely resolved by interband scattering between the holelike bands. The resolution follows from an excellent agreement between experimental quasiparticle scattering data and T-matrix QPI calculations (based on experimental band structure data), which allows disentangling interband and intraband scattering processes.

Construction and performance of a dilution-refrigerator based spectroscopic-imaging scanning tunneling microscope

We report on the set-up and performance of a dilution-refrigerator based spectroscopic imaging scanning tunneling microscope. It operates at temperatures below 10 mK and in magnetic fields up to 14T. The system allows for sample transfer and in situ cleavage. We present first-results demonstrating atomic resolution and the multi-gap structure of the superconducting gap of NbSe(2) at base temperature. To determine the energy resolution of our system we have measured a normal metal/vacuum/superconductor tunneling junction consisting of an aluminum tip on a gold sample. Our system allows for continuous measurements at base temperature on time scales of up to ≈170 h.

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.

Many-body effects in iron pnictides and chalcogenides: nonlocal versus dynamic origin of effective masses

We apply the quasiparticle self-consistent GW approximation (QSGW) to some of the iron pnictide and chalcogenide superconductors. We compute Fermi surfaces and density of states, and find excellent agreement with experiment, substantially improving over standard band-structure methods. Analyzing the QSGW self-energy we discuss nonlocal and dynamic contributions to effective masses. We present evidence that the two contributions are mostly separable, since the quasiparticle weight is found to be essentially independent of momentum. The main effect of nonlocality is captured by the static but nonlocal QSGW effective potential. Moreover, these nonlocal self-energy corrections, absent in, e.g., dynamical mean field theory, can be relatively large. We show, on the other hand, that QSGW only partially accounts for dynamic renormalizations at low energies. These findings suggest that QSGW combined with dynamical mean field theory will capture most of the many-body physics in the iron pnictides and chalcogenides.

Specific heat versus field for LiFe(1-x)Cu(x)As

LiFeAs is one of the new class of iron superconductors with a bulk [Formula: see text] in the 15-17 K range. We report on the specific heat characterization of single crystal material prepared by self-flux growth techniques with significantly improved properties, including a much decreased residual gamma, γ(r) (≡C/T as T → 0), in the superconducting state. Thus, in contrast to previous explanations of a finite γ(r) in LiFeAs being due to intrinsic states in the superconducting gap, the present work shows that such a finite residual γ in LiFeAs is instead a function of sample quality. Further, since LiFeAs has been characterized as nodeless with multiple superconducting gaps, we report here on its specific heat properties in zero and applied magnetic fields, to compare to similar results on nodal iron superconductors. For comparison, we also investigate LiFe(0.98)Cu(0.02)As, which has the reduced T(c) of ≈9 K and an H(c2) of 15 T. Interestingly, although presumably both LiFeAs and LiFe(0.98)Cu(0.02)As are nodeless, they clearly show a non-linear dependence of the electronic density of states (is proportional to specific heat γ) at the Fermi energy in the mixed state with the applied field, similar to the Volovik effect for nodal superconductors. However, rather than indicating nodal behavior, the satisfactory comparison with a recent theory for γ(H) for a superconductor with two isotropic gaps in the presence of impurities argues for nodeless behavior. Thus, in terms of specific heat in a magnetic field, LiFeAs can serve as the prototypical multiband, nodeless iron superconductor.

Multiorbital effects on the transport and the superconducting fluctuations in LiFeAs

The resistivity, Hall effect, and transverse magnetoresistance have been measured in low residual resistivity single crystals of LiFeAs. A comparison with angle resolved photoemission spectroscopy and quantum oscillation data implies that four carrier bands unevenly contribute to the transport. However the scattering rates of the carriers all display the T(2) behavior expected for a Fermi liquid. Near T(c) low field deviations of the magnetoresistance with respect to a H(2) variation permit us to extract the superconducting fluctuation contribution to the conductivity. Though below T(c) the anisotropy of superconductivity is rather small, the superconducting fluctuation displays a quasi-ideal two-dimensional behavior which persists up to 1.4 T(c). These results call for a refined theoretical understanding of the multiband behavior of superconductivity in this pnictide.

Orbital selective Fermi surface shifts and mechanism of high T(c) superconductivity in correlated AFeAs (A=Li, Na)

Based on the dynamical mean field theory and angle resolved photoemission spectroscopy, we have investigated the mechanism of high T(c) superconductivity in stoichiometric LiFeAs. The calculated spectrum is in excellent agreement with the measured angle resolved photoemission spectroscopy. The Fermi surface (FS) nesting, which is predicted in the conventional density functional theory method, is suppressed due to the orbital-dependent correlation effect within the dynamical mean field theory method. We have shown that such marginal breakdown of the FS nesting is an essential condition to the spin-fluctuation mediated superconductivity, while the good FS nesting in NaFeAs induces a spin density wave ground state. Our results indicate that a fully charge self-consistent description of the correlation effect is crucial in the description of the FS nesting-driven instabilities.

Scanning tunneling spectroscopy of superconducting LiFeAs single crystals: evidence for two nodeless energy gaps and coupling to a bosonic mode

The superconducting compound LiFeAs is studied by scanning tunneling microscopy and spectroscopy. A gap map of the unreconstructed surface indicates a high degree of homogeneity in this system. Spectra at 2 K show two nodeless superconducting gaps with Δ(1)=5.3±0.1 meV and Δ(2)=2.5±0.2 meV. The gaps close as the temperature is increased to the bulk T(c), indicating that the surface accurately represents the bulk. A dip-hump structure is observed below T(c) with an energy scale consistent with a magnetic resonance recently reported by inelastic neutron scattering.

Three dimensionality and orbital characters of the Fermi surface in (Tl,Rb)(y)Fe(2-x)Se2

We report a comprehensive angle-resolved photoemission spectroscopy study of the tridimensional electronic bands in the recently discovered Fe selenide superconductor ((Tl,Rb)(y)Fe(2-x)Se2 (T(c)=32  K). We determined the orbital characters and the k(z) dependence of the low energy electronic structure by tuning the polarization and the energy of the incident photons. We observed a small 3D electron Fermi surface pocket near the Brillouin zone center and a 2D like electron Fermi surface pocket near the zone boundary. The photon energy dependence, the polarization analysis and the local-density approximation calculations suggest a significant contribution from the Se 4p(z) and Fe 3d(xy) orbitals to the small electron pocket. We argue that the emergence of Se 4p(z) states might be the cause of the different magnetic properties between Fe chalcogenides and Fe pnictides.

Theoretical investigation on the structural and thermodynamic properties of FeSe at high pressure and high temperature

A theoretical investigation on structural and thermodynamic properties of 11-type iron-based superconductor FeSe at high pressure and high temperature was performed by employing the first-principles method based on the density functional theory. Some structural parameters of FeSe in both tetragonal and hexagonal phases are reported. According to the fourth-order Birch-Murnaghan equation of states, the transition pressure P(t) of FeSe from the PbO-type phase to the NiAs-type phase was determined. The calculated results are found to be in good agreement with the available experimental data. Based on the quasi-harmonic Debye model, the pressure and temperature dependence of the thermodynamic properties for hexagonal phase FeSe were investigated. Our theoretical calculations suggest that the pressure and temperature have significant effects on the heat capacity, vibrational internal energy, vibrational entropy, vibrational Helmholtz free energy, thermal expansion coefficient and Debye temperature. Even though few theoretical reports on the structural properties of FeSe are found in the current literature, to our knowledge, this is a novel theoretical investigation on the structural and thermodynamic properties of FeSe at high temperature. We hope that the theoretical results reported here can give more insight into the structural and thermodynamic properties of other iron-based superconductors at high temperature.

Probing the unconventional superconducting state of LiFeAs by quasiparticle interference

A crucial step in revealing the nature of unconventional superconductivity is to investigate the symmetry of the superconducting order parameter. Scanning tunneling spectroscopy has proven a powerful technique to probe this symmetry by measuring the quasiparticle interference (QPI) which sensitively depends on the superconducting pairing mechanism. A particularly well-suited material to apply this technique is the stoichiometric superconductor LiFeAs as it features clean, charge neutral cleaved surfaces without surface states and a relatively high T(c)∼18  K. Our data reveal that in LiFeAs the quasiparticle scattering is governed by a van Hove singularity at the center of the Brillouin zone which is in stark contrast to other pnictide superconductors where nesting is crucial for both scattering and s(±) superconductivity. Indeed, within a minimal model and using the most elementary order parameters, calculations of the QPI suggest a dominating role of the holelike bands for the quasiparticle scattering. Our theoretical findings do not support the elementary singlet pairing symmetries s(++), s(±), and d wave. This brings to mind that the superconducting pairing mechanism in LiFeAs is based on an unusual pairing symmetry such as an elementary p wave (which provides optimal agreement between the experimental data and QPI simulations) or a more complex order parameter (e.g., s+id wave symmetry).

Inelastic neutron-scattering measurements of incommensurate magnetic excitations on superconducting LiFeAs single crystals

Magnetic correlations in superconducting LiFeAs were studied by elastic and by inelastic neutron-scattering experiments. There is no indication for static magnetic ordering, but inelastic correlations appear at the incommensurate wave vector (0.5±δ,0.5-/+δ,0) with δ~0.07 slightly shifted from the commensurate ordering observed in other FeAs-based compounds. The incommensurate magnetic excitations respond to the opening of the superconducting gap by a transfer of spectral weight.

de Haas-van Alphen study of the Fermi surfaces of superconducting LiFeP and LiFeAs

We report a de Haas-van Alphen oscillation study of the 111 iron pnictide superconductors LiFeAs with T(c) ≈ 18 K and LiFeP with T(c) ≈ 5 K. We find that for both compounds the Fermi surface topology is in good agreement with density functional band-structure calculations and has almost nested electron and hole bands. The effective masses generally show significant enhancement, up to ~3 for LiFeP and ~5 for LiFeAs. However, one hole Fermi surface in LiFeP shows a very small enhancement, as compared with its other sheets. This difference probably results from k-dependent coupling to spin fluctuations and may be the origin of the different nodal and nodeless superconducting gap structures in LiFeP and LiFeAs, respectively.

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.

Unconventional anisotropic s-wave superconducting gaps of the LiFeAs iron-pnictide superconductor

We have performed high-resolution angle-resolved photoemission spectroscopy on Fe-based superconductor LiFeAs (T(c)=18 K). We reveal multiple nodeless superconducting (SC) gaps with 2Δ/k(B)T(c) ratios varying from 2.8 to 6.4, depending on the Fermi surface (FS). We also succeeded in directly observing a gap anisotropy along the FS with magnitude up to ~30%. The anisotropy is fourfold symmetric with an antiphase between the hole and electron FSs, suggesting complex anisotropic interactions for the SC pairing. The observed momentum dependence of the SC gap offers an excellent opportunity to investigate the underlying pairing mechanism.

Kinetic frustration and the nature of the magnetic and paramagnetic states in iron pnictides and iron chalcogenides

The iron pnictide and chalcogenide compounds are a subject of intensive investigations owing to their surprisingly high temperature superconductivity. They all share the same basic building blocks, but there is significant variation in their physical properties, such as magnetic ordered moments, effective masses, superconducting gaps and transition temperature (T(c)). Many theoretical techniques have been applied to individual compounds but no consistent description of the microscopic origin of these variations is available. Here we carry out a comparative theoretical study of a large number of iron-based compounds in both their magnetic and paramagnetic states. Taking into account correlation effects and realistic band structures, we describe well the trends in all of the physical properties such as the ordered moments, effective masses and Fermi surfaces across all families of iron compounds, and find them to be in good agreement with experiments. We trace variation in physical properties to variations in the key structural parameters, rather than changes in the screening of the Coulomb interactions. Our results also provide a natural explanation of the strongly Fermi-surface-dependent superconducting gaps observed in experiments.

Magnetic order in orbital models of the iron pnictides

We examine the appearance of the experimentally observed stripe spin-density-wave magnetic order in five different orbital models of the iron pnictide parent compounds. A restricted mean-field ansatz is used to determine the magnetic phase diagram of each model. Using the random phase approximation, we then check this phase diagram by evaluating the static spin susceptibility in the paramagnetic state close to the mean-field phase boundaries. The momenta for which the susceptibility is peaked indicate in an unbiased way the actual ordering vector of the nearby mean-field state. The dominant orbitally resolved contributions to the spin susceptibility are also examined to determine the origin of the magnetic instability. We find that the observed stripe magnetic order is possible in four of the models, but it is extremely sensitive to the degree of nesting between the electron and hole Fermi pockets. In the more realistic five-orbital models, this order competes with a strong-coupling incommensurate state which appears to be controlled by details of the electronic structure below the Fermi energy. We conclude by discussing the implications of our work for the origin of the magnetic order in the pnictides.

Nodeless superconducting gap in A(x)Fe2Se2 (A=K,Cs) revealed by angle-resolved photoemission spectroscopy

Pairing symmetry is a fundamental property that characterizes a superconductor. For the iron-based high-temperature superconductors, an s(±)-wave pairing symmetry has received increasing experimental and theoretical support. More specifically, the superconducting order parameter is an isotropic s-wave type around a particular Fermi surface, but it has opposite signs between the hole Fermi surfaces at the zone centre and the electron Fermi surfaces at the zone corners. Here we report the low-energy electronic structure of the newly discovered superconductors, A(x)Fe(2)Se(2) (A=K,Cs) with a superconducting transition temperature (Tc) of about 30 K. We found A(x)Fe(2)Se(2) (A=K,Cs) is the most heavily electron-doped among all iron-based superconductors. Large electron Fermi surfaces are observed around the zone corners, with an almost isotropic superconducting gap of ~10.3 meV, whereas there is no hole Fermi surface near the zone centre, which demonstrates that interband scattering or Fermi surface nesting is not a necessary ingredient for the unconventional superconductivity in iron-based superconductors. Thus, the sign change in the s(±) pairing symmetry driven by the interband scattering as suggested in many weak coupling theories becomes conceptually irrelevant in describing the superconducting state here. A more conventional s-wave pairing is probably a better description.

Interplay among Coulomb interaction, spin-orbit interaction, and multiple electron-boson interactions in Sr2RuO4

Using polarization- and hν-dependent angle-resolved photoemission spectroscopy, we uncovered the fine details of a quasiparticle's dynamics of a typical multiband superconductor, Sr2RuO4. We found strong hybridization between the in-plane and out-of-plane quasiparticles via the Coulomb and spin-orbit interactions. This effect enhances the quasiparticle mass due to the inflow of out-of-plane quasiparticles into the two-dimensional Fermi surface sheet, where the quasiparticles are further subjected to the multiple electron-boson interactions. We suggest that the spin-triplet p-wave superconductivity of Sr2RuO4 is phonon mediated.

Electronic-structure-driven magnetic and structure transitions in superconducting NaFeAs single crystals measured by angle-resolved photoemission spectroscopy

The electronic structure of NaFeAs is studied with angle-resolved photoemission spectroscopy on high quality single crystals. Large portions of the band structure start to shift around the structural transition temperature and smoothly evolve as the temperature lowers through the spin density wave transition. Moreover, band folding due to magnetic order emerges slightly above the structural transition. Our observation provides direct evidence that the structural and magnetic transitions share the same origin and could both be driven by the electronic structure reconstruction in Fe-based superconductors instead of Fermi surface nesting. We did not observe any sign of a gap in the superconducting state, which is likely related to weakened superconductivity in the presence of the spin density wave.