Heavy Fermion Superconductor CeCu2Si2 Research Articles

Multiorbital singlet pairing and d\u2009+\u2009d superconductivity

Recent experiments in multiband Fe-based and heavy-fermion superconductors have challenged the long-held dichotomy between simple s- and d-wave spin-singlet pairing states. Here, we advance several time-reversal-invariant irreducible pairings that go beyond the standard singlet functions through a matrix structure in the band/orbital space, and elucidate their naturalness in multiband systems. We consider the sτ3 multiorbital superconducting state for Fe-chalcogenide superconductors. This state, corresponding to a d + d intra- and inter-band pairing, is shown to contrast with the more familiar d + id state in a way analogous to how the B- triplet pairing phase of 3He superfluid differs from its A- phase counterpart. In addition, we construct an analog of the sτ3 pairing for the heavy-fermion superconductor CeCu2Si2, using degrees-of-freedom that incorporate spin-orbit coupling. Our results lead to the proposition that d-wave superconductors in correlated multiband systems will generically have a fully-gapped Fermi surface when they are examined at sufficiently low energies.

Electronic structure evolution accompanying heavy fermion formation in CeCu2Si2

The cooper pairs in the heavy-fermion superconductor CeCu2Si2 are formed of heavy fermions. Therefore, the heavy fermions are fundamental to the emergence of unconventional superconductivity and associated non-Fermi-liquid behavior in the normal state. The interplay between localization and itinerancy manifested on the electronic structure is key for understanding the heavy-fermion behavior. Here, via the first-principle density functional theory (DFT) combined with single-site dynamical mean-field theory (DMFT), we investigate the temperature ( T ) evolution of the electronic structure of CeCu2Si2 in the normal state, focusing on the role of the 4 f states in the low energy regime. Two characteristic temperature scales of this evolution, which accompanied the heavy-fermion formation, are established. The coherence onset temperature is around 130 K, whereas the heavy-fermion band formation temperature is between 40 and 80 K; both characteristic temperature scales are higher than the transport coherence temperature. Furthermore, the heavy-fermion formation is confirmed by calculating its effective mass variation with the temperature. Based on the calculated T- dependent evolution of the 4 f orbital occupancy and electronic structure, an explanation on the behavior of the temperature evolution of the correlation strength of CeCu2Si2 is provided. Our results offer a comprehensive microscopic picture of the heavy-fermion formation in CeCu2Si2, which is essential for further understanding the emergent superconducting pairing mechanism.

Fully gapped d-wave superconductivity in CeCu2Si2

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 [Formula: see text] 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.

A phenomenological theory of heavy fermion superconductivity in CeCoIn<sub>5</sub>

Unconventional superconductivity was first discovered in heavy fermion materials which exhibit a rich variety of superconducting quantum phenomena. Understanding the microscopic origin of heavy fermion superconductivity will help us understand the nature of high-temperature superconductivity and explore new class of unconventional superconductors. In this article, we give a brief introduction to the recent theoretical and experimental studies on heavy fermion superconductors. In particular, it has been shown that previous understandings of the pairing mechanism based on oversimplified single-band model calculations may not explain the recent experimental observations of the superconducting gap symmetry and therefore need to be revisited. For example, the heavy fermion superconductors CeCu2Si2 and UBe13, which have long been believed to have nodal superconducting gap structures for over three decades, are now found to exhibit nodeless behaviors in many new experiments. While these may be partially explained by using realistic band structures in combination with random phase approximation (RPA) for the dynamic susceptibility, we point out that for strongly correlated systems such as heavy fermions, RPA fails to capture the true behavior of quantum critical fluctuations which act as the pairing force for the unconventional superconductivity. We argue that there are three major issues that need to be taken into account in order to develop a good understanding of the heavy fermion superconductivity: (1) the strong electronic correlations and the two-fluid behavior of the f electrons; (2) the quantum critical nature of the superconducting pairing force that cannot be obtained based on RPA; (3) the multi-band or multi-orbital properties that rely on real materials and may be crucial for the gap structures. Following these considerations, we propose a new framework based on the strong-coupling Eliashberg theory that combines previous phenomenological theory of the spin-fluctuation-induced pairing mechanism and realistic band structures from either experimental measurements or first-principles calculations. As an example, we apply our model to the prototype heavy fermion superconductors CeCoIn5 and CeRhIn5. By using a single-band model derived from the scanning tunneling spectroscopy, we solve the linearized Eliashberg equation and produce the correct d-wave superconducting gap structure, in agreement with experimental observations. We further predict a simple formula for the superconducting transition temperature T c as a function of the pairing strength and the spin fluctuation energy. We then extend the formula to general cases and use the two-fluid prediction on the heavy electron density of states to calculate the pressure-variation of T c. Our results agree well with experiment and explain the dome structure of T c. For multi-band systems, we have studied the superconductivity in CeCu2Si2. In contrast to previous calculations that predict either d-wave or nodal s-wave gap, we found that the inter-band scattering plays an essential role and may cause a nodeless gap structure. This work is still under progress. We believe that the success of the new framework suggests that it may provide a promising basis for treating the above issues and will help our understanding of the properties of heavy fermion superconductivity. In the future, we hope to extend our study to other heavy fermion superconductors and take into consideration the detailed orbital characters and the dual nature of f electrons. The latter would possibly require a reformulation of the Eliashberg equations.

McPhase model calculations of the magnetic phase diagram of CeCu2Ge2 – Prediction of a double q magnetic structure

The magnetic (H,T)-phase diagram of CeCu2Ge2 has been studied by model calculations using the McPhase program. Aiming at the best possible description of the magnetic properties model parameters were varied and the complexity of the model approach was increased. A double-q magnetic structure was predicted with q+ = (hhl) and q- = (h-hl) that changes to a single-q one at applied in plane magnetic field. The extent and stability of the double-q magnetic structure was investigated and physical properties are compared to available experimental data. The calculations reveal the principal shape of magnetisation curves and the calculated (H,T)-phase diagram agrees satisfactorily to that deduced from experiments. The consistence of experimental results and theoretical model is important for the understanding of magnetism in CeCu2Ge2 and the heavy fermion superconductor CeCu2Si2.

Pressure-Induced Valence Transition and Heavy Fermion State in Eu2Ni3Ge5 and EuRhSi3

We succeeded in growing single crystals of Eu2Ni3Ge5 and EuRhSi3 by the In-flux method, and measured the electrical resistivity under pressures. Both compounds are Eu-divalent antiferromagnets with the Neel temperatures TN = 18.6 and 47.7 K, respectively. With increasing pressure, the resistivity in Eu2Ni3Ge5 indicates a clear kink at Tv = 220 K under 8.0 GPa, for example, which corresponds to a valence transition. The valence of Eu ions deviates from divalence toward trivalence. Correspondingly, antiferromagnetic ordering disappears completely. The low-temperature resistivity is, surprisingly, very similar to the resistivity of a well-known heavy fermion superconductor CeCu2Si2, possessing a two-peak-structure based on the Kondo effect. In fact, the A value of the resistivity ρ = ρ0 + AT2 in the Fermi liquid relation becomes large, A = 0.3 µΩ·cm/K2 at 8.0 GPa. The similar characteristic features are observed in another compound EuRhSi3.

Soft x-ray angle-resolved and resonance photoemission study of CeCu2Ge2 and LaCu2Ge2

We have performed bulk-sensitive soft x-ray angle-resolved photoemission spectroscopy for CeCu2Ge2 isostructural to a heavy fermion superconductor CeCu2Si2, indicating the localized 4f character in ambient pressure. Resonance enhancement is seen at the La 3d5/2-edge for LaCu2Ge2 in both angle-resolved and integrated photoemission although the magnitude of enhancement is less than that in the Ce 3d5/2-edge resonance photoemission for CeCu2Ge2, which indicates that the rare-earth 5d contributions can also be enhanced in addition to the 4f contributions at the resonance conditions.

Low-energy Magnetic Excitations of CeCu2Ge2 Investigated by Inelastic Neutron Scattering

CeCu2Ge2, the magnetic counterpart of the heavy-fermion superconductor CeCu2Si2, exhibits an antiferromagnetic ground state below TN = 4.15K with an incommensurate propagation vector of τ = (0.28 0.28 0.54). The magnetism is determined by local Ce 4f-moments and the ordering RKKY interaction as well as the onset of Kondo screening by conduction electrons. Tuning the energy scale of the Kondo effect and RKKY interaction towards enhanced Kondo screening may result in quantum critical phenomena at low temperature. While the existence of quantum critical phenomena induced by external pressure or chemical substitution is well known, the situation is less clear for magnetic field tuning. We will present an investigation of the spin excitation spectrum in magnetic field by inelastic neutron scattering and compare it to mean-field (McPhase) simulations of the antiferromagnetic spin wave excitation spectrum. We argue that our data can be described by the presence of spin wave excitations.

Investigation of Magnetic and Magnetoelastic Properties of the Unconventional Heavy-fermion Compound CeCu2Ge2

Heavy-fermion compounds, high-Tc cuprates or iron pnictides are characterized by adjacent properties and a rich magnetic phase diagram with unconventional or competing states at low temperatures. CeCu2Ge2, the counterpart of the heavy-fermion superconductor CeCu2Si2, exhibits an incommensurate antiferromagnetically long-range ordered ground state with τ1 = (0.28 0.28 0.54) up to TN = 4.1K which is strongly affected by a screening of the Ce 4f-moments by conduction electrons expressed by a Kondo temperature of TK = (6–10) K.The similar energy scales of the magnetic exchange and the Kondo effect result in a complex magnetic phase diagram with the possibility of quantum criticality at very low temperatures. The magnetic properties of CeCu2Ge2 were studied by magnetization measurements and, using the strong magnetoelastic coupling, by magnetostrictive investigations over a wide temperature range and in fields up to 50 T. Especially, the magnetostriction curves reveal clearly the details of the temperature and field dependence of the phase transitions. Here we present experimental results used for a refinement of the H − T phase diagram in [100] and [110] direction.

Field Dependence of the Magnetic Propagation Vector of the Heavy Fermion Compound CeCu2Ge2 Studied by Neutron Diffraction

CeCu2Ge2, the counterpart of the heavy-fermion superconductor CeCu2Si2, exhibits an in-commensurate antiferromagnetically long-range ordered ground state with τ = (0.28 0.28 0.54) below TN = 4.15K. The magnetism is strongly affected by a Kondo screening of the Ce 4f-moments by conduction electrons. The similar energy scale of both, Kondo and exchange interactions, results in a complex magnetic phase diagram and gives rise to potential quantum critical phenomena at very low temperatures. We present elastic neutron diffraction data obtained on a CeCu2Ge2 single crystal employing the cold triple axis spectrometer PANDA at MLZ and the diffractometer D23 at ILL.The field dependence of the magnetic propagation vector was measured at T ≤ 400 mK in the [110]/[001] plane with vertical magnetic fields applied along [1̄10]. We observe a low-field incommensurate magnetic phase AF1, a first order phase transition around 7.8 T with the coexistence of two phases AF1 and AF2 with slightly different propagation vectors, the disappearance of AF1 at 8 T and the existence of AF2 up to 12 T with a possible modification at 10 T. At 12.6 T, yet still well below the value of 26 T of the saturation for magnetic fields in [110] direction, the AF2-type magnetic order is lost and magnetic intensities are not to be found at incommensurate positions in the [110]/[001] plane any more. These new results contradict a previously suggested scenario with a QCP located at 8 T and contribute new information to the B − T phase diagram of CeCu2Ge2 in [110] direction.

Crystal field excitations in CeCu2Ge2: Revisited employing a single crystal and inelastic neutron scattering

The intermetallic compound, CeCu2Ge2, is the counterpart of the heavy-fermion superconductor CeCu2Si2. CeCu2Ge2 is a magnetically ordering (TN = 4.1K) Kondo lattice with a moderate Sommerfeld coefficient of 140 mJ/ molK2. Earlier inelastic neutron measurements on a polycrystalline sample revealed a doublet ground state and a quasi-quartet excited state at 16.5 meV, although a splitting of the 4f1 (J = 5/2) ground state multiplet into 3 doublets is expected from the point symmetry of the Ce3+ ions. We performed detailed inelastic neutron scattering experiments on a single crystal at the thermal triple-axis spectrometer PUMA at FRM II for different crystallographic directions. From our results we infer that the quasi-quartet, in fact, consists of two doublets at 17.0 and 18.3 meV which exhibit a strong directional dependence of their transition matrix elements to the ground state doublet. Finally, we will present a new set of crystal field parameters.

Electronic structure of LaFe2X2 (X = Si,Ge)

Recently found iron-pnictide superconductor (Ba,K)Fe2As2 and the heavy-fermion superconductor CeCu2Si2 both have the same crystal structure. In this paper we have calculated the electronic structure of LaFe2Si2 and LaFe2Ge2 from first-principles. These compounds also have the same crystal structure and closely related to both of (Ba,K)Fe2As2 and CeRu2Ge2. The obtained Fermi surfaces of LaFe2Si2 and LaFe2Ge2 resemble those of LaRu2Ge2, which are already found that they well explain the results of the dHvA experiments of CeRu2Ge2. Their density of states curves show the common feature with CaFe2As2. The density of states at the Fermi level strongly depends on the distortion of the FeX4 tetrahedra and/or the height of the X atom from the two-dimensional Fe plane, as also found in iron-pnictide system. The electronic specific heat coefficient is 11.8mJ/molK2 for LaFe2Si2 and 12.5mJ/molK2 for LaFe2Ge2, which is about 1/3 and 1/2 of experimental results, respectively.

Effect of Pressure on the Electronic State in Antiferromagnets UPt2Si2 and UIr2Si2

RT2X2 (R: rare earth or actinide, T: transition metal, and X: Si or Ge) is one of the typical compounds in the f electron systems. RT2X2 has two different kinds of crystal structures: ThCr2Si2 type (I4/mmm) and CaBe2Ge2 type (P4/nmm). A heavy fermion superconductor CeCu2Si2 2) and a heavy fermion compound CeRu2Si2 with an extremely large cyclotron mass of 120m0 (m0: rest mass of an electron) possess the ThCr2Si2-type structure. In the past years, extensive studies have been carried out to investigate the pressure effect on RT2X2 with a ThCr2Si2-type crystal structure such as CeCu2Ge2, 4) where an antiferromagnet CeCu2Ge2 is changed into a superconductor under pressure as in CeCu2Si2. On the other hand, no experimental studies were reported for RT2X2 with the CaBe2Ge2-type crystal structure. In the present paper, we investigated the pressure effect on antiferromagnets UPt2Si2 and UIr2Si2 with the CaBe2Ge2type crystal structure. Both compounds are antiferromagnets of which the Neel temperature TN, the ordered moment, and the electronic specific heat coefficient are 35K, 1.67 B/U and 32mJ/(K mol) for UPt2Si2 and 4.9K, 0.1 B/U and 290mJ/(K mol) for UIr2Si2, respectively. Single crystals of UPt2Si2 and UIr2Si2 were grown by the Czochralski method in a tetra-arc furnace. The starting materials were 3N (99.9% pure)-U, 4N-Pt or 4N-Ir and 5N-Si. The single crystal of UPt2Si2 was purified by the electro-transport method in high vacuum of 1 10 10 Torr. The single crystal of UIr2Si2 was wrapped in Ta-foil and annealed for 5 days at 800 C. The electrical resistivity was measured using the usual four-probe DC method. The pressure experiment was carried out using a cubic anvil cell at pressures up to 8GPa. As a pressuretransmitting medium, we used a mixture of Fluorinert No. FC70 and FC77. Figure 1 shows the temperature dependence of the electrical resistivity for UPt2Si2 under various pressures. The Neel temperature in the present sample is 34K at ambient pressure, which is almost the same as the previous value of TN 1⁄4 35K. With increasing pressure, the Neel temperatures (shown by arrows in Fig. 1) shift to lower temperatures. Figure 2(a) shows the pressure dependence of TN. Here, TN was defined as a temperature indicating a maximum of d =dT. The peak of d =dT broadens as a function of pressure, where an error in the definition of TN is shown by a bar in Fig. 2(a). We found that the Neel temperature decreases from 34K at 200

A change of electronic state tuned by pressure: pressure-induced superconductivity of the antiferromagnetCe2Ni3Ge5

We measured the electrical resistivity of an antiferromagnetCe2Ni3Ge5 with the orthorhombic crystal structure under pressure. The Néel temperatureTN = 5.2 K decreases withincreasing pressure P and becomes zero at a critical GPa. The A and ρ0 values of the low-temperature electrical resistivityρ = ρ0+AT2 in the Fermi liquid relation increase steeply above 3 GPa. A value ofA = 10.7 µΩ cm K−2 at 3.9 GPa iscomparableto A = 10 µΩ cm K−2 in a heavyfermionsuperconductor CeCu2Si2. The heavy fermion state was found to be formed aroundPc, in which pressure region superconductivity was found below 0.26 K.

Effect of impurity scattering on the superconductivity of CeCu2Si2

The archetypal heavy fermion superconductor CeCu2Si2 exhibits an unusual pressure–temperature (P–T) phase diagram, in which superconductivity survives over a broad region in pressure (>10 GPa) and the superconducting transition temperature Tc follows a complicated pressure dependence. To understand these unique properties, in this paper, we study a series of Ge-substituted single crystals CeCu2(Si1−xGex)2 (x = 0.01, 0.1 and 0.25). It is found that superconductivity is significantly weakened due to the elevated impurity scattering resulting from the partial Ge/Si substitution. For the sample with x = 0.01, a minimum of Tc(p) is revealed around 3 GPa. Upon further increasing x, the continuous superconducting region in the pure compounds breaks up into two disconnected superconducting domes. Superconductivity vanishes at x ≃ 0.25. These findings suggest that two different superconducting states, one magnetic and the other charge density fluctuations mediated, merge in CeCu2Si2.

Effect of pressure on the electrical resistivity of CeCu2Si2

We have performed electrical resistivity measurements at different pressures on two kinds of samples (low-Tc and high-Tc), which differ in physical properties of the heavy-fermion superconductor CeCu2Si2. It was found that one with lower Tc shows ∂Tc/∂P of negative and the other with higher Tc shows ∂Tc/∂P of positive. Therefore, the superconductivity for these two samples may have different origins.

Transport measurements of the heavy fermion superconductor CeCu2Si2 under pressure

Superconducting and normal state properties of a single crystal of CeCu2Si2 have been investigated by resistivity measurements under hydrostatic pressure and magnetic field. The low temperature resistivity behaviour (ρ = ρ0 + AT2, which is observed up to a temperature TA) is considered within the self-consistent renormalized (SCR) spin fluctuation model. Contrary to the model predictions, the product AT2A increases on approaching the quantum critical point (QCP). The temperature dependence of the upper critical field is analyzed assuming strong coupling and an intermediate regime between the clean and dirty limits. Both the low temperature resistivity behaviour at high pressure and the parameters deduced from the fits of Hc2 point to a pressure induced decrease of the quasi-particle effective mass m*. The anisotropy of the initial slope of Hc2(T) and therefore that of the effective mass was found to change under pressure.

Lateral-Size Effects and Supercurrent Blockade at Mechanical-Controllable Break Junctions of the Heavy-Fermion Superconductors

Break junctions of the heavy-fermion superconductors CeCu 2 Si 2 , UBe 13 , UPt 3 , URu 2 Si 2 , UPd 2 Al 3 , and UNi 2 Al 3 have been investigated. Josephson-like superconducting anomalies could be found only for low-ohmic contacts, but without the oscillatory Fraunhofer pattern of the critical current in a magnetic field. A systematic study on the contact radius demonstrates that these anomalies are mainly due to Maxwell's resistance being suppressed in the superconducting heavy-fermion phase rather than due to Josephson effect and Andreev reflection. We could not find any superconducting features by vacuum-tunneling spectroscopy.

Are heavy-fermion metals Fermi liquids?

We present the results of specific-heat and resistivity measurements as a function of temperature, magnetic field and hydrostatic pressure on the Kondo lattice CeNi2Ge2, the heavy-fermion superconductors CeCu2Si2 and UBe13 as well as the low-carrier-density system Yb4As3. “Non-Fermi-liquid” effects in the low-temperature normalstate properties of the three former systems are consistent with the existence of a “nearby” quantum critical point, presumably of antiferromagnetic type. Yb4As3, though showing the outward appearance of a Landau-type heavy-fermion metal, behaves very differently, i.e. as an extreme two-fluid system.

Nuclear magnetic resonance study of magnetic correlation in the heavy-fermion superconductor CeCu2Si2

Magnetic correlation in the heavy-fermion superconductor CeCu2Si2 has been investigated by Cu nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR). For CeCu2.02Si2 with Tc=0.72 K, a magnetic transition has been found at around 0.8 K in applied fields up to 3.5 T, which presumably also exists in zero magnetic field. Below the transition temperature, Cu NMR loses intensity suddenly without any broadening and shift of the spectrum, and the spin-echo decay rate, 1/T2, at H=13.3 kOe, increases with decreasing temperature, which is different from the behaviour expected in a static magnetically ordered state. The magnetic transition just above Tc is quite unusual in the sense that the ordered state is not in a completely static regime, but possesses some dynamic aspect. The unusual magnetic state is considered to coexist with superconductivity below Tc. The authors present a magnetic phase diagram in the field-temperature plane for CeCu2.02Si2.