Anisotropic atomic displacements, local orthorhombicity and anomalous local magnetic moment in Ba0.6K0.4Fe2As2 superconductor

We have investigated the in-plane local structure of the Ba0.6K0.4Fe2As2 superconductor by polarized Fe K-edge extended X-ray absorption fine structure (EXAFS) measurements with temperature. The near neighbor bond distances and their stiffness, measured by polarized EXAFS in two orthogonal directions, are different suggesting in-plane anisotropy of the atomic displacements and local orthorhombicity in the title system. The X-ray absorption near edge structure (XANES) spectra reveal anisotropy of valence electronic structure that changes anomalously below ∼100 K. The local iron magnetic moment, measured by Fe Kβ X-ray emission spectroscopy (XES), increases below the anomalous temperature and shows a decrease in the vicinity of the superconducting transition temperature (Tc ∼ 36 K). The results provide a clear evidence of coupled local lattice, electronic and magnetic degrees of freedom to induce possible nematic fluctuations in an optimally hole doped iron-based superconductor.

Nematic Spin Correlations Pervading the Phase Diagram of FeSe_{1-x}S_{x}

We use resonant inelastic x-ray scattering (RIXS) at the Fe-L_{3} edge to study the spin excitations of uniaxial-strained and unstrained FeSe_{1-x}S_{x} (0≤x≤0.21) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range 0200  K in x=0.18 and reaches a maximum around the nematic quantum critical doping (x_{c}≈0.17). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and highlight the capability of uniaxial strain in tuning spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity.

Suppression of Superconductivity and Nematic Order in Fe1-ySe1-xSx (0 ≤ x ≤ 1; y ≤ 0.1) Crystals by Anion Height Disorder

Connections between crystal chemistry and critical temperature T_c have been in the focus of superconductivity, one of the most widely studied phenomena in physics, chemistry, and materials science alike. In most Fe-based superconductors, materials chemistry and physics conspire so that T_c correlates with the average anion height above the Fe plane, i.e., with the geometry of the FeAs₄ or FeCh₄ (Ch = Te, Se, or S) tetrahedron. By synthesizing Fe_1-ySe_1-xS_x (0 ≤ x ≤ 1; y ≤ 0.1), we find that in alloyed crystals T_c is not correlated with the anion height like it is for most other Fe superconductors. Instead, changes in T_c(x) and tetragonal-to-orthorhombic (nematic) transition T_s(x) upon cooling are correlated with disorder in Fe vibrations in the direction orthogonal to Fe planes, along the crystallographic c-axis. The disorder stems from the random nature of S substitution, causing deformed Fe(Se,S)₄ tetrahedra with different Fe-Se and Fe-S bond distances. Our results provide evidence of T_c and T_s suppression by disorder in anion height. The connection to local crystal chemistry may be exploited in computational prediction of new superconducting materials with FeSe/S building blocks.

Anomalous Contribution to the Nematic Electronic States from the Structural Transition in FeSe Revealed by Time- and Angle-Resolved Photoemission Spectroscopy

High-resolution time- and angle-resolved photoemission measurements were made on FeSe superconductors. With ultrafast photoexcitation, two critical excitation fluences that correspond to two ultrafast electronic phase transitions were found only in the d_{yz}-orbit-derived band near the Brillouin-zone center within our time and energy resolution. Upon comparison to the detailed temperature dependent measurements, we conclude that there are two equilibrium electronic phase transitions (at approximately 90 and 120 K) above the superconducting transition temperature, and an anomalous contribution on the scale of 10 meV to the nematic states from the structural transition is experimentally determined. Our observations strongly suggest that the electronic phase transition at 120 K must be taken into account in the energy band development of FeSe, and, furthermore, the contribution of the structural transition plays an important role in the nematic phase of iron-based high-temperature superconductors.

Preferred Spin Excitations in the Bilayer Iron-Based Superconductor CaK(Fe_{0.96}Ni_{0.04})_{4}As_{4} with Spin-Vortex Crystal Order

Spin-orbit coupling (SOC) is a key to understand the magnetically driven superconductivity in iron-based superconductors, where both local and itinerant electrons are present and the orbital angular momentum is not completely quenched. Here, we report a neutron scattering study on the bilayer compound CaK(Fe_{0.96}Ni_{0.04})_{4}As_{4} with superconductivity coexisting with a noncollinear spin-vortex crystal magnetic order that preserves the tetragonal symmetry of the Fe-Fe plane. In the superconducting state, two spin resonance modes with odd and even L symmetries due to the bilayer coupling are found similar to the undoped compound CaKFe_{4}As_{4} but at lower energies. Polarization analysis reveals that the odd mode is c-axis polarized, and the low-energy spin anisotropy can persist to the paramagnetic phase at high temperature, which closely resembles other systems with in-plane collinear and c-axis biaxial magnetic orders. These results provide the missing piece of the puzzle on the SOC effect in iron-pnictide superconductors, and also establish a common picture of c-axis preferred magnetic excitations below T_{c} regardless of the details of magnetic pattern or lattice symmetry.

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.

Two distinct superconducting states controlled by orientations of local wrinkles in LiFeAs

For iron-based superconductors, the phase diagrams under pressure or strain exhibit emergent phenomena between unconventional superconductivity and other electronic orders, varying in different systems. As a stoichiometric superconductor, LiFeAs has no structure phase transitions or entangled electronic states, which manifests an ideal platform to explore the pressure or strain effect on unconventional superconductivity. Here, we observe two types of superconducting states controlled by orientations of local wrinkles on the surface of LiFeAs. Using scanning tunneling microscopy/spectroscopy, we find type-I wrinkles enlarge the superconducting gaps and enhance the transition temperature, whereas type-II wrinkles significantly suppress the superconducting gaps. The vortices on wrinkles show a C₂ symmetry, indicating the strain effects on the wrinkles. By statistics, we find that the two types of wrinkles are categorized by their orientations. Our results demonstrate that the local strain effect with different directions can tune the superconducting order parameter of LiFeAs very differently, suggesting that the band shifting induced by directional pressure may play an important role in iron-based superconductivity.

The evolution of superconductivity in LiFeAs with respect to pressure or strain remains elusive. Here, the authors observe different response of superconducting states due to different orientations of local wrinkles on the surface of LiFeAs.

The transport-structural correspondence across the nematic phase transition probed by elasto X-ray diffraction

Electronic nematicity in iron pnictide materials is coupled to both the lattice and the conducting electrons, which allows both structural and transport observables to probe nematic fluctuations and the order parameter. Here we combine simultaneous transport and X-ray diffraction measurements with in-situ tunable strain (elasto X-ray diffraction) to measure the temperature dependence of the shear modulus and elastoresistivity above the nematic transition and the spontaneous orthorhombicity and resistivity anisotropy below the nematic transition, all within a single sample of Ba(Fe_0.96Co_0.04)₂As₂. The ratio of transport to structural quantities is nearly temperature independent over a 74 K range and agrees between the ordered and disordered phases. These results show that elasto X-ray diffraction is a powerful technique to probe the nemato-elastic and nemato-transport couplings, which have important implications to the nearby superconductivity. It also enables the measurement in the large strain limit, where the breakdown of the mean-field description reveals the intertwined nature of nematicity.

Quadrupolar charge dynamics in the nonmagnetic FeSe1-x S x superconductors

We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic [Formula: see text] superconductor. We observe two types of long-wavelength [Formula: see text] symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at [Formula: see text], a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the [Formula: see text] symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward [Formula: see text] The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration [Formula: see text], while the pseudogap size decreases with the suppression of [Formula: see text] We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

In-plane uniaxial pressure-induced out-of-plane antiferromagnetic moment and critical fluctuations in BaFe2As2

A small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe2As2, which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature Ts. Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature TN ( < Ts) and create in-plane resistivity anisotropy above Ts. Here we use neutron polarization analysis to show that such a strain on BaFe2As2 also induces a static or quasi-static out-of-plane (c-axis) AF order and its associated critical spin fluctuations near TN/Ts. Therefore, uniaxial pressure necessary to detwin single crystals of BaFe2As2 actually rotates the easy axis of the collinear AF order near TN/Ts, and such effects due to spin-orbit coupling must be taken into account to unveil the intrinsic electronic/magnetic properties of the system.

On the Remarkable Superconductivity of FeSe and Its Close Cousins

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

Evolution of the Nematic Susceptibility in LaFe_{1-x}Co_{x}AsO

We report a systematic elastoresistivity study on LaFe_{1-x}Co_{x}AsO single crystals, which have well separated structural and magnetic transition lines. All crystals show a Curie-Weiss-like nematic susceptibility in the tetragonal phase. The extracted nematic temperature is monotonically suppressed upon cobalt doping, and changes sign around the optimal doping level, indicating a possible nematic quantum critical point beneath the superconducting dome. The amplitude of the nematic susceptibility shows a peculiar double-peak feature. This could be explained by a combined effect of different contributions to the nematic susceptibility, which are amplified at separated doping levels of LaFe_{1-x}Co_{x}AsO.

Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from 2×2 Fe Clusters in KFe_{0.8}Ag_{1.2}Te_{2}

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}, KFAT) is a local-moment magnet consisting of well-separated 2×2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the 2×2 clusters act as the spin analog of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter.

Anisotropic spin fluctuations in detwinned FeSe

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe, detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (±1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies, 3-5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.6 meV) at QAF with incommensurate scattering around 5-6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations.

In-plane and out-of-plane properties of a BaFe2As2 single crystal

Anisotropy of transport and magnetic properties of parent compounds of iron based superconductors is a key ingredient of superconductivity. In this work, we investigate in-plane and out-of-plane properties, namely thermal, electric, thermoelectric transport and magnetic susceptibility in a high quality BaFe₂As₂ single crystal of the 122 parent compound, using a combined experimental and theoretical approach. Combining the ab initio calculation of the band structure and the measured in-plane and out-of-plane resistivity, we evaluate the scattering rates which turn out to be strongly anisotropic and determined by spin excitations in the antiferromagnetic state. The observed anisotropy of thermal conductivity is discussed in terms of anisotropy of sound velocities which we estimate to be [Formula: see text]. Remarkably, we find that thermal conductivity is characterized by a sizeable electronic contribution at low temperature, which is ascribed to the high purity of our crystal.

Pressure tuning of iron-based superconductor Ca10(Pt3As8) ((Fe0.95Pt0.05)2As2)5

Systematic high pressure transport measurements were performed on underdoped Ca₁₀(Pt₃As₈)((Fe_0.95Pt_0.05)₂As₂)₅ single crystal sample. At ambient pressure, the sample shows a metallic behavior at high temperatures and then increases with further decreasing temperature. The resistivity dip, which is associated with metal to semiconductor transition is monotonically suppressed by increasing pressure. In contrast, the superconducting transition temperature [Formula: see text] first increases with pressure and then decreases with further increasing pressure. Magnetization measurements, which gives the bulk [Formula: see text], show the same trend as the one obtained from resistivity measurements. An upward curvature is observed in the temperature dependence of the upper critical field [Formula: see text], which suggests the multiband nature of the superconductivity. The constructed temperature-pressure (T-P) phase diagram is very similar to the reported temperature-doping (T  -  x) phase diagram, suggesting the similar role played by pressure and chemical doping.

Evidence of nematic order and nodal superconducting gap along [110] direction in RbFe2As2

Unconventional superconductivity often intertwines with various forms of order, such as the nematic order which breaks the rotational symmetry of the lattice. Here we report a scanning tunneling microscopy study on RbFe₂As₂, a heavily hole-doped Fe-based superconductor (FeSC). We observe significant symmetry breaking in its electronic structure and magnetic vortex which differentiates the (π, π) and (π, -π) directions of the unfolded Brillouin zone. It is thus a novel nematic state, distinct from the nematicity of undoped/lightly-doped FeSCs which breaks the (π, 0)/(0, π) equivalence. Moreover, we observe a clear V-shaped superconducting gap. The gap is suppressed on surface Rb vacancies and step edges, and the suppression is particularly strong at the [110]-oriented edges. This is possibly due to a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{d}}_{{{x}}^2 - {{y}}^2}$$\end{document}dx2-y2 like pairing component with nodes along the [110] directions. Our results thus highlight the intimate connection between nematicity and superconducting pairing in iron-based superconductors.

Exotic electronic order may emerge and intertwine with superconductivity in iron-based superconductors. Here, the authors observe asymmetric electronic and superconducting gap structure in heavily hole-doped RbFe₂As₂ along the (π, π) and (π, -π) directions in reciprocal space, suggesting a novel (π, π) nematic phase emerging.

The driving mechanism of the d-wave orbital order in the iron-based superconductors

We study the driving mechanism and the form of the orbital order in the electronic nematic phase of the iron-based superconductors (IBSs) within the random phase approximation of a 5-band model. We find the magnetic correlation energy of the system can be significantly improved when an orbital order of the d-wave form is spontaneously generated. On the other hand, the magnetic correlation energy increases as one introduce either an on-site or an extended s-wave orbital order. More specifically, we find that the on-site orbital order is disfavored by the Hund's rule coupling and the extended s-wave orbital order is disfavored by the stripy magnetic correlation pattern in the IBSs. Our work indicates that the orbital order and the spin nematic order in the IBSs develop in a cooperative fashion in the electronic nematic phase of the IBSs and should be both understood as a component of a composite order.

Spectral Evidence for Emergent Order in Ba_{1-x}Na_{x}Fe_{2}As_{2}

We report an angle-resolved photoemission spectroscopy study of the iron-based superconductor family, Ba_{1-x}Na_{x}Fe_{2}As_{2}. This system harbors the recently discovered double-Q magnetic order appearing in a reentrant C_{4} phase deep within the underdoped regime of the phase diagram that is otherwise dominated by the coupled nematic phase and collinear antiferromagnetic order. From a detailed temperature-dependence study, we identify the electronic response to the nematic phase in an orbital-dependent band shift that strictly follows the rotational symmetry of the lattice and disappears when the system restores C_{4} symmetry in the low temperature phase. In addition, we report the observation of a distinct electronic reconstruction that cannot be explained by the known electronic orders in the system.

Spin Waves in Detwinned BaFe_{2}As_{2}

Understanding magnetic interactions in the parent compounds of high-temperature superconductors forms the basis for determining their role for the mechanism of superconductivity. For parent compounds of iron pnictide superconductors such as AFe_{2}As_{2} (A=Ba, Ca, Sr), although spin excitations have been mapped out throughout the entire Brillouin zone, the respective measurements were carried out on twinned samples and did not allow for a conclusive determination of the spin dynamics. Here we use inelastic neutron scattering to completely map out spin excitations of ∼100% detwinned BaFe_{2}As_{2}. By comparing observed spectra with theoretical calculations, we conclude that the spin excitations can be well described by an itinerant model when taking into account moderate electronic correlation effects.

Multi-band effects in in-plane resistivity anisotropy of strain-detwinned disordered Ba(Fe1-xRux)2As2

In-plane resistivity anisotropy was measured in strain-detwinned as-grown and partially annealed samples of isovalently-substituted [Formula: see text] ([Formula: see text]) and the results were contrasted with previous reports on anneal samples with low residual resistivity. In samples with high residual resistivity, detwinned with application of strain, the difference of the two components of in-plane resistivity in the orthorhombic phase, [Formula: see text], was found to obey Matthiessen rule irrespective of sample composition, which is in stark contrast with observations on annealed samples. Our findings are consistent with two-band transport model in which contribution from high mobility carriers of small pockets of the Fermi surface has negligible anisotropy of residual resistivity and is eliminated by disorder. Our finding suggests that magnetic/nematic order has dramatically different effect on different parts of the Fermi surface. It predominantly affects inelastic scattering for small pocket high mobility carriers and elastic impurity scattering for larger sheets of the Fermi surface.

Tuning the interplay between nematicity and spin fluctuations in Na1-xLi x FeAs superconductors

Strong interplay of spin and charge/orbital degrees of freedom is the fundamental characteristic of the iron-based superconductors (FeSCs), which leads to the emergence of a nematic state as a rule in the vicinity of the antiferromagnetic state. Despite intense debate for many years, however, whether nematicity is driven by spin or orbital fluctuations remains unsettled. Here, by use of transport, magnetization, and 75As nuclear magnetic resonance (NMR) measurements, we show a striking transformation of the relationship between nematicity and spin fluctuations (SFs) in Na1-xLi x FeAs; For x ≤ 0.02, the nematic transition promotes SFs. In contrast, for x ≥ 0.03, the system undergoes a non-magnetic phase transition at a temperature T0 into a distinct nematic state that suppresses SFs. Such a drastic change of the spin fluctuation spectrum associated with nematicity by small doping is highly unusual, and provides insights into the origin and nature of nematicity in FeSCs.

Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe2As2

The iron-based high temperature superconductors exhibit a rich phase diagram reflecting a complex interplay between spin, lattice, and orbital degrees of freedom. The nematic state observed in these compounds epitomizes this complexity, by entangling a real-space anisotropy in the spin fluctuation spectrum with ferro-orbital order and an orthorhombic lattice distortion. A subtle and less-explored facet of the interplay between these degrees of freedom arises from the sizable spin-orbit coupling present in these systems, which translates anisotropies in real space into anisotropies in spin space. We present nuclear magnetic resonance studies, which reveal that the magnetic fluctuation spectrum in the paramagnetic phase of BaFe₂As₂ acquires an anisotropic response in spin-space upon application of a tetragonal symmetry-breaking strain field. Our results unveil an internal spin structure of the nematic order parameter, indicating that electronic nematic materials may offer a route to magneto-mechanical control.

A fundamental understanding of nematic order is one of the most important issues to explore in the high temperature superconductors. Here, the authors unveil an internal spin structure of the nematic order in BaFe₂As₂ by using nuclear magnetic resonance under precisely controlled tunable strain.

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, T _c, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.

Transverse fields to tune an Ising-nematic quantum phase transition

The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated with spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.

Driving force of the orbital-relevant electronic nematicity in Fe-based superconductors

The electronic nematic responses in Fe-based superconductors have been observed ubiquitously in various experimental probes. One novel nematic character is the d-wave bond orbital-relevant nematic charge order which was firstly proposed by symmetry analysis and then conformed by angle-resolved photoemission spectroscopy. In this paper, we present a mechanism that the driving force of the orbital-relevant nematic charge order is the reduction of the large Hubbard energy in the particle-hole charge channel by virtual hopping processes. This is one scenario from strong-coupling consideration. The same virtual hopping processes can lead to a super-exchange interaction for the spin magnetic order in the particle-hole spin channel and a pairing interaction for the superconducting order in the particle-particle channel. Thus the electronic nematic order, the spin magnetic order and the pairing superconducting order are intrinsically entangled and they can all stem from the same microscopic virtual hopping processes in reduction of the Hubbard energy. The electronic nematicity, the spin magnetism and the pairing superconductivity in unconventional superconductors are proposed to be unified within this mechanism.

Spin-wave excitations in the spin-density wave state of doped iron pnictides

We investigate spin-wave excitations in the spin-density wave state of doped iron pnictides within a five-orbital model. We find that the excitations along ([Formula: see text])  →  ([Formula: see text]) are very sensitive to dopings whereas they do not exhibit a similar sensitivity along ([Formula: see text])  →  ([Formula: see text]). Secondly, the ellipticity of the elliptical ring-like excitations around ([Formula: see text]) is also very much dependent on doping. Thirdly, the spin-wave spectral weight shifts towards the low-energy region as it moves away from zero doping. We find several features to be in qualitative agreement with the inelastic neutron-scattering measurements for the doped pnictides.

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.

Low-energy microscopic models for iron-based superconductors: a review

The development of sensible microscopic models is essential to elucidate the normal-state and superconducting properties of the iron-based superconductors. Because these materials are mostly metallic, a good starting point is an effective low-energy model that captures the electronic states near the Fermi level and their interactions. However, in contrast to cuprates, iron-based high-T _c compounds are multi-orbital systems with Hubbard and Hund interactions, resulting in a rather involved 10-orbital lattice model. Here we review different minimal models that have been proposed to unveil the universal features of these systems. We first review minimal models defined solely in the orbital basis, which focus on a particular subspace of orbitals, or solely in the band basis, which rely only on the geometry of the Fermi surface. The former, while providing important qualitative insight into the role of the orbital degrees of freedom, do not distinguish between high-energy and low-energy sectors and, for this reason, generally do not go beyond mean-field. The latter allow one to go beyond mean-field and investigate the interplay between superconducting and magnetic orders as well as Ising-nematic order. However, they cannot capture orbital-dependent features like spontaneous orbital order. We then review recent proposals for a minimal model that operates in the band basis but fully incorporates the orbital composition and symmetries of the low-energy excitations. We discuss the results of the renormalization group study of such a model, particularly of the interplay between superconductivity, magnetism, and spontaneous orbital order, and compare theoretical predictions with experiments on iron pnictides and chalcogenides. We also discuss the impact of the glide-plane symmetry on the low-energy models, highlighting the key role played by the spin-orbit coupling.

Competing superconducting channels in iron pnictides from the strong coupling theory with biquadratic spin interactions

We study the symmetry and strength of the superconducting pairing in a two-orbital [Formula: see text] model for iron pnictides using the slave boson strong coupling approach. We show that the nearest-neighbor biquadratic interaction [Formula: see text] strongly affects the superconducting pairing phase diagram by promoting the [Formula: see text] B _1g and the [Formula: see text] A _1g channels. The resulting phase diagram consists of several competing pairing channels, including the isotropic [Formula: see text] A _1g channel, an anisotropic [Formula: see text] B _1g channel, and two [Formula: see text] pairing channels. We have investigated the evolution of superconducting states with electron doping, and find that the biquadratic interaction plays a crucial role in stabilizing the [Formula: see text] and even pure d-wave pairing in the heavily electron- and hole-doped regimes. In addition, we identify a novel orbital-B _1g pairing channel, which has a s-wave form factor but a B _1g symmetry. This channel has a comparable pairing amplitude to the d-wave pairing, and may strongly influence the superconducting gap anisotropy of the system in the overdoped regime. These findings are crucial in understanding the doping evolution of the superconducting gap anisotropy observed by angle resolved photoemission spectroscopy in the iron pnictides and iron chalcogenides, including the heavily K-doped BaFe₂As₂ and K-doped FeSe films.

Effect of Nematic Order on the Low-Energy Spin Fluctuations in Detwinned BaFe_{1.935}Ni_{0.065}As_{2}

The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,π) should decrease with decreasing temperature below the structural transition temperature T_{s}. Here, we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe_{1.935}Ni_{0.065}As_{2} under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length at (0,π) happens just below T_{s}, suggesting the strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order.

Nematic Quantum Critical Fluctuations in BaFe_{2-x}Ni_{x}As_{2}

We have systematically studied the nematic fluctuations in the electron-doped iron-based superconductor BaFe_{2-x}Ni_{x}As_{2} by measuring the in-plane resistance change under uniaxial pressure. While the nematic quantum critical point can be identified through the measurements along the (110) direction, as studied previously, quantum and thermal critical fluctuations cannot be distinguished due to similar Curie-Weiss-like behaviors. Here we find that a sizable pressure-dependent resistivity along the (100) direction is present in all doping levels, which is against the simple picture of an Ising-type nematic model. The signal along the (100) direction becomes maximum at optimal doping, suggesting that it is associated with nematic quantum critical fluctuations. Our results indicate that thermal fluctuations from striped antiferromagnetic order dominate the underdoped regime along the (110) direction. We argue that either there is a strong coupling between the quantum critical fluctuations and the fermions, or more exotically, a higher symmetry may be present around optimal doping.

Origin of the Resistivity Anisotropy in the Nematic Phase of FeSe

The in-plane resistivity anisotropy is studied in strain-detwinned single crystals of FeSe. In contrast to other iron-based superconductors, FeSe does not develop long-range magnetic order below the tetragonal-to-orthorhombic transition at T_{s}≈90  K. This allows for the disentanglement of the contributions to the resistivity anisotropy due to nematic and magnetic orders. Comparing direct transport and elastoresistivity measurements, we extract the intrinsic resistivity anisotropy of strain-free samples. The anisotropy peaks slightly below T_{s} and decreases to nearly zero on cooling down to the superconducting transition. This behavior is consistent with a scenario in which the in-plane resistivity anisotropy is dominated by inelastic scattering by anisotropic spin fluctuations.

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.

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'.

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.

Strong interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe

In iron-based superconductors the interactions driving the nematic order (that breaks four-fold rotational symmetry in the iron plane) may also mediate the Cooper pairing. The experimental determination of these interactions, which are believed to depend on the orbital or the spin degrees of freedom, is challenging because nematic order occurs at, or slightly above, the ordering temperature of a stripe magnetic phase. Here, we study FeSe (ref. )-which exhibits a nematic (orthorhombic) phase transition at Ts = 90 K without antiferromagnetic ordering-by neutron scattering, finding substantial stripe spin fluctuations coupled with the nematicity that are enhanced abruptly on cooling through Ts. A sharp spin resonance develops in the superconducting state, whose energy (∼4 meV) is consistent with an electron-boson coupling mode revealed by scanning tunnelling spectroscopy. The magnetic spectral weight in FeSe is found to be comparable to that of the iron arsenides. Our results support recent theoretical proposals that both nematicity and superconductivity are driven by spin fluctuations.

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.

Weak-coupling superconductivity in a strongly correlated iron pnictide

Iron-based superconductors have been found to exhibit an intimate interplay of orbital, spin, and lattice degrees of freedom, dramatically affecting their low-energy electronic properties, including superconductivity. Albeit the precise pairing mechanism remains unidentified, several candidate interactions have been suggested to mediate the superconducting pairing, both in the orbital and in the spin channel. Here, we employ optical spectroscopy (OS), angle-resolved photoemission spectroscopy (ARPES), ab initio band-structure, and Eliashberg calculations to show that nearly optimally doped NaFe0.978Co0.022As exhibits some of the strongest orbitally selective electronic correlations in the family of iron pnictides. Unexpectedly, we find that the mass enhancement of itinerant charge carriers in the strongly correlated band is dramatically reduced near the Γ point and attribute this effect to orbital mixing induced by pronounced spin-orbit coupling. Embracing the true band structure allows us to describe all low-energy electronic properties obtained in our experiments with remarkable consistency and demonstrate that superconductivity in this material is rather weak and mediated by spin fluctuations.

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.

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.

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.

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.