Unconventional superconductivity and antiferromagnetic quantum critical behavior in the isovalent-doped BaFe2(As1-xPx)2

Robust superconductivity and the suppression of charge-density wave in the quasi-skutteruditesCa3(Ir1-xRhx)4Sn13single crystals at ambient pressure

Single crystals of the quasi-skutterudite compounds Ca3(Ir1-xRhx)4Sn13(3-4-13) were synthesized by flux growth and characterized by x-ray diffraction, energy dispersive x-ray spectroscopy, magnetization, resistivity, and radio frequency magnetic susceptibility techniques. The coexistence and competition between the charge density wave (CDW) and superconductivity was studied by varying the Rh/Ir ratio. The superconducting transition temperature,Tc, varies from 7 K in pure Ir (x = 0) to 8.3 K in pure Rh (x = 1). Temperature-dependent electrical resistivity reveals monotonic suppression of the CDW transition temperature,TCDW(x). The CDW starts in pure Ir,x = 0, atTCDW≈ 40 K and extrapolates roughly linearly to zero atxc≈0.53-0.58 under the superconducting dome. Magnetization and transport measurements show a significant influence of CDW on superconducting and normal states. Meissner expulsion is substantially reduced in the CDW region, indicating competition between the CDW and superconductivity. The low-temperature resistivity is higher in the CDW part of the phase diagram, consistent with the reduced density of states due to CDW gapping. Its temperature dependence just aboveTcshows signs of non-Fermi liquid behavior in a cone-like composition pattern. We conclude that the Ca3(Ir1-xRhx)4Sn13alloy is a good candidate for a composition-driven quantum critical point at ambient pressure.

Research Progress of FeSe-based Superconductors Containing Ammonia/Organic Molecules Intercalation

As an important part of Fe-based superconductors, FeSe-based superconductors have become a hot field in condensed matter physics. The exploration and preparation of such superconducting materials form the basis of studying their physical properties. With the help of various alkali/alkaline-earth/rare-earth metals, different kinds of ammonia/organic molecules have been intercalated into the FeSe layer to form a large number of FeSe-based superconductors with diverse structures and different layer spacing. Metal cations can effectively provide carriers to the superconducting FeSe layer, thus significantly increasing the superconducting transition temperature. The orientation of organic molecules often plays an important role in structural modification and can be used to fine-tune superconductivity. This review introduces the crystal structures and superconducting properties of several typical FeSe-based superconductors containing ammonia/organic molecules intercalation discovered in recent years, and the effects of FeSe layer spacing and superconducting transition temperature are briefly summarized.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Controlling unconventional superconductivity in artificially engineeredf-electron Kondo superlattices

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials, including high-T_ccuprates, iron pnictides, and heavy-fermion compounds. Interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures provide a new approach to this most fundamental and hotly debated subject. We have been able to use a recent state-of-the-art molecular-beam-epitaxy technique to fabricate superlattices consisting of different heavy-fermion compounds with atomic thickness. These Kondo superlattices provide a unique opportunity to study the mutual interaction between unconventional superconductivity and magnetic order through the atomic interface. Here, we design and fabricate hybrid Kondo superlattices consisting of alternating layers of superconducting CeCoIn₅withd-wave pairing symmetry and nonmagnetic metal YbCoIn₅or antiferromagnetic heavy fermion metals such as CeRhIn₅and CeIn₃. In these Kondo superlattices, superconducting heavy electrons are confined within the two-dimensional CeCoIn₅block layers and interact with neighboring nonmagnetic or magnetic layers through the interface. Superconductivity is strongly influenced by local inversion symmetry breaking at the interface in CeCoIn₅/YbCoIn₅superlattices. The superconducting and antiferromagnetic states coexist in spatially separated layers in CeCoIn₅/CeRhIn₅and CeCoIn₅/CeIn₃superlattices, but their mutual coupling via the interface significantly modifies the superconducting and magnetic properties. The fabrication of a wide variety of hybrid superlattices paves a new way to study the relationship between unconventional superconductivity and magnetism in strongly correlated materials.

One Structure, Two Elements-LuGe2 Superconductor vs Ordinary Metallic Conductor LuSn2. A Case Study on How Site-Selective Germanium for Tin Atom Substitution Leads to Modulating of the Charge Distribution

The substitution of chemically similar elements in a given crystal structure is an effective way to enhance physical properties, but the understanding on such improvements is usually impeded because the substitutions are random, and the roles of the different atoms cannot be distinguished by crystallographic symmetry. Herein, we provide a detailed crystallographic analysis and property measurements for the continuous solid solutions LuGe_xSn_2-x (0 < x < 2). The results show that there is no apparent change of the global symmetry, with the end-members LuGe₂ and LuSn₂, as well as the intermediate LuGe_xSn_2-x compositions adopting the ZrSi₂ type structure (space group Cmcm, Pearson index oC12). Yet, the refinements of the crystal structures from single-crystal X-ray diffraction data show that Ge-Sn atom substitutions are not random, but occur preferentially at the zigzag chain. The patterned distribution of two group 14 elements leads to a significant variation in chemical bonding and charge ordering within the other structural fragment, the 2D square nets, thereby resulting in tuned electron transport. The enhancement is greater than that for the typical Bloch-Gruneisen model and more akin to that for the parallel-resistor model. Magnetization measurements on single crystals show bulk superconductivity in all LuGe_xSn_2-x samples with shielding fractions as high as 90%. Specific heat data confirm the effect to originate from residual metallic tin in the material, indicating that Sn atom substitutions in the 2D square nets cause disruptions of the hypervalent bonding and local anisotropy, which ultimately leads to vanishing of the superconducting state in the end-member LuGe₂. This work sheds light on how the complexity in chemical interactions by two different carbon congeners leads to changes in the physical properties and how they can be correlated with the induced charge distribution. These studies also provide a general approach to modulation of charge density and. thus, of emerging physical properties in other classes of intermetallic systems based on the main-group elements of groups 13 to 15.

Structural, magnetic, and electronic evolution of the spin-ladder system BaFe2S3-x Se x with isoelectronic substitution

We report experimental studies of a series of BaFe2S3-x Se x (0 ⩽ x ⩽ 3) single crystals and powder specimens using x-ray diffraction, neutron-diffraction, muon-spin-relaxation, and electrical transport measurements. A structural transformation from Cmcm (BaFe2S3) to Pnma (BaFe2Se3) was identified around x = 0.7 - 1. Neutron-diffraction measurements on the samples with x = 0.2, 0.4, and 0.7 reveal that the Néel temperature of the stripe antiferromagnetic order is gradually suppressed from ~120 to 85 K, while the magnitude of the ordered Fe2+ moments shows very little variation. Similarly, the block antiferromagnetic order in BaFe2Se3 remains robust for 1.5 ⩽ x ⩽ 3 with negligible variation in the ordered moment and a slight decrease of the Néel temperature from 250 K (x = 3) to 225 K (x = 1.5). The sample with x = 1 near the Cmcm and Pnma border shows coexisting, two-dimensional, short-range stripe- and block-type antiferromagnetic correlations. The system remains insulating for all x, but the thermal activation gap shows an abrupt increase when traversing the boundary from the Cmcm stripe phase to the Pnma block phase. The results demonstrate that the crystal structure, magnetic order, and electronic properties are strongly coupled in the BaFe2S3-x Se x system.

Electrical resistivity across a nematic quantum critical point

Correlated electron systems are highly susceptible to various forms of electronic order. By tuning the transition temperature towards absolute zero, striking deviations from conventional metallic (Fermi-liquid) behaviour can be realized. Evidence for electronic nematicity, a correlated electronic state with broken rotational symmetry, has been reported in a host of metallic systems^1-5 that exhibit this so-called quantum critical behaviour. In all cases, however, the nematicity is found to be intertwined with other forms of order, such as antiferromagnetism^5-7 or charge-density-wave order⁸, that might themselves be responsible for the observed behaviour. The iron chalcogenide FeSe_1-xS_x is unique in this respect because its nematic order appears to exist in isolation^9-11, although until now, the impact of nematicity on the electronic ground state has been obscured by superconductivity. Here we use high magnetic fields to destroy the superconducting state in FeSe_1-xS_x and follow the evolution of the electrical resistivity across the nematic quantum critical point. Classic signatures of quantum criticality are revealed: an enhancement in the coefficient of the T² resistivity (due to electron-electron scattering) on approaching the critical point and, at the critical point itself, a strictly T-linear resistivity that extends over a decade in temperature T. In addition to revealing the phenomenon of nematic quantum criticality, the observation of T-linear resistivity at a nematic critical point also raises the question of whether strong nematic fluctuations play a part in the transport properties of other 'strange metals', in which T-linear resistivity is observed over an extended regime in their respective phase diagrams.

Effect of pressure on the self-hole-doped superconductor RbGd2Fe4As4O2

RbGd₂Fe₄As₄O₂ is a newly discovered self-hole-doped stoichiometric superconductor, which has a hybrid structure with separated double FeAs layers and exhibits a high superconducting transition temperature T _c  =  35 K. Here, we report the effect of pressure (P) on its T _c and normal-state transport properties by measuring the temperature dependence of resistivity ρ(T) under various pressures up to 14 GPa with a cubic anvil cell apparatus. We found that the T _c is suppressed monotonically to ca. 12.5 K upon increasing pressure to 14 GPa with a slope change of T _c(P) at around 4 GPa. In addition, the low-temperature normal-state ρ(T), which is proportional to T ⁿ , also evolves gradually from a non-Fermi-liquid with n  =  1 at ambient pressure to a Fermi liquid with n  =  2 at P  ⩾  4 GPa. Accompanying with the non-Fermi-liquid to Fermi-liquid crossover, the quadratic temperature coefficient of resistivity, which reflects the effective mass of charge carriers, also experiences a significant reduction as commonly observed in the vicinity of a magnetic quantum critical point (QCP). Our results indicate that the stoichiometric RbGd₂Fe₄As₄O₂ at ambient pressure might be located near a QCP such that the enhanced critical spin fluctuations lead to high-T _c superconductivity. The application of pressure should broaden the electronic bandwidth and weaken the spin fluctuations, and then restore a Fermi-liquid ground state with lower T _c.

Unconventional Antiferromagnetic Quantum Critical Point in Ba(Fe_{0.97}Cr_{0.03})_{2}(As_{1-x}P_{x})_{2}

We have systematically studied physical properties of Ba(Fe_{0.97}Cr_{0.03})_{2}(As_{1-x}P_{x})_{2}, where superconductivity in BaFe_{2}(As_{1-x}P_{x})_{2} is fully suppressed by just 3% of Cr substitution of Fe. A quantum critical point is revealed at x∼0.42, where non-Fermi-liquid behaviors similar to those in BaFe_{2}(As_{1-x}P_{x})_{2} are observed. Neutron diffraction and inelastic neutron scattering measurements suggest that the quantum critical point is associated with the antiferromagnetic order, which is not of conventional spin-density-wave type as evidenced by the ω/T scaling of spin excitations. On the other hand, no divergence of low-temperature nematic susceptibility is observed when x is decreased to 0.42 from higher doping level, demonstrating that there are no nematic quantum critical fluctuations. Our results suggest that non-Fermi-liquid behaviors in iron-based superconductors can be solely resulted from the antiferromagnetic quantum critical fluctuations, which cast doubts on the role of nematic fluctuations played in the normal-state properties in iron-based superconductors.

Progress in Cr- and Mn-based superconductors: a key issues review

The presence of magnetic ions was first believed to be detrimental to superconductivity. However, unconventional superconductivity has been widely induced by doping or applying external pressure in magnetic systems such as heavy fermion, cuprate and iron-based superconductors in which magnetic fluctuations are suggested to serve as the pairing glue for Cooper pairs. The discovery of superconductivity in the magnetic compounds CrAs and MnP under high pressures has further expanded this family of superconductors and provided new platforms for investigating the interplay between magnetism and superconductivity. CrAs and MnP represent the first superconductors among the transition metal Cr- and Mn-based compounds in which the electronic states near the Fermi level are dominated by Cr/Mn 3d electrons. Shortly after their discovery, new types of Cr-based quasi-one-dimensional superconductors A₂Cr₃As₃ and ACr₃As₃ (A [Formula: see text] K, Rb, Cs or Na) were discovered at ambient pressure. The close proximity of superconductivity to magnetic instability in these systems suggests that spin fluctuations may play crucial roles in mediating the Cooper pairing. In this article we review the basic physical properties of these novel superconductors and the progress achieved in recent studies.

Hedgehog Spin-Vortex Crystal Antiferromagnetic Quantum Criticality in CaK(Fe_{1-x}Ni_{x})_{4}As_{4} Revealed by NMR

Two ordering states, antiferromagnetism and nematicity, have been observed in most iron-based superconductors (SCs). In contrast to those SCs, the newly discovered SC CaK(Fe_{1-x}Ni_{x})_{4}As_{4} exhibits an antiferromagnetic (AFM) state, called hedgehog spin-vortex crystal (SVC) structure, without nematic order, providing the opportunity for the investigation into the relationship between spin fluctuations and SC without any effects of nematic fluctuations. Our ^{75}As nuclear magnetic resonance studies on CaK(Fe_{1-x}Ni_{x})_{4}As_{4} (0≤x≤0.049) revealed that CaKFe_{4}As_{4} is located close to a hidden hedgehog SVC AFM quantum-critical point (QCP). The magnetic QCP without nematicity in CaK(Fe_{1-x}Ni_{x})_{4}As_{4} highlights the close connection of spin fluctuations and superconductivity in iron-based SCs. The advantage of stoichiometric composition also makes CaKFe_{4}As_{4} an ideal platform for further detailed investigation of the relationship between magnetic QCP and superconductivity in iron-based SCs without disorder effects.

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.

Domain Meissner state and spontaneous vortex-antivortex generation in the ferromagnetic superconductor EuFe2(As0.79P0.21)2

The interplay between superconductivity and magnetism is one of the oldest enigmas in physics. Usually, the strong exchange field of ferromagnet suppresses singlet superconductivity via the paramagnetic effect. In EuFe2(As0.79P0.21)2, a material that becomes not only superconducting at 24.2 K but also ferromagnetic below 19 K, the coexistence of the two antagonistic phenomena becomes possible because of the unusually weak exchange field produced by the Eu subsystem. We demonstrate experimentally and theoretically that when the ferromagnetism adds to superconductivity, the Meissner state becomes spontaneously inhomogeneous, characterized by a nanometer-scale striped domain structure. At yet lower temperature and without any externally applied magnetic field, the system locally generates quantum vortex-antivortex pairs and undergoes a phase transition into a domain vortex-antivortex state characterized by much larger domains and peculiar Turing-like patterns. We develop a quantitative theory of this phenomenon and put forth a new way to realize superconducting superlattices and control the vortex motion in ferromagnetic superconductors by tuning magnetic domains-unprecedented opportunity to consider for advanced superconducting hybrids.

A tale of two metals: contrasting criticalities in the pnictides and hole-doped cuprates

The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting (SC) properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the SC dome. In this review, we critically examine these claims and highlight significant differences in the bulk physical properties of both systems. While there is now a large body of evidence supporting the presence of a (magnetic) QCP in the iron pnictides, the situation in the cuprates is much less apparent, at least for the end point of the pseudogap phase. We argue that the opening of the normal state pseudogap in cuprates, so often tied to a putative QCP, arises from a momentum-dependent breakdown of quasiparticle coherence that sets in at much higher doping levels but which is driven by the proximity to the Mott insulating state at half filling. Finally, we present a new scenario for the cuprates in which this loss of quasiparticle integrity and its evolution with momentum, temperature and doping plays a key role in shaping the resultant phase diagram.

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.

Selective mass enhancement close to the quantum critical point in BaFe2(As1-x P x )2

A quantum critical point (QCP) is currently being conjectured for the BaFe₂(As_1-x P _x )₂ system at the critical value x _c  ≈ 0.3. In the proximity of a QCP, all thermodynamic and transport properties are expected to scale with a single characteristic energy, given by the quantum fluctuations. Such a universal behavior has not, however, been found in the superconducting upper critical field H _c2. Here we report H _c2 data for epitaxial thin films extracted from the electrical resistance measured in very high magnetic fields up to 67 Tesla. Using a multi-band analysis we find that H _c2 is sensitive to the QCP, implying a significant charge carrier effective mass enhancement at the doping-induced QCP that is essentially band-dependent. Our results point to two qualitatively different groups of electrons in BaFe₂(As_1-x P _x )₂. The first one (possibly associated to hot spots or whole Fermi sheets) has a strong mass enhancement at the QCP, and the second one is insensitive to the QCP. The observed duality could also be present in many other quantum critical systems.

Absence of low energy magnetic spin-fluctuations in isovalently and aliovalently doped LaCo2B2 superconducting compounds

Magnetization, resistivity and (11)B, (59)Co NMR measurements have been performed on the Pauli paramagnet [Formula: see text], and the superconductors [Formula: see text] ([Formula: see text] K) and [Formula: see text] ([Formula: see text] K). The site selective NMR experiment reveals the multiband nature of the Fermi surface in these systems. The temperature independent Knight shift and 1/T 1 T clearly indicate the absence of correlated low energy magnetic spin-fluctuations in the normal state, which is in contrast to other Fe-based pnictides. The density of states (DOS) of Co 3d electrons has been enhanced in superconducting [Formula: see text] and [Formula: see text] with respect to the non superconducting reference compound [Formula: see text]. The occurrence of superconductivity is related to the DOS enhancement.

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.

Competing Magnetic Fluctuations in Iron Pnictide Superconductors: Role of Ferromagnetic Spin Correlations Revealed by NMR

In the iron pnictide superconductors, theoretical calculations have consistently shown enhancements of the static magnetic susceptibility at both the stripe-type antiferromagnetic and in-plane ferromagnetic (FM) wave vectors. However, the possible existence of FM fluctuations has not yet been examined from a microscopic point of view. Here, using ^{75}As NMR data, we provide clear evidence for the existence of FM spin correlations in both the hole- and electron-doped BaFe_{2}As_{2} families of iron-pnictide superconductors. These FM fluctuations appear to compete with superconductivity and are thus a crucial ingredient to understanding the variability of T_{c} and the shape of the superconducting dome in these and other iron-pnictide families.

Structural and Magnetic Phase Transitions near Optimal Superconductivity in BaFe2(As(1-x)Px)2

We use nuclear magnetic resonance (NMR), high-resolution x-ray, and neutron scattering studies to study structural and magnetic phase transitions in phosphorus-doped BaFe2(As(1-x)P(x)2. Previous transport, NMR, specific heat, and magnetic penetration depth measurements have provided compelling evidence for the presence of a quantum critical point (QCP) near optimal superconductivity at x=0.3. However, we show that the tetragonal-to-orthorhombic structural (T{s}) and paramagnetic to antiferromagnetic (AF, TN) transitions in BaFe2(As(1-x)Px)2 are always coupled and approach T{N}≈T{s}≥T{c} (≈29  K) for x=0.29 before vanishing abruptly for x≥0.3. These results suggest that AF order in BaFe_{2}(As(1-x)Px)2 disappears in a weakly first-order fashion near optimal superconductivity, much like the electron-doped iron pnictides with an avoided QCP.

NMR investigation of the quasi-one-dimensional superconductor K(2)Cr(3)As(3)

We report ^{75}As NMR measurements on the new quasi-one-dimensional superconductor K_{2}Cr_{3}As_{3} (T_{c}∼6.1  K) [J. K. Bao et al., Phys. Rev. X 5, 011013 (2015)]. We found evidence for strong enhancement of Cr spin fluctuations above T_{c} in the [Cr_{3}As_{3}]_{∞} double-walled subnanotubes based on the nuclear spin-lattice relaxation rate 1/T_{1}. The power-law temperature dependence, 1/T_{1}T∼T^{-γ} (γ∼0.25), is consistent with the Tomonaga-Luttinger liquid. Moreover, absence of the Hebel-Slichter coherence peak of 1/T_{1} just below T_{c} suggests an unconventional nature of superconductivity.

Detection of an unconventional superconducting phase in the vicinity of the strong first-order magnetic transition in CrAs using (75)As-nuclear quadrupole resonance

Pressure-induced superconductivity was recently discovered in the binary helimagnet CrAs. We report the results of measurements of nuclear quadrupole resonance for CrAs under pressure. In the vicinity of the critical pressure P(c) between the helimagnetic (HM) and paramagnetic (PM) phases, a phase separation is observed. The large internal field remaining in the phase-separated HM state indicates that the HM phase disappears through a strong first-order transition. This indicates the absence of a quantum critical point in CrAs; however, the nuclear spin-lattice relaxation rate 1/T(1) reveals that substantial magnetic fluctuations are present in the PM state. The absence of a coherence effect in 1/T(1) in the superconducting state provides evidence that CrAs is the first Cr-based unconventional superconductor.

Anomalous critical fields in quantum critical superconductors

Fluctuations around an antiferromagnetic quantum critical point (QCP) are believed to lead to unconventional superconductivity and in some cases to high-temperature superconductivity. However, the exact mechanism by which this occurs remains poorly understood. The iron-pnictide superconductor BaFe₂(As_1−xP_x)₂ is perhaps the clearest example to date of a high-temperature quantum critical superconductor, and so it is a particularly suitable system to study how the quantum critical fluctuations affect the superconducting state. Here we show that the proximity of the QCP yields unexpected anomalies in the superconducting critical fields. We find that both the lower and upper critical fields do not follow the behaviour, predicted by conventional theory, resulting from the observed mass enhancement near the QCP. Our results imply that the energy of superconducting vortices is enhanced, possibly due to a microscopic mixing of antiferromagnetism and superconductivity, suggesting that a highly unusual vortex state is realized in quantum critical superconductors.

Superconductivity in the iron pnictides is believed to be related to quantum critical fluctuations. Putzke et al. observe unexpected anomalies in the critical fields of BaFe₂(As_1−xP_x)₂ that emerge close to its magnetic critical point, which they argue is a generic feature of quantum critical superconductivity.

Magnetic and structural transitions of SrFe2As2 at high pressure and low temperature

One of key issues in studying iron based superconductors is to understand how the magnetic phase of the parent compounds evolves. Here we report the systematic investigation of paramagnetic to antiferromagnetic and tetragonal to orthorhombic structural transitions of “122” SrFe₂As₂ parent compound using combined high resolution synchrotron Mössbauer spectroscopy and x-ray diffraction techniques in a cryogenically cooled high pressure diamond anvil cell. It is found that although the two transitions are coupled at 205 K at ambient pressure, they are concurrently suppressed to much lower temperatures near a quantum critical pressure of approximately 4.8 GPa where the antiferromagnetic state transforms into bulk superconducting state. Our results indicate that the lattice distortions and magnetism jointly play a critical role in inducing superconductivity in iron based compounds.

Coexistence of cluster spin glass and superconductivity in Ba(Fe(1-x)Co(x))2As2 for 0.060≤x≤0.071

We present 75As nuclear magnetic resonance data from measurements of a series of Ba(Fe(1-x)Co(x))2As2 crystals with 0.00≤x≤0.075 that reveals the coexistence of frozen antiferromagnetic domains and superconductivity for 0.060≤x≤0.071. Although bulk probes reveal no long range antiferromagnetic order beyond x=0.06, we find that the local spin dynamics reveal no qualitative change across this transition. The characteristic domain sizes vary by more than an order of magnitude, reaching a maximum variation at x=0.06. This inhomogeneous glassy dynamics may be an intrinsic response to the competition between superconductivity and antiferromagnetism in this system.

Effect of magnetic criticality and Fermi-surface topology on the magnetic penetration depth

We investigate the effect of antiferromagnetic (AF) quantum criticality on the magnetic penetration depth λ(T) in line-nodal superconductors, including the cuprates, the iron pnictides, and the heavy-fermion superconductors. The critical magnetic fluctuation renormalizes the current vertex and drastically enhances the zero-temperature penetration depth λ(0), which is more remarkable in the iron-pnictide case due to the Fermi-surface topology. Additional temperature (T) dependence of the current renormalization makes the expected T-linear behavior at low temperatures approach T(1.5) asymptotically. These anomalous behaviors are consistent with experimental observations. We stress that λ(T) is a good probe to detect the AF quantum critical point in the superconducting state.

Scaling between magnetic and lattice fluctuations in iron pnictide superconductors

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

Hidden T-linear scattering rate in Ba0.6K0.4Fe2As2 revealed by optical spectroscopy

The optical properties of Ba0.6K0.4Fe2As2 have been determined in the normal state for a number of temperatures over a wide frequency range. Two Drude terms, representing two groups of carriers with different scattering rates (1/τ), well describe the real part of the optical conductivity σ1(ω). A "broad" Drude component results in an incoherent background with a T-independent 1/τb, while a "narrow" Drude component reveals a T-linear 1/τn resulting in a resistivity ρn≡1/σ1n(ω→0) also linear in temperature. An arctan(T) low-frequency spectral weight is also strong evidence for a T-linear 1/τ. A comparison to other materials with similar behavior suggests that the T-linear 1/τn and ρn in Ba0.6K0.4Fe2As2 originate from scattering from spin fluctuations and hence that an antiferromagnetic quantum critical point is likely to exist in the superconducting dome.

Quasiparticle mass enhancement close to the quantum critical point in BaFe2(As(1-x)P(x))2

We report a combined study of the specific heat and de Haas-van Alphen effect in the iron-pnictide superconductor BaFe2(As(1-x)P(x))2. Our data when combined with results for the magnetic penetration depth give compelling evidence for the existence of a quantum critical point close to x=0.30 which affects the majority of the Fermi surface by enhancing the quasiparticle mass. The results show that the sharp peak in the inverse superfluid density seen in this system results from a strong increase in the quasiparticle mass at the quantum critical point.

Thermopower as a sensitive probe of electronic nematicity in iron pnictides

We study the in-plane anisotropy of the thermoelectric power and electrical resistivity on detwinned single crystals of isovalent substituted EuFe(2)(As(1-x)P(x))(2). Compared to the resistivity anisotropy, the thermopower anisotropy is more pronounced and clearly visible already at temperatures much above the structural and magnetic phase transitions. Most remarkably, the thermopower anisotropy changes sign below the structural transition. This is associated with the interplay of two contributions due to anisotropic scattering and orbital polarization, which dominate at high and low temperatures, respectively.

Microscopic Coexistence of Superconductivity and Antiferromagnetism in Underdoped Ba(Fe(1-x)Ru(x))2As2

We use (75)As nuclear magnetic resonance to investigate the local electronic properties of Ba(Fe(1-x)Ru(x))(2)As(2) (x = 0.23). We find two phase transitions: to antiferromagnetism at T(N) ≈ 60 K and to superconductivity at T(C) ≈ 15 K. Below T(N), our data show that the system is fully magnetic, with a commensurate antiferromagnetic structure and a moment of 0.4μ(B)/Fe. The spin-lattice relaxation rate 1/(75)T(1) is large in the magnetic state, indicating a high density of itinerant electrons induced by Ru doping. On cooling below T(C), 1/(75)T(1) on the magnetic sites falls sharply, providing unambiguous evidence for the microscopic coexistence of antiferromagnetism and superconductivity.

High-Tc nodeless s±-wave superconductivity in (Y,La)FeAsO(1-y) with Tc=50 K:75As-NMR study

We report on an (75)As-NMR study on the Fe-pnictide high-T(c) superconductor Y(0.95)La(0.05)FeAsO(1-y) (Y(0.95)La(0.05)1111) with T(c)=50 K that includes no magnetic rare-earth elements. The measurement of the nuclear-spin lattice-relaxation rate (75)(1/T(1)) has revealed that the nodeless bulk superconductivity takes place at T(c)=50 K while antiferromagnetic spin fluctuations develop moderately in the normal state. These features are consistently described by the multiple fully gapped s(±)-wave model based on the Fermi-surface nesting. Incorporating the theory based on band calculations, we propose that the reason that T(c)=50 K in Y(0.95)La(0.05)1111 is larger than T(c)=28 K in La1111 is that the Fermi-surface multiplicity is maximized, and hence the Fermi-surface nesting condition is better than that in La1111.

A sharp peak of the zero-temperature penetration depth at optimal composition in BaFe2(As(1-x)P(x))2

In a superconductor, the ratio of the carrier density, n, to its effective mass, m*, is a fundamental property directly reflecting the length scale of the superfluid flow, the London penetration depth, λ(L). In two-dimensional systems, this ratio n/m* (~1/λ(L)(2)) determines the effective Fermi temperature, T(F). We report a sharp peak in the x-dependence of λ(L) at zero temperature in clean samples of BaFe(2)(As(1)(-x)P(x))(2) at the optimum composition x = 0.30, where the superconducting transition temperature T(c) reaches a maximum of 30 kelvin. This structure may arise from quantum fluctuations associated with a quantum critical point. The ratio of T(c)/T(F) at x = 0.30 is enhanced, implying a possible crossover toward the Bose-Einstein condensate limit driven by quantum criticality.

Infrared measurement of the pseudogap of P-doped and Co-doped high-temperature BaFe2As2 superconductors

We report on infrared studies of charge dynamics in a prototypical pnictide system: the BaFe2As2 family. Our experiments have identified hallmarks of the pseudogap state in the BaFe2As2 system that mirror the spectroscopic manifestations of the pseudogap in the cuprates. The magnitude of the infrared pseudogap is in accord with that of the spin-density-wave gap of the parent compound. By monitoring the superconducting gap of both P- and Co-doped compounds, we find that the infrared pseudogap is unrelated to superconductivity. The appearance of the pseudogap is found to correlate with the evolution of the antiferromagnetic fluctuations associated with the spin-density-wave instability. The strong-coupling analysis of infrared data further reveals the interdependence between the magnetism and the pseudogap in the iron pnictides.

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

Electronic nematicity, a unidirectional self-organized state that breaks the rotational symmetry of the underlying lattice, has been observed in the iron pnictide and copper oxide high-temperature superconductors. Whether nematicity plays an equally important role in these two systems is highly controversial. In iron pnictides, the nematicity has usually been associated with the tetragonal-to-orthorhombic structural transition at temperature T(s). Although recent experiments have provided hints of nematicity, they were performed either in the low-temperature orthorhombic phase or in the tetragonal phase under uniaxial strain, both of which break the 90° rotational C(4) symmetry. Therefore, the question remains open whether the nematicity can exist above T(s) without an external driving force. Here we report magnetic torque measurements of the isovalent-doping system BaFe(2)(As(1-x)P(x))(2), showing that the nematicity develops well above T(s) and, moreover, persists to the non-magnetic superconducting regime, resulting in a phase diagram similar to the pseudogap phase diagram of the copper oxides. By combining these results with synchrotron X-ray measurements, we identify two distinct temperatures-one at T*, signifying a true nematic transition, and the other at T(s) (<T*), which we show not to be a true phase transition, but rather what we refer to as a 'meta-nematic transition', in analogy to the well-known meta-magnetic transition in the theory of magnetism.

Coexistence and competition of the short-range incommensurate antiferromagnetic order with the superconducting state of BaFe(2-x)Ni(x)As2

Superconductivity in the iron pnictides develops near antiferromagnetism, and the antiferromagnetic (AF) phase appears to overlap with the superconducting phase in some materials such as BaFe(2-x)T(x)As2 (where T=Co or Ni). Here we use neutron scattering to demonstrate that genuine long-range AF order and superconductivity do not coexist in BaFe(2-x)Ni(x)As2 near optimal superconductivity. In addition, we find a first-order-like AF-to-superconductivity phase transition with no evidence for a magnetic quantum critical point. Instead, the data reveal that incommensurate short-range AF order coexists and competes with superconductivity, where the AF spin correlation length is comparable to the superconducting coherence length.

Pressure-driven quantum criticality in iron-selenide superconductors

We report a finding of a pressure-induced quantum critical transition in K0.8Fe(x)Se2 (x = 1.7 and 1.78) superconductors through in situ high-pressure electrical transport and x-ray diffraction measurements in diamond anvil cells. Transitions from metallic Fermi liquid behavior to non-Fermi liquid behavior and from antiferromagnetism to paramagnetism are found in the pressure range of 9.2-10.3 GPa, in which superconductivity tends to disappear. The change around the quantum critical point from the coexisting antiferromagnetism state and the Fermi liquid behavior to the paramagnetism state and the non-Fermi liquid behavior in the iron-selenide superconductors demonstrates a unique mechanism for their quantum critical transition.

Antiferromagnetic spin fluctuations above the dome-shaped and full-gap superconducting states of LaFeAsO1-xFx revealed by (75)As-nuclear quadrupole resonance

We report a systematic study by (75)As nuclear-quadrupole resonance in LaFeAsO(1-x)F(x). The antiferromagnetic spin fluctuation found above the magnetic ordering temperature T(N) = 58 K for x = 0.03 persists in the regime 0.04 ≤ x ≤ 0.08, where superconductivity sets in. A dome-shaped x dependence of the superconducting transition temperature T(c) is found, with the highest T(c) = 27 K at x = 0.06, which is realized under significant antiferromagnetic spin fluctuation. With increasing x further, the antiferromagnetic spin fluctuation decreases, and so does T(c). These features resemble closely the cuprates La(2-x)Sr(x)CuO(4). In x = 0.06, the spin-lattice relaxation rate (1/T(1)) below T(c) decreases exponentially down to 0.13T(c), which unambiguously indicates that the energy gaps are fully opened. The temperature variation of 1/T(1) below T(c) is rendered nonexponential for other x by impurity scattering.

(75)As NMR study of antiferromagnetic fluctuations in Ba(Fe(1-x)Ru(x))(2)As(2)

The evolution of (75)As NMR parameters with composition and temperature was probed in the Ba(Fe(1-x)Ru(x))(2)As(2) system where Fe is replaced by isovalent Ru. While the Ru end member was found to be a conventional Fermi liquid, the composition (x = 0.5) corresponding to the highest T(c) (20 K) in this system shows an upturn in the (75)As [Formula: see text] below about 80 K, evidencing the presence of antiferromagnetic (AFM) fluctuations. These results are similar to those obtained in another system with isovalent substitution, BaFe(2)(As(1-x)P(x))(2) (Nakai et al 2010 Phys. Rev. Lett. 105 107003) and point to a possible role of AFM fluctuations in driving superconductivity.

Antiferromagnetic spin fluctuations and unconventional nodeless superconductivity in an iron-based new superconductor (Ca4Al2O(6-y))(Fe2As2): 75As nuclear quadrupole resonance study

We report 75As nuclear quadrupole resonance studies on (Ca4Al2O(6-y))(Fe2As2) with T(c) = 27  K. Measurement of nuclear-spin-relaxation rate 1/T1 has revealed a significant development of two-dimensional antiferromagnetic spin fluctuations down to T(c) in association with the smallest As-Fe-As bond angle. Below T(c), the temperature dependence of 1/T1 without any trace of the coherence peak is well accounted for by a nodeless s(±)-wave multiple-gaps model. From the fact that its T(c) is comparable to T(c) = 28  K in the optimally doped LaFeAsO(1-y) in which antiferromagnetic spin fluctuations are not dominant, we remark that antiferromagnetic spin fluctuations are not a unique factor for enhancing T(c) among Fe-based superconductors, but a condition for optimizing superconductivity should be addressed from the lattice structure point of view.

Proximity of iron pnictide superconductors to a quantum tricritical point

In several materials, unconventional superconductivity appears nearby a quantum phase transition where long-range magnetic order vanishes as a function of a control parameter like charge doping, pressure or magnetic field. The nature of the quantum phase transition is of key relevance, because continuous transitions are expected to favour superconductivity, due to strong fluctuations. Discontinuous transitions, on the other hand, are not expected to have a similar role. Here we determine the nature of the magnetic quantum phase transition, which occurs as a function of doping, in the iron-based superconductor LaFeAsO(1-x)F(x). We use constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The outcome is intriguing, as this material turns out to be remarkably close to a quantum tricritical point, where the transition changes from continuous to discontinuous, and several susceptibilities diverge simultaneously. We discuss the consequences for superconductivity and the phase diagram.

Quantum criticality in the iron pnictides and chalcogenides

Superconductivity in the iron pnictides and chalcogenides arises at the border of antiferromagnetism, which raises the question of the role of quantum criticality. In this topical review, we describe the theoretical work that led to the prediction of a magnetic quantum critical point arising out of a competition between electronic localization and itinerancy, and the proposal for accessing it by using isoelectronic P substitution for As in the undoped iron pnictides. We go on to compile the emerging experimental evidence in support of the existence of such a quantum critical point in isoelectronically tuned iron pnictides. We close by discussing the implications of these results for the physics of the iron pnictides and chalcogenides.

77Se NMR study of the pairing symmetry and the spin dynamics in K(y)Fe(2-x)Se2

We present a 77Se NMR study of the newly discovered iron selenide superconductor K(y)Fe(2-x)Se2, in which T(c) = 32  K. Below T(c), the Knight shift 77K drops sharply with temperature, providing strong evidence for singlet pairing. Above T(c), Korringa-type relaxation indicates Fermi-liquid behavior. Our experimental results set strict constraints on the nature of possible theories for the mechanism of high-T(c) superconductivity in this iron selenide system.