Electronic nematicity above the structural and superconducting transition in BaFe2(As(1-x)P(x))2

Giant superconducting fluctuations in the compensated semimetal FeSe at the BCS-BEC crossover

The physics of the crossover between weak-coupling Bardeen–Cooper–Schrieffer (BCS) and strong-coupling Bose–Einstein condensate (BEC) limits gives a unified framework of quantum-bound (superfluid) states of interacting fermions. This crossover has been studied in the ultracold atomic systems, but is extremely difficult to be realized for electrons in solids. Recently, the superconducting semimetal FeSe with a transition temperature T_c=8.5 K has been found to be deep inside the BCS–BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe, whose energy scale is comparable to the Fermi energies. In stark contrast to usual superconductors, large non-linear diamagnetism by far exceeding the standard Gaussian superconducting fluctuations is observed below T*∼20 K, providing thermodynamic evidence for prevailing phase fluctuations of superconductivity. Nuclear magnetic resonance and transport data give evidence of pseudogap formation at ∼T*. The multiband superconductivity along with electron–hole compensation in FeSe may highlight a novel aspect of the BCS–BEC crossover physics.

The crossover between the weak-coupling limit and strong-coupling limit provides important information for quantum bound states of interacting fermions. Here, Kasahara et al. report thermodynamic evidence for prevailing phase fluctuations of superconductivity, highlighting unusual normal state in the BCS-BEC crossover regime.

Multi-orbital quantum antiferromagnetism in iron pnictides-effective spin couplings and quantum corrections to sublattice magnetization

Effective spin couplings and spin fluctuation induced quantum corrections to sublattice magnetization are obtained in the [Formula: see text] AF state of a realistic three-orbital interacting electron model involving xz, yz and xy Fe 3d orbitals, providing insight into the multi-orbital quantum antiferromagnetism in iron pnictides. The xy orbital is found to be mainly responsible for the generation of strong ferromagnetic spin coupling in the b direction, which is critically important to fully account for the spin wave dispersion as measured in inelastic neutron scattering experiments. The ferromagnetic spin coupling is strongly suppressed as the xy band approaches half filling, and is ascribed to particle-hole exchange in the partially filled xy band. The strongest AF spin coupling in the a direction is found to be in the orbital off-diagonal sector involving the xz and xy orbitals. First order quantum corrections to sublattice magnetization are evaluated for the three orbitals, and yield a significant [Formula: see text] average reduction from the Hartree-Fock value.

Influence of interstitial Fe to the phase diagram of Fe1+yTe1-xSex single crystals

Superconductivity (SC) with the suppression of long-range antiferromagnetic (AFM) order is observed in the parent compounds of both iron-based and cuprate superconductors. The AFM wave vectors are bicollinear (π, 0) in the parent compound FeTe different from the collinear AFM order (π, π) in most iron pnictides. Study of the phase diagram of Fe1+yTe1-xSex is the most direct way to investigate the competition between bicollinear AFM and SC. However, presence of interstitial Fe affects both magnetism and SC of Fe1+yTe1-xSex, which hinders the establishment of the real phase diagram. Here, we report the comparison of doping-temperature (x-T) phase diagrams for Fe1+yTe1-xSex (0 ≤ x ≤ 0.43) single crystals before and after removing interstitial Fe. Without interstitial Fe, the AFM state survives only for x < 0.05, and bulk SC emerges from x = 0.05, and does not coexist with the AFM state. The previously reported spin glass state, and the coexistence of AFM and SC may be originated from the effect of the interstitial Fe. The phase diagram of Fe1+yTe1-xSex is found to be similar to the case of the "1111" system such as LaFeAsO1-xFx, and is different from that of the "122" system.

Angular dependent torque measurements on CaFe0.88Co0.12AsF

Out-of-plane angular dependent torque measurements were performed on CaFe0.88Co0.12AsF (Ca1 1 1 1) single crystals. In the normal state, the torque data shows [Formula: see text] angular dependence and H (2) magnetic field dependence, as a result of paramagnetism. In the mixed state, the torque signal is a combination of the vortex torque and paramagnetic torque, and the former allows the determination of the anisotropy parameter γ. At T   =  11.5 K, γ (11.5 K ≃ 0.5 T c)  =  19.1, which is similar to the result of SmFeAsO0.8F0.2, [Formula: see text] at [Formula: see text]. So the 11 1 1 is more anisotropic compared to 11 and 122 families of iron-based superconductors. This may suggest that the electronic coupling between layers in 1 1 1 1 is less effective than in 11 and 122 families.

The influence of the structural transition on magnetic fluctuations in NaFeAs

NaFeAs belongs to a class of Fe-based superconductors which have parent compounds that show separated structural and magnetic transitions. Effects of the structural transition on spin dynamics therefore can be investigated separately from the magnetic transition. A plateau in dynamic spin response is observed in a critical region around the structural transition temperature T S. It is interpreted as being due to the stiffening of spin fluctuations along the in-plane magnetic hard axis due to the d xz and d yz orbital ordering. The appearance of anisotropic spin dynamics in the critical region above the T S at T (*) offers a dynamic magnetic scattering mechanism for anisotropic electronic properties in the commonly referred 'nematic phase'.

Hall-plot of the phase diagram for Ba(Fe1-xCox)2As2

The Hall effect is a powerful tool for investigating carrier type and density. For single-band materials, the Hall coefficient is traditionally expressed simply by , where e is the charge of the carrier, and n is the concentration. However, it is well known that in the critical region near a quantum phase transition, as it was demonstrated for cuprates and heavy fermions, the Hall coefficient exhibits strong temperature and doping dependencies, which can not be described by such a simple expression, and the interpretation of the Hall coefficient for Fe-based superconductors is also problematic. Here, we investigate thin films of Ba(Fe_1−xCo_x)₂As₂ with compressive and tensile in-plane strain in a wide range of Co doping. Such in-plane strain changes the band structure of the compounds, resulting in various shifts of the whole phase diagram as a function of Co doping. We show that the resultant phase diagrams for different strain states can be mapped onto a single phase diagram with the Hall number. This universal plot is attributed to the critical fluctuations in multiband systems near the antiferromagnetic transition, which may suggest a direct link between magnetic and superconducting properties in the BaFe₂As₂ system.

Ultrafast dynamics of quasiparticles and coherent acoustic phonons in slightly underdoped (BaK)Fe2As2

We have utilized ultrafast optical spectroscopy to study carrier dynamics in slightly underdoped (BaK)Fe₂As₂ crystals without magnetic transition. The photoelastic signals due to coherent acoustic phonons have been quantitatively investigated. According to our temperature-dependent results, we found that the relaxation component of superconducting quasiparticles persisted from the superconducting state up to at least 70 K in the normal state. Our findings suggest that the pseudogaplike feature in the normal state is possibly the precursor of superconductivity. We also highlight that the pseudogap feature of K-doped BaFe₂As₂ is different from that of other iron-based superconductors, including Co-doped or P-doped BaFe₂As₂.

A study of temperature dependent local atomic displacements in a Ba(Fe(1-x)Co(x))2As2 superconductor

We have studied the local structure of a Ba(Fe(1-x)Co(x))2As2 superconductor using temperature dependent extended X-ray absorption fine structure (EXAFS) measurements. Polarized EXAFS at the Fe K-edge on an optimally doped (x = 0.06) single crystal has permitted us to determine atomic displacements across the superconducting transition temperature (T(c)). The Fe-As bondlength hardly shows any change with temperature; however, the Fe-Fe sublattice reveals a sharp anomaly across T(c), indicated by a significant drop in mean square relative displacements, similar to the one known for cuprates and A15-type superconductors. We have also found a large atomic disorder around the substituted Co, revealed by polarized Co K-edge EXAFS measurements. The Co-Fe/Co bonds are more flexible than the Fe-Fe bonds with the As-height in Co-containing tetrahedra being larger than the one in FeAs4. The results suggest that the local Fe-Fe bondlength fluctuations and the atomic disorder in this sub-lattice should have some important role in the superconductivity of Ba(Fe(1-x)Co(x))2As2 pnictides.

Phase separation in Ca(1-x)La(x)Fe₂As₂ superconductors: a ⁵⁷Fe Mössbauer study

We report a detailed 57Fe Mössbauer study of lanthanum doped CaFe2As2 superconductors. The quadrupole splitting distribution (QSD) method was adopted to analyze the Mössbauer spectra of Ca(1-x) La(x)Fe2As2 (x  =  0.2, 0.3) single crystals. For both compounds we observed two QSD contributions centered at 0.31 mm s(-1) and  -0.32 mm s(-1) at room temperature. The first principles calculations of the electronic structures and the electric field gradient (EFG) of Ca(1-y)La(y)Fe2As2 model systems reveal that the EFG changes from positive to negative with increasing dopant concentration, indicating that the La atoms distribute heterogeneously in the compounds. The two QSD components behave differently with decreasing temperature. The minority La-rich phase undergoes superconducting transition, while short range spin fluctuations and/or spin-phonon coupling appear in the majority La-poor phase. Our experiments provide new evidence of the phase separation picture at low temperatures in Ca(1-x)La(x)Fe2As2 superconductors.

NMR Evidence for Inhomogeneous Nematic Fluctuations in BaFe_{2}(As_{1-x}P_{x})_{2}

We present evidence for nuclear spin-lattice relaxation driven by glassy nematic fluctuations in isovalent P-doped BaFe_{2}As_{2} single crystals. Both the ^{75}As and ^{31}P sites exhibit a stretched-exponential relaxation similar to the electron-doped systems. By comparing the hyperfine fields and the relaxation rates at these sites we find that the As relaxation cannot be explained solely in terms of magnetic spin fluctuations. We demonstrate that nematic fluctuations couple to the As nuclear quadrupolar moment and can explain the excess relaxation. These results suggest that glassy nematic dynamics are a common phenomenon in the iron-based superconductors.

Nematic Resonance in the Raman Response of Iron-Based Superconductors

In a fully gapped superconductor the electronic Raman response has a pair-breaking peak at twice the superconducting gap Δ, if the Bogoliubov excitations are uncorrelated. Motivated by the iron based superconductors, we study how this peak is modified if the superconducting phase hosts a nematic-structural quantum critical point. We show that, upon approaching this point by tuning, e.g., doping, the growth of nematic correlations between the quasiparticles transforms the pair-breaking peak into a nematic resonance. The mode energy is below 2Δ, and stays finite at the quantum critical point, where its spectral weight is sharply enhanced. The latter is consistent with recent experiments on electron-doped iron based superconductors and provides direct evidence of nematic correlations in their superconducting phases.

Nematic Crossover in BaFe(2)As(2) under Uniaxial Stress

Raman scattering can detect spontaneous point-group symmetry breaking without resorting to single-domain samples. Here, we use this technique to study BaFe(2)As(2), the parent compound of the "122" Fe-based superconductors. We show that an applied compression along the Fe-Fe direction, which is commonly used to produce untwinned orthorhombic samples, changes the structural phase transition at temperature T(s) into a crossover that spans a considerable temperature range above T(s). Even in crystals that are not subject to any applied force, a distribution of substantial residual stress remains, which may explain phenomena that are seemingly indicative of symmetry breaking above T(s). Our results are consistent with an onset of spontaneous nematicity only below T(s).

Evidence for orbital order and its relation to superconductivity in FeSe0.4Te0.6

The emergence of nematic electronic states accompanied by a structural phase transition is a recurring theme in many correlated electron materials, including the high-temperature copper oxide- and iron-based superconductors. We provide evidence for nematic electronic states in the iron-chalcogenide superconductor FeSe0.4Te0.6 from quasi-particle scattering detected in spectroscopic maps. The symmetry-breaking states persist above T c into the normal state. We interpret the scattering patterns by comparison with quasi-particle interference patterns obtained from a tight-binding model, accounting for orbital ordering. The relation to superconductivity and the influence on the coherence length are discussed.

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

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

Room-Temperature Ba(Fe1-x Cox)2 As2 is not Tetragonal: Direct Observation of Magnetoelastic Interactions in Pnictide Superconductors

Lattice distortions corresponding to Ba displacements with respect to the FeAs sublattice are revealed to break the room-temperature tetragonal symmetry in Ba(Fe1-x Cox)2 As2. The displacements yield twin domains of the size of ≈10 nm. The domain size correlates with the magnitude of the local Fe magnetic moment and its non-monotonic dependence on Co concentration.

The form and origin of orbital ordering in the electronic nematic phase of iron-based superconductors

We investigated the form of orbital ordering in the electronic nematic phase of iron-based superconductors by applying a group theoretical analysis on a realistic five-band model. We find the orbital order can be either of the inter-orbital s-wave form or intra-orbital d-waveform. From the comparison with existing ARPES measurements of band splitting, we find the orbital ordering in the 122 system is dominated by an intra-orbital d-wave component, while that of the 111 system is dominated by an inter-orbital s-wave component. We find both forms of orbital order are strongly entangled with the nematicity in the spin correlation of the system.The condensation energy of the magnetic ordered phase is found to be significantly improved (by more than 20%) when the degeneracy between the (π, 0) and (0, π) ordering pattern is lifted by the orbital order. We argue there should be a large difference in both the scattering rate and the size of the possible pseudogap on the electron pocket around the X = (π, 0) and Y = (0, π) point in the electronic nematic phase. We propose this as a possible origin for the observed nematicity in resistivity measurements.

Effects of Lifshitz transition on charge transport in magnetic phases of Fe-based superconductors

The unusual temperature dependence of the resistivity and its in-plane anisotropy observed in the Fe-based superconducting materials, particularly Ba(Fe_{1-x}Co_{x})_{2}As_{2}, has been a long-standing puzzle. Here, we consider the effect of impurity scattering on the temperature dependence of the average resistivity within a simple two-band model of a dirty spin density wave metal. The sharp drop in resistivity below the Néel temperature T_{N} in the parent compound can only be understood in terms of a Lifshitz transition following Fermi surface reconstruction upon magnetic ordering. We show that the observed resistivity anisotropy in this phase, arising from nematic defect structures, is affected by the Lifshitz transition as well.

Neutron-scattering measurements of spin excitations in LaFeAsO and Ba(Fe(0.953)Co(0.047))(2)As(2): evidence for a sharp enhancement of spin fluctuations by nematic order

Inelastic neutron scattering is employed to investigate the impact of electronic nematic order on the magnetic spectra of LaFeAsO and Ba(Fe(0.953)Co(0.047))(2)As(2). These materials are ideal to study the paramagnetic-nematic state, since the nematic order, signaled by the tetragonal-to-orthorhombic transition at T(S), sets in well above the stripe antiferromagnetic ordering at T(N). We find that the temperature-dependent dynamic susceptibility displays an anomaly at T(S) followed by a sharp enhancement in the spin-spin correlation length, revealing a strong feedback effect of nematic order on the low-energy magnetic spectrum. Our findings can be consistently described by a model that attributes the structural or nematic transition to magnetic fluctuations, and unveils the key role played by nematic order in promoting the long-range stripe antiferromagnetic order in iron pnictides.

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.

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-xP_x)₂ (x = 0.30, T_c = 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.

Persistent Detwinning of Iron-Pnictide EuFe_{2}As_{2} Crystals by Small External Magnetic Fields

Our comprehensive study on EuFe_{2}As_{2} reveals a dramatic reduction of magnetic detwinning fields compared to other AFe_{2}As_{2} (A=Ba, Sr, Ca) iron pnictides by indirect magnetoelastic coupling of the Eu^{2+} ions. We find that only ∼0.1  T are sufficient for persistent detwinning below the local Eu^{2+} ordering; above T_{Eu}=19  K, higher fields are necessary. Even after the field is switched off, a significant imbalance of twin domains remains constant up to the structural and electronic phase transition (190 K). This persistent detwinning provides the unique possibility to study the low temperature electronic in-plane anisotropy of iron pnictides without applying any symmetry-breaking external force.

Manipulation of gap nodes by uniaxial strain in iron-based superconductors

In the iron pnictides and chalcogenides, multiple orbitals participate in the superconducting state, enabling different gap structures to be realized in distinct materials. Here we argue that the spectral weights of these orbitals can, in principle, be controlled by a tetragonal symmetry-breaking uniaxial strain, due to the enhanced nematic susceptibility of many iron-based superconductors. By investigating multiorbital microscopic models in the presence of orbital order, we show that not only Tc can be enhanced, but pairs of accidental gap nodes can be annihilated and created in the Fermi surface by an increasing external strain. We explain our results as a mixture of nearly degenerate superconducting states promoted by strain, and show that the annihilation and creation of nodes can be detected experimentally via anisotropic penetration depth measurements. Our results provide a promising framework to externally control the superconducting properties of iron-based materials.

Emergent defect states as a source of resistivity anisotropy in the nematic phase of iron pnictides

We consider the role of potential scatterers in the nematic phase of Fe-based superconductors above the transition temperature to the (π, 0) magnetic state but below the orthorhombic structural transition. The anisotropic spin fluctuations in this region can be frozen by disorder, to create elongated magnetic droplets whose anisotropy grows as the magnetic transition is approached. Such states act as strong anisotropic defect potentials that scatter with much higher probability perpendicular to their length than parallel, although the actual crystal symmetry breaking is tiny. We calculate the scattering potentials, relaxation rates, and conductivity in this region and show that such emergent defect states are essential for the transport anisotropy observed in experiments.

Phonon anomalies, orbital-ordering and electronic raman scattering in iron-pnictide Ca(Fe0.97Co0.03)2As2: temperature-dependent Raman study

We report inelastic light scattering studies on Ca(Fe0.97Co0.03)2As2 in a wide spectral range of 120-5200 cm( - 1) from 5 to 300 K, covering the tetragonal to orthorhombic structural transition as well as magnetic transition at Tsm ~ 160 K. The mode frequencies of two first-order Raman modes B1g and Eg, both involving the displacement of Fe atoms, show a sharp increase below Tsm. Concomitantly, the linewidths of all the first-order Raman modes show anomalous broadening below Tsm, attributed to strong spin-phonon coupling. The high frequency modes observed between 400 and 1200 cm( - 1) are attributed to electronic Raman scattering involving the crystal field levels of d-orbitals of Fe(2+). The splitting between xz and yz d-orbital levels is shown to be ~25 meV, which increases as temperature decreases below Tsm. A broad Raman band observed at ~3200 cm( - 1) is assigned to two-magnon excitation of the itinerant Fe 3d antiferromagnet.

Linear response theory for shear modulus C66 and Raman quadrupole susceptibility: evidence for nematic orbital fluctuations in Fe-based superconductors

The emergence of the nematic order and fluctuations has been discussed as a central issue in Fe-based superconductors. To clarify the origin of the nematicity, we focus on the shear modulus C(66) and the Raman quadrupole susceptibility χ(x)(2)-y(2))(Raman). Because of the Aslamazov-Larkin vertex correction, the nematic-type orbital fluctuations are induced, and they enhance both 1/C(66) and χ(x(2)-y(2))(Raman) strongly. However, χ(x)(2)-y(2))(Raman) remains finite even at the structure transition temperature T(S), because of the absence of the band Jahn-Teller effect and the Pauli (intraband) contribution, as proved in terms of the linear response theory. The present study clarifies that the origin of the nematicity in Fe-based superconductors is the nematic orbital order and fluctuations.

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.

High-Tc superconductivity near the anion height instability in Fe-based superconductors: analysis of LaFeAsO(1-x)H(x)

The isostructural transition in the tetragonal phase with a sizable change in the anion height, is realized in heavily H-doped LaFeAsO and (La,P) codoped CaFe2As2. In these compounds, the superconductivity with higher Tc (40-50 K) is realized near the isostructural transition. To find the origin of the anion-height instability and the role in realizing the higher-Tc state, we develop the orbital-spin fluctuation theory by including the vertex correction. We analyze LaFeAsO(1-x)H(x) and find that the non-nematic orbital fluctuations, which induce the anion-height instability, are automatically obtained at x∼0.5, in addition to the conventional nematic orbital fluctuations at x∼0. The non-nematic orbital order triggers the isostructural transition, and its fluctuation would be a key ingredient to realize higher-Tc superconductivity of order 50 K.

Note: nonlinear susceptibility from high DC field torque magnetometry

Torque magnetometry is a convenient technique to measure the magnetic properties of anisotropic materials. Advances in micromachining have made torque magnetometers precise and reliable even in adverse conditions such as very high magnetic fields and very low temperatures. In most applications with such magnetometers the measured torque signals are used to arrive at the linear magnetic susceptibility. In this short note we extend torque magnetometry to measure nonlinear susceptibilities and illustrate our methods with representative data on the heavy fermion compound UPt3.

Doping dependence of the anisotropic quasiparticle interference in NaFe(1-x)Co(x)As iron-based superconductors

We use scanning tunneling microscopy to investigate the doping dependence of quasiparticle interference (QPI) in NaFe1-xCoxAs iron-based superconductors. The goal is to study the relation between nematic fluctuations and Cooper pairing. In the parent and underdoped compounds, where fourfold rotational symmetry is broken macroscopically, the QPI patterns reveal strong rotational anisotropy. At optimal doping, however, the QPI patterns are always fourfold symmetric. We argue this implies small nematic susceptibility and, hence, insignificant nematic fluctuation in optimally doped iron pnictides. Since TC is the highest this suggests nematic fluctuation is not a prerequistite for strong Cooper pairing.

Strong coupling of the iron-quadrupole and anion-dipole polarizations in Ba(Fe(1-x)Co(x))2As2

We use a quantitative convergent beam electron diffraction based method to image the valence electron density distribution in Ba(Fe1-xCox)2As2. We show a remarkable increase in both the charge quadrupole of the Fe cations and the charge dipole of the arsenic anions upon Co doping from x=0 (Tc=0  K) to x=0.1 (Tc=22.5  K). Our data suggest that an unexpected electronic correlation effect, namely strong coupling of Fe orbital fluctuation and anion electronic polarization, is present in iron-based superconductors.

Ultrafast observation of critical nematic fluctuations and giant magnetoelastic coupling in iron pnictides

Many of the iron pnictides have strongly anisotropic normal-state characteristics, important for the exotic magnetic and superconducting behaviour these materials exhibit. Yet, the origin of the observed anisotropy is unclear. Electronically driven nematicity has been suggested, but distinguishing this as an independent degree of freedom from magnetic and structural orders is difficult, as these couple together to break the same tetragonal symmetry. Here we use time-resolved polarimetry to reveal critical nematic fluctuations in unstrained Ba(Fe1-xCox)2As2. The femtosecond anisotropic response, which arises from the two-fold in-plane anisotropy of the complex refractive index, displays a characteristic two-step recovery absent in the isotropic response. The fast recovery appears only in the magnetically ordered state, whereas the slow one persists in the paramagnetic phase with a critical divergence approaching the structural transition temperature. The dynamics also reveal a gigantic magnetoelastic coupling that far exceeds electron-spin and electron-phonon couplings, opposite to conventional magnetic metals.

Nematic susceptibility of hole-doped and electron-doped BaFe2As2 iron-based superconductors from shear modulus measurements

The nematic susceptibility, χφ, of hole-doped Ba(1-x)K(x)Fe2As2 and electron-doped Ba(Fe(1-x)Co(x))2As2 iron-based superconductors is obtained from measurements of the elastic shear modulus using a three-point bending setup in a capacitance dilatometer. Nematic fluctuations, although weakened by doping, extend over the whole superconducting dome in both systems, suggesting their close tie to superconductivity. Evidence for quantum critical behavior of χφ is, surprisingly, only found for Ba(Fe(1-x)Co(x))2As2 and not for Ba(1-x)K(x)Fe2As2--the system with the higher maximal Tc value.

Observation of incipient charge nematicity in Ba(Fe(1-x)Co(x))2As2

Using electronic Raman spectroscopy, we report direct measurements of charge nematic fluctuations in the tetragonal phase of strain-free Ba(Fe(1-x)Co(x))2As2 single crystals. The strong enhancement of the Raman response at low temperatures unveils an underlying charge nematic state that extends to superconducting compositions and which has hitherto remained unnoticed. Comparison between the extracted charge nematic susceptibility and the elastic modulus allows us to disentangle the charge contribution to the nematic instability, and to show that charge nematic fluctuations are weakly coupled to the lattice.

Existence of orbital order and its fluctuation in superconducting Ba(Fe(1-x)Co(x))2As2 single crystals revealed by x-ray absorption spectroscopy

We performed temperature dependent x-ray linear dichroism (XLD) experiments on an iron pnictide system, Ba(Fe(1-x)Co(x))2As2 with x=0.00, 0.05, 0.08, and 0.10 to experimentally verify the existence of orbital ordering (OO). Substantial XLD was observed in polarization dependent x-ray absorption spectra of Fe L edges. By exploiting the difference in the temperature dependent behaviors, OO, and structure contributions to XLD could be clearly separated. The observed OO signal indicates different occupation numbers for d(yz) and d(zx) orbitals and supports the existence of ferro-OO. The results are also consistent with the theoretical prediction. Moreover, we find substantial OO signal well above the structural and magnetic transition temperatures, which suggests the existence of strong OO fluctuations up to high temperatures.

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.

Singularity of the London penetration depth at quantum critical points in superconductors

We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents and ratios of amplitudes on the two sides of the transition are universal, an overall sign depends upon the interplay between the critical theory and the underlying Fermi surface. We determine these features for critical points to spin density wave and nematic ordering, and for a topological transition between a superconductor with Z2 fractionalization and a conventional superconductor. We note implications for recent measurements of the London penetration depth in BaFe2(As(1-x)P(x))2 [K. Hashimoto et al., Science 336, 1554 (2012)].

Pressure-decoupled magnetic and structural transitions of the parent compound of iron-based 122 superconductors BaFe2As2

The recent discovery of iron ferropnictide superconductors has received intensive concern in connection with magnetically involved superconductors. Prominent features of ferropnictide superconductors are becoming apparent: the parent compounds exhibit an antiferromagnetic ordered spin density wave (SDW) state, the magnetic-phase transition is always accompanied by a crystal structural transition, and superconductivity can be induced by suppressing the SDW phase via either chemical doping or applied external pressure to the parent state. These features generated considerable interest in the interplay between magnetism and structure in chemically doped samples, showing crystal structure transitions always precede or coincide with magnetic transition. Pressure-tuned transition, on the other hand, would be more straightforward to superconducting mechanism studies because there are no disorder effects caused by chemical doping; however, remarkably little is known about the interplay in the parent compounds under controlled pressure due to the experimental challenge of in situ measuring both of magnetic and crystal structure evolution at high pressure and low temperatures. Here we show from combined synchrotron Mössbauer and X-ray diffraction at high pressures that the magnetic ordering surprisingly precedes the structural transition at high pressures in the parent compound BaFe2As2, in sharp contrast to the chemical-doping case. The results can be well understood in terms of the spin fluctuations in the emerging nematic phase before the long-range magnetic order that sheds light on understanding how the parent compound evolves from a SDW state to a superconducting phase, a key scientific inquiry of iron-based superconductors.

Scaling between magnetic and lattice fluctuations in iron pnictide superconductors

The phase diagram of the iron arsenides is dominated by a magnetic and a structural phase transition, which need to be suppressed in order for superconductivity to appear. The proximity between the two transition temperature lines indicates correlation between these two phases, whose nature remains unsettled. Here, we find a scaling relation between nuclear magnetic resonance and shear modulus data in the tetragonal phase of electron-doped Ba(Fe1-xCox)2As2 compounds. Because the former probes the strength of magnetic fluctuations while the latter is sensitive to orthorhombic fluctuations, our results provide strong evidence for a magnetically driven structural transition.

Nematicity as a probe of superconducting pairing in iron-based superconductors

In several families of iron-based superconducting materials, a d-wave pairing instability may compete with the leading s-wave instability. Here, we show that when both states have comparable free energies, superconducting and nematic degrees of freedom are strongly coupled. Whereas nematic order causes a sharp nonanalytic increase in T(c), nematic fluctuations can change the character of the s-wave to d-wave transition, favoring an intermediate state that does not break time-reversal symmetry but does break tetragonal symmetry. The coupling between superconductivity and nematicity is also manifested in the strong softening of the shear modulus across the superconducting transition. Our results show that nematicity can be used as a diagnostic tool to search for unconventional pairing states in iron pnictides and chalcogenides.

Spin excitation anisotropy as a probe of orbital ordering in the paramagnetic tetragonal phase of superconducting BaFe1.904Ni0.09As2

We use polarized neutron scattering to demonstrate that in-plane spin excitations in electron doped superconducting BaFe1.904Ni0.096As2 (Tc=19.8  K) change from isotropic to anisotropic in the tetragonal phase well above the antiferromagnetic (AFM) ordering and tetragonal-to-orthorhombic lattice distortion temperatures (TN≈Ts=33±2  K) without an uniaxial pressure. While the anisotropic spin excitations are not sensitive to the AFM order and tetragonal-to-orthorhombic lattice distortion, superconductivity induces further anisotropy for spin excitations along the [110] and [110] directions. These results indicate that the spin excitation anisotropy is a probe of the electronic anisotropy or orbital ordering in the tetragonal phase of iron pnictides.

Nematic order in a degenerate Hubbard model with spin-orbit coupling

Using Bogoliubov's inequality we rigorously show that the multiorbital Hubbard model with narrow bands, even in the presence of spin-orbit coupling, does not exhibit long-range nematic order, in low dimensions. This result holds at any finite temperature for both repulsive and attractive Coulomb interactions, with and without spin-orbit coupling.

Nematic state of pnictides stabilized by interplay between spin, orbital, and lattice degrees of freedom

The nematic state of the iron-based superconductors is studied in the undoped limit of the three-orbital (xz, yz, xy) spin-fermion model via the introduction of lattice degrees of freedom. Monte Carlo simulations show that in order to stabilize the experimentally observed lattice distortion and nematic order, and to reproduce photoemission experiments, both the spin-lattice and orbital-lattice couplings are needed. The interplay between their respective coupling strengths regulates the separation between the structural and Néel transition temperatures. Experimental results for the temperature dependence of the resistivity anisotropy and the angle-resolved photoemission orbital spectral weight are reproduced by the present numerical simulations.