Observation of Two Distinct Superconducting Phases in CeCu 2 Si 2

Probing the Phase Transition to a Coherent 2D Kondo Lattice

Kondo lattices are systems with unusual electronic properties that stem from strong electron correlation, typically studied in intermetallic 3D compounds containing lanthanides or actinides. Lowering the dimensionality of the system enhances the role of electron correlations providing a new tuning knob for the search of novel properties in strongly correlated quantum matter. The realization of a 2D Kondo lattice by stacking a single-layer Mott insulator on a metallic surface is reported. The temperature of the system is steadily lowered and by using high-resolution scanning tunneling spectroscopy, the phase transition leading to the Kondo lattice is followed. Above 27 K the interaction between the Mott insulator and the metal is negligible and both keep their original electronic properties intact. Below 27 K the Kondo screening of the localized electrons in the Mott insulator begins and below 11 K the formation of a coherent quantum electronic state extended to the entire sample, i.e., the Kondo lattice, takes place. By means of density functional theory, the electronic properties of the system and its evolution with temperature are explained. The findings contribute to the exploration of unconventional states in 2D correlated materials.

Much more to explore with an oxidation state of nearly four: Pr valence instability in intermetallic m-Pr2Co3Ge5

For some intermetallic compounds containing lanthanides, structural transitions can result in intermediate electronic states between trivalency and tetravalency; however, this is rarely observed for praseodymium compounds. The dominant trivalency of praseodymium limits potential discoveries of emergent quantum states in itinerant 4f1 systems accessible using Pr4+-based compounds. Here, we use in situ powder x-ray diffraction and in situ electron energy-loss spectroscopy (EELS) to identify an intermetallic example of a dominantly Pr4+ state in the polymorphic system Pr2Co3Ge5. The structure-valence transition from a nearly full Pr4+ electronic state to a typical Pr3+ state shows the potential of Pr-based intermetallic compounds to host valence-unstable states and provides an opportunity to discover previously unknown quantum phenomena. In addition, this work emphasizes the need for complementary techniques like EELS when evaluating the magnetic and electronic properties of Pr intermetallic systems to reveal details easily overlooked when relying on bulk magnetic measurements alone.

Superconductivity beyond the Conventional Pauli Limit in High-Pressure CeSb_{2}

We report the discovery of superconductivity at a pressure-induced magnetic quantum phase transition in the Kondo lattice system CeSb_{2}, sustained up to magnetic fields that exceed the conventional Pauli limit eightfold. Like CeRh_{2}As_{2}, CeSb_{2} is locally noncentrosymmetric around the Ce site, but the evolution of critical fields and normal state properties as CeSb_{2} is tuned through the quantum phase transition motivates a fundamentally different explanation for its resilience to applied field.

Electronic landscape of the f-electron intermetallics with the ThCr2Si2 structure

Although strongly correlated f-electron systems are well known as reservoirs for quantum phenomena, a persistent challenge is to design specific states. What is often missing are simple ways to determine whether a given compound can be expected to exhibit certain behaviors and what tuning vector(s) would be useful to select the ground state. In this review, we address this question by aggregating information about Ce, Eu, Yb, and U compounds with the ThCr₂Si₂ structure. We construct electronic/magnetic state maps that are parameterized in terms of unit cell volumes and d-shell filling, which reveals useful trends including that (i) the magnetic and nonmagnetic examples are well separated, and (ii) the crossover regions harbor the examples with exotic states. These insights are used to propose structural/chemical regions of interest in these and related materials, with the goal of accelerating discovery of the next generation of f-electron quantum materials.

Pressure-Induced Structural Phase Transition in EuNi2P2

EuNi₂P₂ was studied with a diamond anvil cell (DAC) and X-ray diffraction (XRD). The structural evolution of powder crystal EuNi₂P₂ under high pressure up to 137 GPa and its single-crystal structure up to 9 GPa were reported. The unique structural phase transition of this 122-type crystal occurred above 70 GPa in powder crystal EuNi₂P₂. The diffraction data from single-crystal EuNi₂P₂ revealed the coordinate change of the P atom, and the stability of the crystal at 9 GPa was confirmed. The crystal EuNi₂P₂ remained stable with a tetragonal phase without obvious symmetry changes during compression to 137 GPa.

Record-High Superconductivity in Transition Metal Dichalcogenides Emerged in Compressed 2H-TaS2

Pressure has always been an effective method for uncovering novel phenomena and properties in condensed matter physics. Here, an electrical transport study is carried on 2H-TaS₂ up to ≈208 GPa, and an unexpected superconducting state (SC-II) emerging around 86.1 GPa with an initial critical temperature (T_c ) of 9.6 K is found. As pressure increases, the T_c enhances rapidly and reaches a maximum of 16.4 K at 157.4 GPa, which sets a new record for transition metal dichalcogenides (TMDs). The original superconducting state (SC-I) is found to be re-enhanced above 100 GPa after the recession around 10 GPa, and coexists with SC-II to the highest pressure applied in this work. In situ high-pressure X-ray diffraction and Hall effect measurements reveal that the occurrence of SC-II is accompanied by a structural modification and a concurrent enhancement of hole carrier density. The new high-T_c superconducting state in 2H-TaS₂ can be attributed to the change of the electronic states near the Fermi surface, owing to pressure-induced interlayer modulation. It is the first time finding this remarkable superconducting state in TMDs, which not only brings a new broad of perspective on layered materials but also expands the field of pressure-modified superconductivity.

Charge Density Wave Orders and Enhanced Superconductivity under Pressure in the Kagome Metal CsV3 Sb5

Superconductivity in topological kagome metals has recently received great research interests. Here, charge density wave (CDW) orders and the evolution of superconductivity under various pressures in CsV₃ Sb₅ single crystal with V kagome lattice are investigated. By using high-resolution scanning tunneling microscopy/spectroscopy (STM/STS), two CDW orders in CsV₃ Sb₅ are observed which correspond to 4a × 1a and 2a × 2a superlattices. By applying pressure, the superconducting transition temperature T_c is significantly enhanced and reaches a maximum value of 8.2 K at around 1 GPa. Accordingly, CDW state is gradually declined as increasing the pressure, which indicates the competing interplay between CDW and superconducting state in this material. The broad superconducting transitions around 0.4-0.8 GPa can be related to the strong competition relation among two CDW states and superconductivity. These results demonstrate that CsV₃ Sb₅ is a new platform for exploring the interplay between superconductivity and CDW in topological kagome metals.

Double Superconducting Dome and Triple Enhancement of T_{c} in the Kagome Superconductor CsV_{3}Sb_{5} under High Pressure

CsV_{3}Sb_{5} is a newly discovered Z_{2} topological kagome metal showing the coexistence of a charge-density-wave (CDW)-like order at T^{*}=94  K and superconductivity (SC) at T_{c}=2.5  K at ambient pressure. Here, we study the interplay between CDW and SC in CsV_{3}Sb_{5} via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6 GPa. We find that the CDW transition decreases with pressure and experience a subtle modification at P_{c1}≈0.6-0.9  GPa before it vanishes completely at P_{c2}≈2  GPa. Correspondingly, T_{c}(P) displays an unusual M-shaped double dome with two maxima around P_{c1} and P_{c2}, respectively, leading to a tripled enhancement of T_{c} to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range P_{c1}≤P≤P_{c2} as evidenced by the broad superconducting transition and reduced superconducting volume fraction. The modification of CDW order around P_{c1} has been discussed based on the band structure calculations. This work not only demonstrates the potential to raise T_{c} of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electron correlations in this novel family of topological kagome metals.

Competing Nodal d-Wave Superconductivity and Antiferromagnetism

Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.

Chemistry in Superconductors

Superconductors with exotic physical properties are critical to current and future technology. In this review, we highlight several important superconducting families and focus on their crystal structure, chemical bonding, and superconductivity correlations. We connect superconducting materials with chemical bonding interactions based on their structure-property relationships, elucidating our empirically chemical approaches and other methods used in the discovery of new superconductors. Furthermore, we provide some technical strategies to synthesize superconductors and basic but important characterization for chemists needed when reporting new superconductors. In the end, we share our thoughts on how to make new superconductors and where chemists can work on in the superconductivity field. This review is written using chemical terms, with a focus on providing some chemically intuitive thoughts on superconducting materials design.

Heavy fermion quantum criticality at dilute carrier limit in CeNi2-δ(As1-xPx)2

We study the quantum phase transitions in the nickel pnctides, CeNi_2−δ(As_1−xP_x)₂ (δ ≈ 0.07–0.22) polycrystalline samples. This series displays the distinct heavy fermion behavior in the rarely studied parameter regime of dilute carrier limit. We systematically investigate the magnetization, specific heat and electrical transport down to low temperatures. Upon increasing the P-content, the antiferromagnetic order of the Ce-4f moment is suppressed continuously and vanishes at x_c ~ 0.55. At this doping, the temperature dependences of the specific heat and longitudinal resistivity display non-Fermi liquid behavior. Both the residual resistivity ρ₀ and the Sommerfeld coefficient γ₀ are sharply peaked around x_c. When the P-content reaches close to 100%, we observe a clear low-temperature crossover into the Fermi liquid regime. In contrast to what happens in the parent compound x = 0.0 as a function of pressure, we find a surprising result that the non-Fermi liquid behavior persists over a nonzero range of doping concentration, x_c < x < 0.9. In this doping range, at the lowest measured temperatures, the temperature dependence of the specific-heat coefficient is logarithmically divergent and that of the electrical resistivity is linear. We discuss the properties of CeNi_2−δ(As_1−xP_x)₂ in comparison with those of its 1111 counterpart, CeNi(As_1−xP_x)O. Our results indicate a non-Fermi liquid phase in the global phase diagram of heavy fermion metals.

A novel cage for actinides: A 6W4Al43 (A = U and Pu)

We report on synthesis and characterization of the compounds A ₆W₄Al₄₃ (A  =  U and Pu), that form in the hexagonal Ho₆Mo₄Al₄₃ caged-structure family. The A ions reside within W/Al cages where the A-A nearest neighbors form dimers between adjacent W/Al cages, with U-U and Pu-Pu distances of 3.3892 [Formula: see text] and 3.4080 [Formula: see text], respectively. While the W/Al networks provide environments similar to those of other cage-like materials (e.g. filled skutterudites), the atomic displacement parameters from single crystal x-ray diffraction measurements show that the A-ions do not exhibit rattling behavior. We find that there is site interchange disorder on one of the W/Al sites. Magnetic susceptibility measurements show that U₆W₄Al₄₃ displays anisotropic Curie-Weiss behavior where it fits to the data yield an effective magnetic moment near 2.0 [Formula: see text]/U. At low temperatures the magnetic susceptibility deviates from the Curie-Weiss temperature dependence and eventually saturates to a constant value. In contrast, Pu₆W₄Al₄₃ displays nearly temperature independent Pauli paramagnetism for all temperatures, as would be expected if the 5f -electrons are delocalized. The electrical resistivity for U₆W₄Al₄₃ increases slightly with the decreasing temperature, suggesting that it is dominated by f -electronic hybridization effects and disorder scattering that originates from the W/Al site interchange. Specific heat measurements for U₆W₄Al₄₃ further reveal an enhanced electronic Sommerfeld coefficient that is consistent with a moderately enhanced charge carrier effective mass. Together these measurements expose these materials as hosts for unstable f -electron magnetism, where the novel cage-like structures control the phenomena through the spacing between the A ions. Through this combination of mild magnetism, the low cost elements of the Al-W cages, and chemical tunability that has been shown for related materials in the same structure, the A ₆W₄Al₄₃ compounds emerge as promising nuclear waste-forms for transuranics, while the wider family of materials makes an appealing environment for studying f -electron physics in a novel structure.

Gap Symmetry of the Heavy Fermion Superconductor CeCu_{2}Si_{2} at Ambient Pressure

Recent observations of two nodeless gaps in superconducting CeCu_{2}Si_{2} have raised intensive debates on its exact gap symmetry, while a satisfactory theoretical basis is still lacking. Here we propose a phenomenological approach to calculate the superconducting gap functions, taking into consideration both the realistic Fermi surface topology and the intra- and interband quantum critical scatterings. Our calculations yield a nodeless s^{±}-wave solution in the presence of strong interband pairing interaction, in good agreement with experiments. This provides a possible basis for understanding the superconducting gap symmetry of CeCu_{2}Si_{2} at ambient pressure and indicates the potential importance of multiple Fermi surfaces and interband pairing interaction in understanding heavy fermion superconductivity.

Fully gapped d-wave superconductivity in CeCu2Si2

Identifying the gap structure of superconductors is vital for understanding the underlying pairing mechanism of the Cooper pairs. The first heavy fermion superconductor to be discovered, CeCu₂Si₂, was thought to be a d-wave superconductor with gap nodes, until recent specific heat measurements provided evidence that the gap is fully open across the Fermi surface. We propose a resolution to this puzzle from measurements of the London penetration depth, which give further evidence for fully gapped superconductivity. We analyze the data using a d-wave band-mixing pairing model, which leads to a fully open superconducting gap. Our model accounts well for the penetration depth and specific heat data, while reconciling the nodeless and sign-changing nature of the gap function.

The nature of the pairing symmetry of the first heavy fermion superconductor CeCu₂Si₂ has recently become the subject of controversy. While CeCu₂Si₂ was generally believed to be a d-wave superconductor, recent low-temperature specific heat measurements showed evidence for fully gapped superconductivity, contrary to the nodal behavior inferred from earlier results. Here, we report London penetration depth measurements, which also reveal fully gapped behavior at very low temperatures. To explain these seemingly conflicting results, we propose a fully gapped d+d band-mixing pairing state for CeCu₂Si₂, which yields very good fits to both the superfluid density and specific heat, as well as accounting for a sign change of the superconducting order parameter, as previously concluded from inelastic neutron scattering results.

Emergence of a new valence-ordered structure and collapse of the magnetic order under high pressure in EuPtP

The layered hexagonal EuPtP is a rare substance that exhibits two successive valence transitions occurring simultaneously with valence ordering transitions and an antiferromagnetic order. Anticipating that the application of pressure to this sample would induce a new valence-ordered structure and/or a new phenomenon associated with valence fluctuation, we examined the electrical resistivity ρ, the Eu L₃-edge x-ray absorption spectroscopy, and the powder x-ray diffraction under high pressure. We found a new valence transition at around P  =  2.5 GPa. After the transition, a new valence-ordered structure is realized at the lowest temperature. The valence-ordered structure is inferred to be stacking of [Formula: see text] (2+: Eu²⁺ layer, 3+: Eu³⁺ layer) along the c-axis. Upon further increases in pressure, the valence-ordered structure is suppressed and another valance-ordered phase is realized up to P  =  6 GPa. The antiferromagnetic order collapses in the pressure range between 6 GPa and 8 GPa.

Quantum valence criticality in a correlated metal

A valence critical end point existing near the absolute zero provides a unique case for the study of a quantum version of the strong density fluctuation at the Widom line in the supercritical fluids. Although singular charge and orbital dynamics are suggested theoretically to alter the electronic structure significantly, breaking down the standard quasi-particle picture, this has never been confirmed experimentally to date. We provide the first empirical evidence that the proximity to quantum valence criticality leads to a clear breakdown of Fermi liquid behavior. Our detailed study of the mixed valence compound α-YbAlB₄ reveals that a small chemical substitution induces a sharp valence crossover, accompanied by a pronounced non-Fermi liquid behavior characterized by a divergent effective mass and unusual T/B scaling in the magnetization.

Cooper Pairing in A Doped 2D Antiferromagnet with Spin-Orbit Coupling

We study the two-dimensional Hubbard model with the Rashba type spin-orbit coupling within and beyond the mean-field theory. The antiferromagnetic ground state for the model at half-filling and the Cooper pairing induced by antiferromagnetic spin fluctuations near half-filling are examined based on the random-phase approximation. We show that the antiferromagnetic order is suppressed and the magnetic susceptibility turns out to be anisotropic in the presence of the spin-orbit coupling. Energy spectrums of transverse spin fluctuations are obtained and the effective interactions between holes mediated by antiferromagnetic spin fluctuations are deduced in the case of low hole doping. It seems that the spin-orbit coupling tends to form s+p-wave Cooper pairs, while the s+d-wave pairing is dominant when the spin-orbit coupling is absent.

Robust zero resistance in a superconducting high-entropy alloy at pressures up to 190 GPa

High-entropy alloys (HEAs) are made from multiple transition-metal elements in equimolar or near-equimolar ratios. The elements in HEAs arrange themselves randomly on the crystallographic positions of a simple lattice. In addition to their excellent mechanical properties, one HEA has been reported to display superconductivity. In this work, we report that the Ta–Nb–Hf–Zr–Ti high-entropy alloy superconductor exhibits extraordinarily robust zero-resistance superconductivity under pressure up to 190.6 GPa. This is an observation of the zero-resistance state of a superconductor all the way from 1-bar pressure to the pressure of the earth’s outer core without structure phase transition, making the superconducting HEA a promising candidate for new application under extreme condition.

We report the observation of extraordinarily robust zero-resistance superconductivity in the pressurized (TaNb)_0.67(HfZrTi)_0.33 high-entropy alloy––a material with a body-centered-cubic crystal structure made from five randomly distributed transition-metal elements. The transition to superconductivity (T_C) increases from an initial temperature of 7.7 K at ambient pressure to 10 K at ∼60 GPa, and then slowly decreases to 9 K by 190.6 GPa, a pressure that falls within that of the outer core of the earth. We infer that the continuous existence of the zero-resistance superconductivity from 1 atm up to such a high pressure requires a special combination of electronic and mechanical characteristics. This high-entropy alloy superconductor thus may have a bright future for applications under extreme conditions, and also poses a challenge for understanding the underlying quantum physics.

Ising-type Magnetic Anisotropy in CePd2As2

We investigated the anisotropic magnetic properties of CePd₂As₂ by magnetic, thermal and electrical transport studies. X-ray diffraction confirmed the tetragonal ThCr₂Si₂-type structure and the high-quality of the single crystals. Magnetisation and magnetic susceptibility data taken along the different crystallographic directions evidence a huge crystalline electric field (CEF) induced Ising-type magneto-crystalline anisotropy with a large c-axis moment and a small in-plane moment at low temperature. A detailed CEF analysis based on the magnetic susceptibility data indicates an almost pure |±5/2〉 CEF ground-state doublet with the dominantly |±3/2〉 and the |±1/2〉 doublets at 290 K and 330 K, respectively. At low temperature, we observe a uniaxial antiferromagnetic (AFM) transition at T_N = 14.7 K with the crystallographic c-direction being the magnetic easy-axis. The magnetic entropy gain up to T_N reaches almost R ln 2 indicating localised 4 f-electron magnetism without significant Kondo-type interactions. Below T_N, the application of a magnetic field along the c-axis induces a metamagnetic transition from the AFM to a field-polarised phase at μ₀H_c0 = 0.95 T, exhibiting a text-book example of a spin-flip transition as anticipated for an Ising-type AFM.

Fully gapped superconductivity with no sign change in the prototypical heavy-fermion CeCu2Si2

In exotic superconductors, including high-Tc copper oxides, the interactions mediating electron Cooper pairing are widely considered to have a magnetic rather than a conventional electron-phonon origin. Interest in this exotic pairing was initiated by the 1979 discovery of heavy-fermion superconductivity in CeCu2Si2, which exhibits strong antiferromagnetic fluctuations. A hallmark of unconventional pairing by anisotropic repulsive interactions is that the superconducting energy gap changes sign as a function of the electron momentum, often leading to nodes where the gap goes to zero. We report low-temperature specific heat, thermal conductivity, and magnetic penetration depth measurements in CeCu2Si2, demonstrating the absence of gap nodes at any point on the Fermi surface. Moreover, electron irradiation experiments reveal that the superconductivity survives even when the electron mean free path becomes substantially shorter than the superconducting coherence length. This indicates that superconductivity is robust against impurities, implying that there is no sign change in the gap function. These results show that, contrary to long-standing belief, heavy electrons with extremely strong Coulomb repulsions can condense into a fully gapped s-wave superconducting state, which has an on-site attractive pairing interaction.

Multiband electronic transport in α-Yb1-x Sr x AlB4 [x = 0, 0.19(3)] single crystals

We report on the evidence for the multiband electronic transport in α-YbAlB4 and α-Yb0.81(2)Sr0.19(3)AlB4. Multiband transport reveals itself below 10 K in both compounds via Hall effect measurements, whereas anisotropic magnetic ground state sets in below 3 K in α-Yb0.81(2)Sr0.19(3)AlB4. Our results show that Sr(2+) substitution enhances conductivity, but does not change the quasiparticle mass of bands induced by heavy fermion hybridization.

Multiple quantum phase transitions and superconductivity in Ce-based heavy fermions

Heavy fermions have served as prototype examples of strongly-correlated electron systems. The occurrence of unconventional superconductivity in close proximity to the electronic instabilities associated with various degrees of freedom points to an intricate relationship between superconductivity and other electronic states, which is unique but also shares some common features with high temperature superconductivity. The magnetic order in heavy fermion compounds can be continuously suppressed by tuning external parameters to a quantum critical point, and the role of quantum criticality in determining the properties of heavy fermion systems is an important unresolved issue. Here we review the recent progress of studies on Ce based heavy fermion superconductors, with an emphasis on the superconductivity emerging on the edge of magnetic and charge instabilities as well as the quantum phase transitions which occur by tuning different parameters, such as pressure, magnetic field and doping. We discuss systems where multiple quantum critical points occur and whether they can be classified in a unified manner, in particular in terms of the evolution of the Fermi surface topology.

Foundations of heavy-fermion superconductivity: lattice Kondo effect and Mott physics

This article overviews the development of heavy-fermion superconductivity, notably in such rare-earth-based intermetallic compounds which behave as Kondo-lattice systems. Heavy-fermion superconductivity is of unconventional nature in the sense that it is not mediated by electron-phonon coupling. Rather, in most cases the attractive interaction between charge carriers is apparently magnetic in origin. Fluctuations associated with an antiferromagnetic (AF) quantum critical point (QCP) play a major role. The first heavy-fermion superconductor CeCu2Si2 turned out to be the prototype of a larger group of materials for which the underlying, often pressure-induced, AF QCP is likely to be of a three-dimensional (3D) spin-density-wave (SDW) variety. For UBe13, the second heavy-fermion superconductor, a magnetic-field-induced 3D SDW QCP inside the superconducting phase can be conjectured. Such a 'conventional', itinerant QCP can be well understood within Landau's paradigm of order-parameter fluctuations. In contrast, the low-temperature normal-state properties of a few heavy-fermion superconductors are at odds with the Landau framework. They are characterized by an 'unconventional', local QCP which may be considered a zero-temperature 4 f-orbital selective Mott transition. Here, as concluded for YbRh2Si2, the breakdown of the Kondo effect concurring with the AF instability gives rise to an abrupt change of the Fermi surface. Very recently, superconductivity was discovered for this compound at ultra-low temperatures. Therefore, YbRh2Si2 along with CeRhIn5 under pressure provide a natural link between the large group of about fifty low-temperature heavy-fermion superconductors and other families of unconventional superconductors with substantially higher T c, e.g. the doped Mott insulators of the perovskite-type cuprates and the organic charge-transfer salts.

Superconductivity in alkali metal intercalated iron selenides

Alkali metal intercalated iron selenide superconductors A x Fe2-y Se2 (where A  =  K, Rb, Cs, Tl/K, and Tl/Rb) are characterized by several unique properties, which were not revealed in other superconducting materials. The compounds crystallize in overall simple layered structure with FeSe layers intercalated with alkali metal. The structure turned out to be pretty complex as the existing Fe-vacancies order below ~550 K, which further leads to an antiferromagnetic ordering with Néel temperature fairly above room temperature. At even lower temperatures a phase separation is observed. While one of these phases stays magnetic down to the lowest temperatures the second is becoming superconducting below ~30 K. All these effects give rise to complex relationships between the structure, magnetism and superconductivity. In particular the iron vacancy ordering, linked with a long-range magnetic order and a mesoscopic phase separation, is assumed to be an intrinsic property of the system. Since the discovery of superconductivity in those compounds in 2010 they were investigated very extensively. Results of the studies conducted using a variety of experimental techniques and performed during the last five years were published in hundreds of reports. The present paper reviews scientific work concerning methods of synthesis and crystal growth, structural and superconducting properties as well as pressure investigations.

From Kondo lattices to Kondo superlattices

The realization of new classes of ground states in strongly correlated electron systems continues to be a major issue in condensed matter physics. Heavy fermion materials, whose electronic structure is essentially three-dimensional, are one of the most suitable systems for obtaining novel electronic states because of their intriguing properties associated with many-body effects. Recently, a state-of-the-art molecular beam epitaxy technique was developed to reduce the dimensionality of heavy electron systems by fabricating artificial superlattices that include heavy fermion compounds; this approach can produce a new type of electronic state in two-dimensional (2D) heavy fermion systems. In artificial superlattices of the antiferromagnetic heavy fermion compound CeIn3 and the conventional metal LaIn3, the magnetic order is suppressed by a reduction in the thickness of the CeIn3 layers. In addition, the 2D confinement of heavy fermions leads to enhancement of the effective electron mass and deviation from the standard Fermi liquid electronic properties, which are both associated with the dimensional tuning of quantum criticality. In the superconducting superlattices of the heavy fermion superconductor CeCoIn5 and nonmagnetic metal YbCoIn5, signatures of superconductivity are observed even at the thickness of one unit-cell layer of CeCoIn5. The most remarkable feature of this 2D heavy fermion superconductor is that the thickness reduction of the CeCoIn5 layers changes the temperature and angular dependencies of the upper critical field significantly. This result is attributed to a substantial suppression of the Pauli pair-breaking effect through the local inversion symmetry breaking at the interfaces of CeCoIn5 block layers. The importance of the inversion symmetry breaking in this system has also been supported by site-selective nuclear magnetic resonance spectroscopy, which can resolve spectroscopic information from each layer separately, even within the same CeCoIn5 block layer. In addition, recent experiments involving CeCoIn5/YbCoIn5 superlattices have shown that the degree of the inversion symmetry breaking and, in turn, the Rashba splitting are controllable, offering the prospect of achieving even more fascinating superconducting states. Thus, these Kondo superlattices pave the way for the exploration of unconventional metallic and superconducting states.

Frustrated magnetism in the spin-chain metal Yb2Fe12P7

Magnetization measurements for magnetic fields [Formula: see text] up to 60 T are reported for the noncentrosymmetric spin-chain metal Yb2Fe12P7. These measurements reveal behavior that is consistent with Ising-like spin chain magnetism that produces pronounced spin degeneracy. In particular, we find that although a Brillouin field dependence is observed in M(H) for [Formula: see text] with a saturation moment that is close to the expected value for free ions of Yb(3+) , non-Brillouin-like behavior is seen for [Formula: see text] with an initial saturation moment that is nearly half the free ion value. In addition, hysteretic behavior that extends above the ordering temperature [Formula: see text] is seen for [Formula: see text] but not for [Formula: see text], suggesting out-of-equilibrium physics. This point of view is strengthened by the observation of a spin reconfiguration in the ordered state for [Formula: see text] which is only seen for [Formula: see text] and after polarizing the spins. Together with the heat capacity data, these results suggest that the anomalous low temperature phenomena that were previously reported (Baumbach 2010 et al Phys. Rev. Lett. 105 106403) are driven by spin degeneracy that is related to the Ising-like one dimensional chain-like configuration of the Yb ions.

Crossover from a heavy fermion to intermediate valence state in noncentrosymmetric Yb2Ni12(P,As)7

We report measurements of the physical properties and electronic structure of the hexagonal compounds Yb₂Ni₁₂Pn₇ (Pn = P, As) by measuring the electrical resistivity, magnetization, specific heat and partial fluorescence yield x-ray absorption spectroscopy (PFY-XAS). These demonstrate a crossover upon reducing the unit cell volume, from an intermediate valence state in Yb₂Ni₁₂As₇ to a heavy-fermion paramagnetic state in Yb₂Ni₁₂P₇, where the Yb is nearly trivalent. Application of pressure to Yb₂Ni₁₂P₇ suppresses T_FL, the temperature below which Fermi liquid behavior is recovered, suggesting the presence of a quantum critical point (QCP) under pressure. However, while there is little change in the Yb valence of Yb₂Ni₁₂P₇ up to 30 GPa, there is a strong increase for Yb₂Ni₁₂As₇ under pressure, before a near constant value is reached. These results indicate that any magnetic QCP in this system is well separated from strong valence fluctuations. The pressure dependence of the valence and lattice parameters of Yb₂Ni₁₂As₇ are compared and at 1 GPa, there is an anomaly in the unit cell volume as well as a change in the slope of the Yb valence, indicating a correlation between structural and electronic changes.

Emergent loop-nodal s(±)-wave superconductivity in CeCu(2)Si(2): similarities to the iron-based superconductors

Heavy-fermion superconductors are prime candidates for novel electron-pairing states due to the spin-orbital coupled degrees of freedom and electron correlations. Superconductivity in CeCu_{2}Si_{2} discovered in 1979, which is a prototype of unconventional (non-BCS) superconductors in strongly correlated electron systems, still remains unsolved. Here we provide the first report of superconductivity based on the advanced first-principles theoretical approach. We find that the promising candidate is an s_{±}-wave state with loop-shaped nodes on the Fermi surface, different from the widely expected line-nodal d-wave state. The dominant pairing glue is magnetic but high-rank octupole fluctuations. This system shares the importance of multiorbital degrees of freedom with the iron-based superconductors. Our findings reveal not only the long-standing puzzle in this material, but also urge us to reconsider the pairing states and mechanisms in all heavy-fermion superconductors.

Avoided valence transition in a plutonium superconductor

The d and f electrons in correlated metals are often neither fully localized around their host nuclei nor fully itinerant. This localized/itinerant duality underlies the correlated electronic states of the high-Tc cuprate superconductors and the heavy-fermion intermetallics and is nowhere more apparent than in the 5f valence electrons of plutonium. Here, we report the full set of symmetry-resolved elastic moduli of PuCoGa5--the highest Tc superconductor of the heavy fermions (Tc = 18.5 K)--and find that the bulk modulus softens anomalously over a wide range in temperature above Tc. The elastic symmetry channel in which this softening occurs is characteristic of a valence instability--therefore, we identify the elastic softening with fluctuations of the plutonium 5f mixed-valence state. These valence fluctuations disappear when the superconducting gap opens at Tc, suggesting that electrons near the Fermi surface play an essential role in the mixed-valence physics of this system and that PuCoGa5 avoids a valence transition by entering the superconducting state. The lack of magnetism in PuCoGa5 has made it difficult to reconcile with most other heavy-fermion superconductors, where superconductivity is generally believed to be mediated by magnetic fluctuations. Our observations suggest that valence fluctuations play a critical role in the unusually high Tc of PuCoGa5.

Superconductivity and structural distortion in BaPt2As2

We report the synthesis of BaPt2As2 single crystals and the discovery of superconductivity and a structural phase transition in this compound by measuring the electrical resistivity, magnetic susceptibility and specific heat as well as the x-ray diffraction at low temperatures. BaPt2As2 crystallizes in the CaBe2Ge2-type tetragonal structure (P4/nmm) at room temperature and undergoes a first-order structural transition at TS ≃ 275 K, which is likely to be associated with a charge-density-wave (CDW) instability. BCS-like superconductivity with two subsequent transitions Tc1 ≃ 1.67 K and Tc2 ≃ 1.33 K is observed. Our results demonstrate that BaPt2As2 may serve as a new system for studying the interplay of superconductivity and the CDW order.

Role of valence fluctuations in the superconductivity of Ce122 compounds

Pressure dependence of the Ce valence in CeCu(2)Ge(2) has been measured up to 24 GPa at 300 K and to 17 GPa at 18-20 K using x-ray absorption spectroscopy in the partial fluorescence yield. A smooth increase of the Ce valence with pressure is observed across the two superconducting (SC) regions without any noticeable irregularity. The chemical pressure dependence of the Ce valence was also measured in Ce(Cu(1-x)Ni(x))(2)Si(2) at 20 K. A very weak, monotonic increase of the valence with x was observed, without any significant change in the two SC regions. Within experimental uncertainties, our results show no evidence for the valence transition with an abrupt change in the valence state near the SC II region, challenging the valence-fluctuation mediated superconductivity model in these compounds at high pressure and low temperature.

Structure and electrical resistivity of mixed-valent EuNi2P2 at high pressure

The structural properties and electrical resistivity of homogeneous mixed-valent EuNi2P2 are studied at pressures up to 45 GPa. No structural phase transition is observed in the whole pressure range and the overall pressure behavior of the structural parameters is similar to that of related compounds in the collapsed tetragonal ThCr2Si2-type structure. Electrical resistivity measured up to 31 GPa at temperatures between 4 and 300 K exhibits continuous changes from the behavior typical for a mixed-valent Eu system to that of a normal metallic system at pressures above 20 GPa, indicating a transition of the strongly mixed-valent Eu atoms with a valence ~2.5 towards a pure trivalent state. No superconductivity was observed in the whole studied pressure-temperature range.

Theoretical prediction and spectroscopic fingerprints of an orbital transition in CeCu2Si2

We show that the heavy-fermion compound CeCu2Si2 undergoes a transition between two regimes dominated by different crystal-field states. At low pressure P and low temperature T the Ce 4f electron resides in the atomic crystal-field ground state, while at high P or T, the electron occupancy and spectral weight is transferred to an excited crystal-field level that hybridizes more strongly with itinerant states. These findings result from first-principles dynamical-mean-field-theory calculations. We predict experimental signatures of this orbital transition in x-ray spectroscopy. The corresponding fluctuations may be responsible for the second high-pressure superconducting dome observed in this and similar materials.

Tunable magnetic orders in CePd2As2-xPx

We report the successful synthesis of the polycrystalline compounds CePd2As2-xPx (0 ≤ x ≤ 2) and their physical properties by measuring transport, magnetic and thermodynamic behaviors as a function of temperature and/or magnetic field. Powder x-ray diffraction indicates that CePd2As2-xPx crystallizes in the ThCr2Si2-type tetragonal structure. CePd2As2 exhibits a moderate Sommerfeld coefficient of γ ≈ 88 mJ mol(-1) K(-2), and undergoes an antiferromagnetic (AFM) transition at the Néel temperature TN ≈ 15 K. Upon substituting As with P, the TN is nearly unchanged up to x ≃ 0.6, while a ferromagnetic (FM) transition develops below TN for x ≃ 0.4. The Curie temperature TC increases with increasing x and eventually merges with the AFM transition at x ≃ 0.6. With further increase of x, the system follows typical FM behaviors and its TC monotonically increases and reaches TC ≈ 28 K in CePd2P2. Moreover, a metamagnetic transition is observed in the As-rich samples, but vanishes for x ≥ 0.4. Such a tunable magnetic ground state may provide an opportunity to explore the possible quantum critical behavior in CePd2As2-xPx.

Direct measurement of the upper critical field in cuprate superconductors

In the quest to increase the critical temperature Tc of cuprate superconductors, it is essential to identify the factors that limit the strength of superconductivity. The upper critical field Hc2 is a fundamental measure of that strength, yet there is no agreement on its magnitude and doping dependence in cuprate superconductors. Here we show that the thermal conductivity can be used to directly detect Hc2 in the cuprates YBa2Cu3Oy, YBa2Cu4O8 and Tl2Ba2CuO6+δ, allowing us to map out Hc2 across the doping phase diagram. It exhibits two peaks, each located at a critical point where the Fermi surface of YBa2Cu3Oy is known to undergo a transformation. Below the higher critical point, the condensation energy, obtained directly from Hc2, suffers a sudden 20-fold collapse. This reveals that phase competition-associated with Fermi-surface reconstruction and charge-density-wave order-is a key limiting factor in the superconductivity of cuprates.

Formation of Nanofoam carbon and re-emergence of Superconductivity in compressed CaC6

Pressure can tune material's electronic properties and control its quantum state, making some systems present disconnected superconducting region as observed in iron chalcogenides and heavy fermion CeCu2Si2. For CaC6 superconductor (Tc of 11.5 K), applying pressure first Tc increases and then suppresses and the superconductivity of this compound is eventually disappeared at about 18 GPa. Here, we report a theoretical finding of the re-emergence of superconductivity in heavily compressed CaC6. The predicted phase III (space group Pmmn) with formation of carbon nanofoam is found to be stable at wide pressure range with a Tc up to 14.7 K at 78 GPa. Diamond-like carbon structure is adhered to the phase IV (Cmcm) for compressed CaC6 after 126 GPa, which has bad metallic behavior, indicating again departure from superconductivity. Re-emerged superconductivity in compressed CaC6 paves a new way to design new-type superconductor by inserting metal into nanoporous host lattice.

Optical study of archetypical valence-fluctuating Eu systems

We have investigated the optical conductivity of the prominent valence-fluctuating compounds EuIr(2)Si(2) and EuNi(2)P(2) in the infrared energy range to get new insights into the electronic properties of valence-fluctuating systems. For both compounds, we observe upon cooling the formation of a renormalized Drude response, a partial suppression of the optical conductivity below 100 meV, and the appearance of a midinfrared peak at 0.15 eV for EuIr(2)Si(2) and 0.13 eV for EuNi(2)P(2). Most remarkably, our results show a strong similarity with the optical spectra reported for many Ce- or Yb-based heavy-fermion metals and intermediate valence systems, although the phase diagrams and the temperature dependence of the valence differ strongly between Eu systems and Ce- or Yb-based systems. This suggests that the hybridization between 4f and conduction electrons, which is responsible for the properties of Ce and Yb systems, plays an important role in valence-fluctuating Eu systems.

Pressure-induced heavy fermion superconductivity in the nonmagnetic quadrupolar system PrTi(2)Al(20)

We report the discovery of a pressure-induced heavy fermion superconductivity in a nonmagnetic orbital ordering state in the cubic compound PrTi(2)Al(20). In particular, we found that the transition temperature and the effective mass associated with the superconductivity are dramatically enhanced as the system approaches the putative quantum critical point of the orbital order. Our experiment indicates that the strong orbital fluctuations may provide a nonmagnetic glue for Cooper pairing.

Possibility of valence-fluctuatsion-mediated superconductivity in Cd-doped CeIrIn(5) probed by In NQR

We report on a pressure-induced evolution of exotic superconductivity and spin correlations in CeIr(In(1-x)Cd(x))(5) by means of in-nuclear-quadrupole-resonance (NQR) studies. Measurements of an NQR spectrum and nuclear-spin-lattice-relaxation rate 1/T(1) have revealed that antiferromagnetism induced by Cd doping emerges locally around Cd dopants, but superconductivity is suddenly induced at T(c)=0.7 and 0.9 K at 2.34 and 2.75 GPa, respectively. The unique superconducting characteristics with a large fraction of the residual density of state at the Fermi level which increases with T(c) differ from those for anisotropic superconductivity mediated by antiferromagnetic correlations. By incorporating the pressure dependence of the NQR frequency pointing to the valence change of Ce, we suggest that unconventional superconductivity in the CeIr(In(1-x)Cd(x))(5) system may be mediated by valence fluctuations.

Kondo destruction and valence fluctuations in an Anderson model

Unconventional quantum criticality in heavy-fermion systems has been extensively analyzed in terms of a critical destruction of the Kondo effect. Motivated by a recent demonstration of quantum criticality in a mixed-valent heavy-fermion system, β-YbAlB(4), we study a particle-hole-asymmetric Anderson impurity model with a pseudogapped density of states. We demonstrate Kondo destruction at a mixed-valent quantum critical point, where a collapsing Kondo energy scale is accompanied by a singular charge-fluctuation spectrum. Both spin and charge responses scale with energy over temperature (ω/T) and magnetic field over temperature (H/T). Implications for unconventional quantum criticality in mixed-valence heavy fermions are discussed.

New universality class of quantum criticality in Ce- and Yb-based heavy fermions

A new universality class of quantum criticality emerging in itinerant electron systems with strong local electron correlations is discussed. The quantum criticality of a Ce- or Yb-valence transition gives us a unified explanation for unconventional criticality commonly observed in heavy fermion metals such as YbRh(2)Si(2), β-YbAlB(4), YbCu(5-x)Al(x), and CeIrIn(5). The key origin is due to the locality of the critical valence fluctuation mode emerging near the quantum critical end point of the first-order valence transition, which is caused by strong electron correlations for f electrons. The wider relevance of this new criticality and important future measurements to uncover its origin are also discussed.

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.

Localized 5f electrons in superconducting PuCoIn₅: consequences for superconductivity in PuCoGa₅

The physical properties of the first In analog of the PuMGa(5) (M = Co, Rh) family of superconductors, PuCoIn(5), are reported. With its unit cell volume being 28% larger than that of PuCoGa(5), the characteristic spin-fluctuation energy scale of PuCoIn(5) is three to four times smaller than that of PuCoGa(5), which suggests that the Pu 5f electrons are in a more localized state relative to PuCoGa(5). This raises the possibility that the high superconducting transition temperature T(c) = 18.5 K of PuCoGa(5) stems from the proximity to a valence instability, while the superconductivity at T(c) = 2.5 K of PuCoIn(5) is mediated by antiferromagnetic spin fluctuations associated with a quantum critical point.

Heat-capacity measurements of energy-gap nodes of the heavy-fermion superconductor CeIrIn5 deep inside the pressure-dependent dome structure of its superconducting phase diagram

We use heat-capacity measurements as a function of field rotation to identify the nodal gap structure of CeIrIn(5) at pressures to 2.05 GPa, deep inside its superconducting dome. A fourfold oscillation in the heat capacity at 0.3 K is observed for all pressures, but with its sign reversed between 1.50 and 0.90 GPa. On the basis of recent theoretical models for the field-angle-dependent specific heat, all data, including the sign reversal, imply a d(x(2)-y(2)) order parameter with nodes along [110], which constrains theoretical models of the pairing mechanism in CeIrIn(5).

Pressure tuning of the interplay of magnetism and superconductivity in CeCu2Si2

We carried out specific-heat and ac-susceptibility experiments under hydrostatic pressure to investigate the interplay of spin-density-wave antiferromagnetism (A) and superconductivity (S) in single-crystalline AS-type CeCu(2)Si(2). We find evidence for a line of magnetic-field- and pressure-tuned quantum critical points in the normal state in the zero-temperature magnetic field-pressure plane. Our analysis suggests an extension of this line into the superconducting state and corroborates the close connection of the underlying mechanisms leading to the formation of the antiferromagnetic and the superconducting states in AS-type CeCu(2)Si(2).