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

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.

Verwey transition as evolution from electronic nematicity to trimerons via electron-phonon coupling

Understanding the driving mechanisms behind metal-insulator transitions (MITs) is a critical step toward controlling material's properties. Since the proposal of charge order-induced MIT in magnetite Fe3O4 in 1939 by Verwey, the nature of the charge order and its role in the transition have remained elusive. Recently, a trimeron order was found in the low-temperature structure of Fe3O4; however, the expected transition entropy change in forming trimeron is greater than the observed value, which arises a reexamination of the ground state in the high-temperature phase. Here, we use electron diffraction to unveil that a nematic charge order on particular Fe sites emerges in the high-temperature structure of bulk Fe3O4 and that, upon cooling, a competitive intertwining of charge and lattice orders arouses the Verwey transition. Our findings discover an unconventional type of electronic nematicity in correlated materials and offer innovative insights into the transition mechanism in Fe3O4 via the electron-phonon coupling.

Nematic-Fluctuation-Mediated Superconductivity Revealed by Anisotropic Strain in Ba(Fe_{1-x}Co_{x})_{2}As_{2}

Anisotropic strain is an external field capable of selectively addressing the role of nematic fluctuations in promoting superconductivity. We demonstrate this using polarization-resolved elasto-Raman scattering by probing the evolution of nematic fluctuations under strain in the normal and superconducting state of the paradigmatic iron-based superconductor Ba(Fe_{1-x}Co_{x})_{2}As_{2}. In the parent compound BaFe_{2}As_{2} we observe a strain-induced suppression of the nematic susceptibility which follows the expected behavior of an Ising order parameter under a symmetry breaking field. For the superconducting compound, the suppression of the nematic susceptibility correlates with the decrease of the critical temperature T_{c}, indicating a significant contribution of nematic fluctuations to electron pairing. Our results validate theoretical scenarios of enhanced T_{c} near a nematic quantum critical point.

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.

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.

Elastocaloric signature of nematic fluctuations

The elastocaloric effect (ECE) relates changes in entropy to changes in strain experienced by a material. As such, ECE measurements can provide valuable information about the entropy landscape proximate to strain-tuned phase transitions. For ordered states that break only point symmetries, bilinear coupling of the order parameter with strain implies that the ECE can also provide a window on fluctuations above the critical temperature and hence, in principle, can also provide a thermodynamic measure of the associated susceptibility. To demonstrate this, we use the ECE to sensitively reveal the presence of nematic fluctuations in the archetypal Fe-based superconductor Ba([Formula: see text])₂[Formula: see text] By performing these measurements simultaneously with elastoresistivity in a multimodal fashion, we are able to make a direct and unambiguous comparison of these closely related thermodynamic and transport properties, both of which are sensitive to nematic fluctuations. As a result, we have uncovered an unanticipated doping dependence of the nemato-elastic coupling and of the magnitude of the scattering of low-energy quasi-particles by nematic fluctuations-while the former weakens, the latter increases dramatically with increasing doping.

Emerging symmetric strain response and weakening nematic fluctuations in strongly hole-doped iron-based superconductors

Electronic nematicity is often found in unconventional superconductors, suggesting its relevance for electronic pairing. In the strongly hole-doped iron-based superconductors, the symmetry channel and strength of the nematic fluctuations, as well as the possible presence of long-range nematic order, remain controversial. Here, we address these questions using transport measurements under elastic strain. By decomposing the strain response into the appropriate symmetry channels, we demonstrate the emergence of a giant in-plane symmetric contribution, associated with the growth of both strong electronic correlations and the sensitivity of these correlations to strain. We find weakened remnants of the nematic fluctuations that are present at optimal doping, but no change in the symmetry channel of nematic fluctuations with hole doping. Furthermore, we find no indication of a nematic-ordered state in the AFe2As2 (A = K, Rb, Cs) superconductors. These results revise the current understanding of nematicity in hole-doped iron-based superconductors.

Nematic quantum criticality in an Fe-based superconductor revealed by strain-tuning

Quantum criticality may be essential to understanding a wide range of exotic electronic behavior; however, conclusive evidence of quantum critical fluctuations has been elusive in many materials of current interest. An expected characteristic feature of quantum criticality is power-law behavior of thermodynamic quantities as a function of a nonthermal tuning parameter close to the quantum critical point (QCP). Here, we observed power-law behavior of the critical temperature of the coupled nematic/structural phase transition as a function of uniaxial stress in a representative family of iron-based superconductors, providing direct evidence of quantum critical nematic fluctuations in this material. These quantum critical fluctuations are not confined within a narrow regime around the QCP but rather extend over a wide range of temperatures and compositions.

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.

Short-Range Nematic Fluctuations in Sr_{1-x}Na_{x}Fe_{2}As_{2} Superconductors

Interactions between nematic fluctuations, magnetic order and superconductivity are central to the physics of iron-based superconductors. Here we report on in-plane transverse acoustic phonons in hole-doped Sr_{1-x}Na_{x}Fe_{2}As_{2} measured via inelastic x-ray scattering, and extract both the nematic susceptibility and the nematic correlation length. By a self-contained method of analysis, for the underdoped (x=0.36) sample, which harbors a magnetically ordered tetragonal phase, we find it hosts a short nematic correlation length ξ∼10  Å and a large nematic susceptibility χ_{nem}. The optimal-doped (x=0.55) sample exhibits weaker phonon softening effects, indicative of both reduced ξ and χ_{nem}. Our results suggest short-range nematic fluctuations may favor superconductivity, placing emphasis on the nematic correlation length for understanding the iron-based superconductors.

Electronic Nematicity in URu_{2}Si_{2} Revisited

The nature of the hidden-order (HO) state in URu_{2}Si_{2} remains one of the major unsolved issues in heavy-fermion physics. Recently, torque magnetometry, x-ray diffraction, and elastoresistivity data have suggested that the HO phase transition at T_{HO}≈ 17.5  K is driven by electronic nematic effects. Here, we search for thermodynamic signatures of this purported structural instability using anisotropic thermal expansion, Young's modulus, elastoresistivity, and specific-heat measurements. In contrast to the published results, we find no evidence of a rotational symmetry breaking in any of our data. Interestingly, our elastoresistivity measurements, which are in full agreement with published results, exhibit a Curie-Weiss divergence, which we however attribute to a volume and not to a symmetry-breaking effect. Finally, clear evidence for thermal fluctuations is observed in our heat-capacity data, from which we estimate the HO correlation length.

Nematic Correlation Length in Iron-Based Superconductors Probed by Inelastic X-Ray Scattering

Nematicity is ubiquitous in electronic phases of high-T_{c} superconductors, particularly in the Fe-based systems. We used inelastic x-ray scattering to extract the temperature-dependent nematic correlation length ξ from the anomalous softening of acoustic phonon modes in FeSe, underdoped Ba(Fe_{0.97}Co_{0.03})_{2}As_{2}, and optimally doped Ba(Fe_{0.94}Co_{0.06})_{2}As_{2}. In all cases, we find that ξ is well described by a power law (T-T_{0})^{-1/2} extending over a wide temperature range. Combined with the previously reported Curie-Weiss behavior of the nematic susceptibility, these results point to the mean-field character of the nematic transition, which we attribute to a sizable nematoelastic coupling that is likely detrimental to superconductivity.

Measurements of elastoresistance under pressure by combining in-situ tunable quasi-uniaxial stress with hydrostatic pressure

Uniaxial stress, as well as hydrostatic pressure are often used to tune material properties in condensed matter physics. Here, we present a setup that allows for the study of the combined effects of quasi-uniaxial stress and hydrostatic pressure. Following earlier designs for measurements under finite stress at ambient pressures [e.g., Chu et al., Science 337, 710 (2012)], the present setup utilizes a piezoelectric actuator to change stress in situ inside the piston-cylinder pressure cell. We show that the actuator can be operated over the full temperature (from 30 K up to 260 K) and pressure range (up to ≈2 GPa), resulting in a clear and measurable quasi-uniaxial strain. To demonstrate functionality, measurements of the elastoresistance (i.e., the change of resistance of a sample as a response to quasi-uniaxial strain) under finite hydrostatic pressure on the iron-based compound BaFe₂As₂ are presented as a proof-of-principle example and discussed in the framework of electronic nematicity. Overall, this work introduces the combination of in situ tunable quasi-uniaxial stress and large (up to ≈2 GPa) hydrostatic pressure as a powerful combination in the study of novel electronic phases. In addition, it also points toward further technical advancements which can be made in the future.

Momentum Dependence of the Nematic Order Parameter in Iron-Based Superconductors

The momentum dependence of the nematic order parameter is an important ingredient in the microscopic description of iron-based high-temperature superconductors. While recent reports on FeSe indicate that the nematic order parameter changes sign between electron and hole bands, detailed knowledge is still missing for other compounds. Combining angle-resolved photoemission spectroscopy with uniaxial strain tuning, we measure the nematic band splitting in both FeSe and BaFe_{2}As_{2} without interference from either twinning or magnetic order. We find that the nematic order parameter exhibits the same momentum dependence in both compounds with a sign change between the Brillouin center and the corner. This suggests that the same microscopic mechanism drives the nematic order in spite of the very different phase diagrams.

Enhancing the homogeneity of YBa2(Cu1−x Fe x )3O7−δsingle crystals by using an Fe-added Y2O3 crucible via top-seeded solution growth

Sizable metal-ion-doped YBa2Cu3O7−δ single crystals with high uniformity have been in great demand for fundamental studies on superconductivity. This article reports a novel approach, based on top-seeded solution growth and characterized by using an Fe-added Y2O3 crucible, to effectively enhance the homogeneity of YBa2(Cu1−x Fe x )3O7−δ single crystals. Because Fe ions are absorbable on or dissolvable from the Fe-Y2O3 crucible, it functions as a reservoir, yielding a stable Fe concentration in the liquid. Consequently, a series of acceptably sized YBa2(Cu1−x Fe x )3O7−δ single crystals with better uniformity than those grown by previous methods were obtained. The new dopant-added crucible, capable of balancing the solution spontaneously, is broadly applicable for preparing other doped single crystals.

Ferroelasticity, anelasticity and magnetoelastic relaxation in Co-doped iron pnictide: Ba(Fe0.957Co0.043)2As2

The hypothesis that strain has a permeating influence on ferroelastic, magnetic and superconducting transitions in 122 iron pnictides has been tested by investigating variations of the elastic and anelastic properties of a single crystal of Ba(Fe_0.957Co_0.043)₂As₂ by resonant ultrasound spectroscopy as a function of temperature and externally applied magnetic field. Non-linear softening and stiffening of C ₆₆ in the stability fields of both the tetragonal and orthorhombic structures has been found to conform quantitatively to the Landau expansion for a pseudoproper ferroelastic transition which is second order in character. The only exception is that the transition occurs at a temperature (T _S  ≈  69 K) ~10 K above the temperature at which C ₆₆ would extrapolate to zero ([Formula: see text]  ≈  59 K). An absence of anomalies associated with antiferromagnetic ordering below T _N  ≈  60 K implies that coupling of the magnetic order parameter with shear strain is weak. It is concluded that linear-quadratic coupling between the structural/electronic and antiferromagnetic order parameters is suppressed due to the effects of local heterogeneous strain fields arising from the substitution of Fe by Co. An acoustic loss peak at ~50-55 K is attributed to the influence of mobile ferroelastic twin walls that become pinned by a thermally activated process involving polaronic defects. Softening of C ₆₆ by up to ~6% below the normal-superconducting transition at T _c  ≈  13 K demonstrates an effective coupling of the shear strain with the order parameter for the superconducting transition which arises indirectly as a consequence of unfavourable coupling of the superconducting order parameter with the ferroelastic order parameter. Ba(Fe_0.957Co_0.043)₂As₂ is representative of 122 pnictides as forming a class of multiferroic superconductors in which elastic strain relaxations underpin almost all aspects of coupling between the structural, magnetic and superconducting order parameters and of dynamic properties of the transformation microstructures they contain.

Strain relaxation behaviour of vortices in a multiferroic superconductor

The elastic and anelastic properties of a single crystal of Co-doped pnictide Ba(Fe_0.957Co_0.043)₂As₂ have been determined by resonant ultrasound spectroscopy in the frequency range 10-500 kHz, both as a function of temperature through the normal-superconducting transition (T _c  ≈  12.5 K) and as a function of applied magnetic field up to 12.5 T. Correlation with thermal expansion, electrical resistivity, heat capacity, DC and AC magnetic data from crystals taken from the same synthetic batch has revealed the permeating influence of strain on coupling between order parameters for the ferroelastic (Q _E) and superconducting (Q _SC) transitions and on the freezing/relaxation behaviour of vortices. Elastic softening through T _c in zero field can be understood in terms of classical coupling of the order parameter with the shear strain e ₆, λe ₆ [Formula: see text], which means that there must be a common strain mechanism for coupling of the form λ [Formula: see text] Q _E. At fields of ~5 T and above, this softening is masked by Debye-like stiffening and acoustic loss processes due to vortex freezing. The first loss peak may be associated with the establishment of superconductivity on ferroelastic twin walls ahead of the matrix and the second is due to the vortex liquid-vortex glass transition. Strain contrast between vortex cores and the superconducting matrix will contribute significantly to interactions of vortices both with each other and with the underlying crystal structure. These interactions imply that iron-pnictides represent a class of multiferroic superconductors in which strain-mediated coupling occurs between the multiferroic properties (ferroelasticity, antiferromagnetism) and superconductivity.

Divergence of the quadrupole-strain susceptibility of the electronic nematic system YbRu2Ge2

A wide range of strongly correlated quantum materials, including some high-temperature superconductors, exhibit “electronic nematic” phases, in which the electronic properties spontaneously break the rotational symmetry of the crystal. However, the role that the corresponding nematic fluctuations play in these complicated systems is unclear, motivating the search for simpler model systems. Here, we identify a particular 4f intermetallic material which exhibits ferroquadrupole order, YbRu2Ge2, as just such a model system. We also provide a robust and accurate method to probe the divergence of an important associated quantity, the quadrupole-strain susceptibility. The temperature dependence of this quantity provides insight into the nature of the interactions that lead to ferroquadrupole order, in this case, magnetoelastic coupling.

Ferroquadrupole order associated with local 4f atomic orbitals of rare-earth ions is a realization of electronic nematic order. However, there are relatively few examples of intermetallic materials which exhibit continuous ferroquadrupole phase transitions, motivating the search for additional materials that fall into this category. Furthermore, it is not clear a priori whether experimental approaches based on transport measurements which have been successfully used to probe the nematic susceptibility in materials such as the Fe-based superconductors will be as effective in the case of 4f intermetallic materials, for which the important electronic degrees of freedom are local rather than itinerant and are consequently less strongly coupled to the charge-carrying quasiparticles near the Fermi energy. In the present work, we demonstrate that the intermetallic compound YbRu2Ge2 exhibits a tetragonal-to-orthorhombic phase transition consistent with ferroquadrupole order of the Yb ions and go on to show that elastoresistivity measurements can indeed provide a clear window on the diverging nematic susceptibility in this system. This material provides an arena in which to study the causes and consequences of electronic nematicity.

Collapse of Critical Nematic Fluctuations in FeSe under Pressure

We report the evolution of the electronic nematic susceptibility in FeSe via Raman scattering as a function of hydrostatic pressure up to 5.8 GPa where the superconducting transition temperature T_{c} reaches its maximum. The critical nematic fluctuations observed at low pressure vanish above 1.6 GPa, indicating they play a marginal role in the fourfold enhancement of T_{c} at higher pressures. The collapse of nematic fluctuations appears to be linked to a suppression of low energy electronic excitations which manifests itself by optical phonon anomalies at around 2 GPa, in agreement with lattice dynamical and electronic structure calculations using local density approximation combined with dynamical mean field theory. Our results reveal two different regimes of nematicity in the phase diagram of FeSe under pressure: a d-wave Pomeranchuk instability of the Fermi surface at low pressure and a magnetic driven orthorhombic distortion at higher pressure.

Imaging Anomalous Nematic Order and Strain in Optimally Doped BaFe_{2}(As,P)_{2}

We present the strain and temperature dependence of an anomalous nematic phase in optimally doped BaFe_{2}(As,P)_{2}. Polarized ultrafast optical measurements reveal broken fourfold rotational symmetry in a temperature range above T_{c} in which bulk probes do not detect a phase transition. Using ultrafast microscopy, we find that the magnitude and sign of this nematicity vary on a 50-100  μm length scale, and the temperature at which it onsets ranges from 40 K near a domain boundary to 60 K deep within a domain. Scanning Laue microdiffraction maps of local strain at room temperature indicate that the nematic order appears most strongly in regions of weak, isotropic strain. These results indicate that nematic order arises in a genuine phase transition rather than by enhancement of local anisotropy by a strong nematic susceptibility. We interpret our results in the context of a proposed surface nematic phase.

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.

Dichotomy between in-plane magnetic susceptibility and resistivity anisotropies in extremely strained BaFe2As2

High-temperature superconductivity in the Fe-based materials emerges when the antiferromagnetism of the parent compounds is suppressed by either doping or pressure. Closely connected to the antiferromagnetic state are entangled orbital, lattice, and nematic degrees of freedom, and one of the major goals in this field has been to determine the hierarchy of these interactions. Here we present the direct measurements and the calculations of the in-plane uniform magnetic susceptibility anisotropy of BaFe₂As₂, which help in determining the above hierarchy. The magnetization measurements are made possible by utilizing a simple method for applying a large symmetry-breaking strain, based on differential thermal expansion. In strong contrast to the large resistivity anisotropy above the antiferromagnetic transition at T _N, the anisotropy of the in-plane magnetic susceptibility develops largely below T _N. Our results imply that lattice and orbital degrees of freedom play a subdominant role in these materials.Interplay between lattice, orbital, magnetic and nematic degrees of freedom is crucial for the superconductivity in Fe-based materials. Here, the authors demonstrate the subdominant roles of pure lattice distortions and/or orbital ordering in BaFe₂As₂ by characterizing the in-plane magnetic susceptibility anisotropy.

Antiferroic electronic structure in the nonmagnetic superconducting state of the iron-based superconductors

A major problem in the field of high-transition temperature (T_c) superconductivity is the identification of the electronic instabilities near superconductivity. It is known that the iron-based superconductors exhibit antiferromagnetic order, which competes with the superconductivity. However, in the nonmagnetic state, there are many aspects of the electronic instabilities that remain unclarified, as represented by the orbital instability and several in-plane anisotropic physical properties. We report a new aspect of the electronic state of the optimally doped iron-based superconductors by using high-energy resolution angle-resolved photoemission spectroscopy. We find spectral evidence for the folded electronic structure suggestive of an antiferroic electronic instability, coexisting with the superconductivity in the nonmagnetic state of Ba_1-x K _x Fe₂As₂. We further establish a phase diagram showing that the antiferroic electronic structure persists in a large portion of the nonmagnetic phase covering the superconducting dome. These results motivate consideration of a key unknown electronic instability, which is necessary for the achievement of high-T_c superconductivity in the iron-based superconductors.

Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point

Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin [Formula: see text] itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting [Formula: see text] enclosing the nematic quantum critical point. For temperatures above [Formula: see text], we see strikingly non-Fermi liquid behavior, including a "nodal-antinodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low-frequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.

Determination of the resistivity anisotropy of orthorhombic materials via transverse resistivity measurements

Measurements of the resistivity anisotropy can provide crucial information about the electronic structure and scattering processes in anisotropic and low-dimensional materials, but quantitative measurements by conventional means often suffer very significant systematic errors. Here we describe a novel approach to measuring the resistivity anisotropy of orthorhombic materials, using a single crystal and a single measurement that is derived from a π4 rotation of the measurement frame relative to the crystallographic axes. In this new basis, the transverse resistivity gives a direct measurement of the resistivity anisotropy, which combined with the longitudinal resistivity also gives the in-plane elements of the conventional resistivity tensor via a 5-point contact geometry. This is demonstrated through application to the charge-density wave compound ErTe₃, and it is concluded that this method presents a significant improvement on existing techniques, particularly when measuring small anisotropies.

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.

Sign-Reversing Orbital Polarization in the Nematic Phase of FeSe due to the C_{2} Symmetry Breaking in the Self-Energy

To understand the nematicity in Fe-based superconductors, nontrivial k dependence of the orbital polarization [ΔE_{xz}(k), ΔE_{yz}(k)] in the nematic phase, such as the sign reversal of the orbital splitting between Γ and X, Y points in FeSe, provides significant information. To solve this problem, we study the spontaneous symmetry breaking with respect to the orbital polarization and spin susceptibility self-consistently. In FeSe, due to the sign-reversing orbital order, the hole and electron pockets are elongated along the k_{y} and k_{x} axes, respectively, consistently with experiments. In addition, an electron pocket splits into two Dirac cone Fermi pockets while increasing the orbital polarization. The orbital order in Fe-based superconductors originates from the strong positive feedback between the nematic orbital order and spin susceptibility.

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.

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).

Direct characterization of photoinduced lattice dynamics in BaFe2As2

Ultrafast light pulses can modify electronic properties of quantum materials by perturbing the underlying, intertwined degrees of freedom. In particular, iron-based superconductors exhibit a strong coupling among electronic nematic fluctuations, spins and the lattice, serving as a playground for ultrafast manipulation. Here we use time-resolved X-ray scattering to measure the lattice dynamics of photoexcited BaFe₂As₂. On optical excitation, no signature of an ultrafast change of the crystal symmetry is observed, but the lattice oscillates rapidly in time due to the coherent excitation of an A_1g mode that modulates the Fe–As–Fe bond angle. We directly quantify the coherent lattice dynamics and show that even a small photoinduced lattice distortion can induce notable changes in the electronic and magnetic properties. Our analysis implies that transient structural modification can be an effective tool for manipulating the electronic properties of multi-orbital systems, where electronic instabilities are sensitive to the orbital character of bands.

In BaFe₂As₂, the lattice couples strongly to the magnetic and electronic degrees of freedom, providing a way to control them. Here, by means of time-resolved X-ray scattering, the authors measure rapid lattice oscillations, which can induce changes in the material's electronic and magnetic properties.

Orbital-driven nematicity in FeSe

A fundamental and unconventional characteristic of superconductivity in iron-based materials is that it occurs in the vicinity of two other instabilities. In addition to a tendency towards magnetic order, these Fe-based systems have a propensity for nematic ordering: a lowering of the rotational symmetry while time-reversal invariance is preserved. Setting the stage for superconductivity, it is heavily debated whether the nematic symmetry breaking is driven by lattice, orbital or spin degrees of freedom. Here, we report a very clear splitting of NMR resonance lines in FeSe at Tnem = 91 K, far above the superconducting Tc of 9.3 K. The splitting occurs for magnetic fields perpendicular to the Fe planes and has the temperature dependence of a Landau-type order parameter. Spin-lattice relaxation rates are not affected at Tnem, which unequivocally establishes orbital degrees of freedom as driving the nematic order. We demonstrate that superconductivity competes with the emerging nematicity.

Origin of the tetragonal-to-orthorhombic phase transition in FeSe: a combined thermodynamic and NMR study of nematicity

The nature of the tetragonal-to-orthorhombic structural transition at T_{s}≈90  K in single crystalline FeSe is studied using shear-modulus, heat-capacity, magnetization, and nuclear magnetic resonance measurements. The transition is shown to be accompanied by a large shear-modulus softening, which is practically identical to that of underdoped Ba(Fe,Co)_{2}As_{2}, suggesting a very similar strength of the electron-lattice coupling. On the other hand, a spin-fluctuation contribution to the spin-lattice relaxation rate is only observed below T_{s}. This indicates that the structural, or "nematic," phase transition in FeSe is not driven by magnetic fluctuations.

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.

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.

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.