Observation of Two Distinct Superconducting Phases in CeCu2Si2

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Science  19 Dec 2003:
Vol. 302, Issue 5653, pp. 2104-2107
DOI: 10.1126/science.1091648


We report the presence of two disconnected superconducting domes in the pressure-temperature phase diagram of partially germanium-substituted CeCu2Si2. The lower density superconducting dome lies on the threshold of antiferromagnetic order, indicating magnetically mediated pairing, whereas the higher density superconducting regime straddles a weakly first-order volume collapse, suggesting a pairing interaction based on spatially extended density fluctuations. Two distinct pairing mechanisms thus appear to operate in the single, wide, superconducting range of stoichiometric CeCu2Si2, both of which might apply more generally to other classes of correlated electron systems.

Quantum order in metals, of which the phenomenon of superconductivity provides one of the most explicit examples, can involve subtle and often unforeseen collective mechanisms. In strongly correlated electron systems, the strength of the local electrostatic Coulomb repulsion present between the charge carriers, when compared to the width of their often-narrow energy bands, precludes the most common kind of superconductivity, which is based on bound electron pairs coupled by deformations of the lattice. However, superconductivity of more subtle origins is observed in many of these complex metals, and the quest for understanding its structure and origin is of interest to a wide community. The phase diagrams that arise when ordering temperatures (magnetic, superconducting, or otherwise) are plotted against external control parameters (such as pressure, magnetic field, or composition) are important tools for recognizing the patterns that emerge in correlated electron systems. Numerous materials, including many organic, cuprate, and heavy fermion superconductors, follow very similar phase diagrams, in which superconductivity is closely linked to magnetism. In particular, in a number of studies in f-electron compounds, which have tracked magnetism and superconductivity as functions of lattice density through the application of hydrostatic pressure, unconventional superconductivity in very pure samples has been tied clearly to the threshold of magnetism (13). These findings suggest that the mechanism that forms Cooper pairs can be of magnetic origin: On the verge of magnetic order, the magnetically soft electron liquid can mediate spin-dependent attractive interactions between the charge carriers. The resulting phase diagram (Fig. 1, left) has been observed in several heavy fermion compounds, such as CePd2Si2, CeIn3, and CeRh2Si2, and roughly similar behavior has been found in the recently discovered Ce 1-1-5 compounds. The material which started the field, however, the archetypal heavy fermion superconductor CeCu2Si2 (4), has so far escaped a similar explanation. Although an analogous magnetic quantum critical point has been demonstrated in CeCu2Si2 (5), the associated superconducting region extends to much higher densities than in the other materials, and the transition temperature (Tc) reaches its maximum far away from the magnetic quantum phase transition (69).

Fig. 1.

Schematic phase diagram of Cebased narrow-band metals. At low density, the Ce 4f orbitals are singly occupied and carry a static moment (arrows), subject to long-range antiferromagnetic order (red line). Increasing the lattice density (e.g., by hydrostatic pressure) raises the hybridization between more extended orbitals (single hatch) and the 4f states, leading to dynamical frustration (Kondo spin-flips, double arrows), which in turn suppresses long-range order and induces an anomalous normal state. In the simplest case, at some distance from the quantum critical point at pc1, where magnetic order is fully suppressed, this state can be modeled as a high–effective carrier mass Fermi liquid. Sufficiently close to pc1, magnetically mediated pairing may induce unconventional superconductivity (red dome). Further increasing the hybridization between localized and extended orbitals leads eventually to a less correlated, metallic state (intermediate valence region), in which the 4f electrons delocalize through stronger hybridization with ligand states and occupy wider energy bands at the Fermi energy (crosshatch). The transition from the heavy fermion to the intermediate valence configuration may proceed through a first-order phase transition that involves a collapse of the unit cell volume with no change in lattice symmetry (green dashed line), driven by the gain in cohesive energy associated with the wide-band 4f electron configuration. If the critical endpoint of the first-order line is low enough, the system may become sufficiently soft at low temperatures to allow a superconducting state to form around the quantum phase transition associated with the volume collapse, at pc2 (green dome).

In a preliminary doping study (10), two disconnected superconducting domes were observed in the alloy CeCu2(Si0.9Ge0.1)2, indicating a promising approach toward this long-standing problem. We give a comprehensive account of the breakup of the robust superconducting regime in CeCu2Si2 on partial substitution of Si with Ge, and we discuss the implications of the observed superconducting and normal-state properties for the pairing mechanisms in the two superconducting domes and hence for our understanding of stoichiometric CeCu2Si2.

It has long been speculated that an explanation for the unusually robust superconducting region in CeCu2Si2 may lie in the existence of a second critical point on the high-density side of the schematic phase diagram (9). Ce and many of its compounds are known to change from a high electronic density of states at low pressure toward a much lower density of states, the so-called intermediate valence regime, at high pressure. In elemental Ce, the gradual change of electronic properties with pressure is interrupted by an abrupt volume collapse, which can reach 15% (11). Reminiscent of the first-order liquid-vapor transition, this density transition traces out a critical line in the pressure-temperature phase diagram, terminated by a critical end point. Although in Ce the density transition line extends to very high temperatures, it has recently been found in CeCu2Ge2 (CeCu2Si2's sister compound) to be observable only at temperatures as low as 10 K (12), and it probably has a critical endpoint well below room temperature. We propose that the first-order volume collapse in CeCu2Si2 may, if sufficiently weak, be associated with slow fluctuations of charge and spin density that would enable the formation of a second superconducting dome around the upper quantum phase transition, pc2 (Fig. 1, right).

To investigate this two-critical-point scenario, we intentionally weakened superconductivity in CeCu2Si2 by introducing additional disorder (10, 13). Partial substitution of Si by isoelectronic Ge causes increased disorder scattering, shortening the mean free path Math, which will destroy unconventional, anisotropic superconductivity when Math drops below the superconducting coherence length ξ. Moreover, the widening of the lattice on Ge substitution moves CeCu2Si2, which is on the verge of magnetism at ambient pressure, to the left on the schematic phase diagram, presenting the opportunity to map out the magnetic part of the phase diagram in greater detail than previously possible. Compensating for this volume increase by applying hydrostatic pressure then allows us to study essentially the same material with a higher level of disorder scattering and to investigate the effects this may have on its superconducting properties. Additional effects of substituting Ge for Si appear to be very small, as evidenced by the almost-identical superconducting phase diagrams of CeCu2Si2 and CeCu2Ge2 when plotted against unit cell volume. Nevertheless, secondary effects, such as increased Cu/Si site interchange, cannot be ruled out completely. The role of partial Ge/Si substitution may be seen, then, in tuning a further control parameter on CeCu2Si2, which varies the unit cell volume and affects superconductivity largely, but possibly not entirely, by changing the quasiparticle mean free path.

Figure 2 summarizes the salient results obtained on the 10 atomic% substituted material CeCu2(Si0.9Ge0.1)2. At pressures well below 1 GPa, two resistive anomalies associated with subsequent magnetic transitions can be identified at temperatures TN and T1 (Fig. 2A), which agree with the thermodynamic transition temperatures observed at zero pressure (Fig. 2A, inset). Following these anomalies with pressure to where TN extrapolates to zero leads us toward a quantum critical point at a critical pressure pc1 ≈ 1.5 GPa. The superconducting transition temperatures, taken from the midpoints of the resistivity jumps, go through a maximum near pc1, at ∼1 GPa, and then decrease to less than 50 mK at ∼2.8 GPa. This confinement of superconductivity to a narrow region around pc1, which has been observed in four samples of CeCu2(Si0.9Ge0.1)2 cut from the same single crystal, is in contrast to the case of pure CeCu2Si2 or CeCu2Ge2, in which Tc is pressure-independent up to ∼2 GPa above pc1 (69). When pressure is increased further (Fig. 2B), superconductivity reemerges and reaches a maximum Tc at p ≈ 5.4 GPa of ∼0.95 K, which, although much less than that of the pure compound, is still far higher than the Tc observed near pc1. Superconductivity finally disappears abruptly above 6 GPa. No superconductivity was observed around pc1 in samples of CeCu2(Si1–xGex)2 with a higher Ge content of x = 0.25, supporting the view that the increased disorder scattering associated with Ge substitution tends to weaken superconductivity in CeCu2Si2.

Fig. 2.

Temperature dependence of the resistivity ρ(T) of CeCu2(Si0.9Ge0.1)2 at (A) low and (B) elevated pressures p near the relative maximum transition temperatures (colored curves). Arrows on the resistivity trace at 0.5 GPa indicate slight kinks linked to magnetic phase transitions, as indicated in the temperature derivative of ρ(T) and confirmed in zero-pressure measurements of the heat capacity (C) (inset). Neutron scattering studies indicate that antiferromagnetic order sets in at TN, and the ordering wave vector readjusts at T1 (20). The low Tc observed at 0.5 GPa (∼0.18K, consistent with the bulk value Tc = 0.12 K determined from specific heat and thermal expansion measurements at p = 0) rises to a maximum of about 0.4 K at 1 GPa, where the magnetic transitions are masked by superconductivity, but reoccurs once superconductivity is suppressed by a magnetic field. When pressure is further increased (to 2.8GPa), superconductivity is suppressed to below 50 mK. At pressures in excess of 3.4 GPa, superconductivity reemerges, reaching a peak Tc of ∼0.95 K at ∼5.4 GPa. Although ρ(T) is nearly linear above Tc at 5.4 GPa, electronic scattering virtually collapses over the narrow pressure interval up to 5.9 GPa, where a very weak, quadratic temperature dependence of the resistivity (ρ0 =76.8 μΩcm, A = 0.13 μΩcm K–2, B = 3.1 × 10–5 μΩcm K–5) is observed (inset).

Plotting the magnetic and superconducting transitions versus the relative pressure Δp = ppc1 (Fig. 3A) makes it possible to overlay results from different materials from the CeCu2(Si/Ge)2 system, demonstrating that the replacement of Si by Ge, as far as magnetism is concerned, can be offset by hydrostatic pressure. For CeCu2(Si0.9Ge0.1)2, we obtained a phase diagram which, in contrast to the behavior of pure CeCu2Si2 and CeCu2Ge2. (Fig. 3A), shows two disconnected superconducting regions. The lower superconducting dome straddles the magnetic quantum critical point, whereas the upper one coincides with the volume collapse transition inferred from high-pressure x-ray diffraction data taken on CeCu2Ge2 (12). The lower superconducting transition temperatures observed in CeCu2(Si0.9Ge0.1)2 compared to the pure compounds, and in particular the disappearance of superconductivity between the two domes, can be attributed to the effect of disorder scattering on an anisotropic superconducting order parameter. Our studies of the temperature dependence of the superconducting upper critical field Bc2 as a function of pressure (14) have revealed that, in CeCu2(Si0.9Ge0.1)2, ξ is of the order of 120 Å at pc1 and increases rapidly with increasing pressure, reaching 300 Å at Δp ≈ 1.5 GPa. These findings are consistent with conventional quantum critical phenomenology, because ξ is linked inversely to the quasiparticle mass, which is expected to diminish with increasing distance to the critical point, Δp. In the doped material CeCu2(Si0.9Ge0.1)2, ξ, which is already close to Math at pc1, can therefore exceed Math quickly when the system is tuned away from the quantum critical point, giving rise to a narrow nonsuperconducting valley in between the two superconducting domes on the phase diagram. By contrast, in stoichiometric CeCu2Si2 the larger mean free path Math exceeds ξ over a much broader pressure range (15, 16), allowing the two domes to merge into one wide superconducting region.

Fig. 3.

Pressure dependence of key properties of the CeCu2(Si1–xGex)2 system. (A) Experimental phase diagram showing antiferromagnetic (TN, open symbols) and superconducting (Tc, closed symbols) transition temperatures versus relative pressure Δp = p – pc1, which reflects the inverse unit cell volume, and against which the magnetic transition lines for x = 0.1 (pc1 = 1.5 GPa, circles), x = 0.25 (pc1 = 2.4 GPa, squares), and x = 1 [pc1 = 11.5 GPa (7), Tc shown by the continuous line] coincide. Pure CeCu2Si2 [(6), Tc shown by the dotted line; (8), Tc shown by the dashed-dotted line] is assumed here to have pc1 = 0.4 GPa. The approximate location of the volume collapse observed in (12) is indicated by a vertical dashed line at Δp = 4 GPa. SC, superconducting; AFM, antiferromagnetic. (B) Residual resistivity ρ0 (right scale) and low-T electronic scattering Δρ = ρ(2K) – ρ0 (left scale) versus relative pressure Δp. (C) Power-law exponent α versus Δp. We obtained residual resistivity ρ0 and the exponent α by fitting the power-law form ρ = ρ0 + ATα to the low-temperature, normal-state resistivity and checking for consistency against the logarithmic derivative dln(ρ – ρ0)/dlnT. The power-law exponent α shows a distinct minimum near Δp ≈ 0 (inset) and a second minimum near Δp ≈ 3.7 GPa, where the exponent approaches α ≈ 1 (Fig. 2B). In the intervening region, the exponent attains a local maximum of α ≈ 1.5, that is, well below the Fermi-liquid value α = 2.

The dependence of the resistivity ρ on temperature T in the normal state also exhibits a distinct pressure dependence. Particularly marked is the pronounced peak of the residual resistivity ρ0 near Δp = 4 GPa and the variation of the steepness of the resistivity trace at low temperature, Δρ = ρ(2K) – ρ0. Figure 2B shows a precipitous decrease in Δρ in the narrow pressure interval between 5.4 GPa and 5.9 GPa, a region where both Tc and ρ0 are near their maximum values (Fig. 3). Detailed scrutiny can also be directed at the exponent α of the power-law variation of the resistivity in the normal state, ρ = ρ0 + AT α, where A is a fitted prefactor. Over the range 0 ≤ Δp ≤ 4.1 GPa, the exponent α remains well below the Fermiliquid value of 2, with a tendency, at any given Δp in the low-pressure superconducting regime, for lower α in samples with lower Ge-content x. In the 10 atomic% substituted (x = 0.1) samples, the exponent reaches two minima (Fig. 3C) at pc1 (α ≈ 1.35) and near Δp ≈ 3.7 GPa, close to the pressure at which ρ(T) becomes essentially linear (Fig. 2B).

Around the magnetic critical point at pc1, the narrow superconducting regime observed below an anomalous, non–Fermi-liquid-like normal state resembles the behavior of other heavy fermion compounds, such as CePd2Si2 and CeIn3 (1). In this region of the phase diagram, the CeCu2(Si/Ge)2 system appears to be unstable toward magnetically mediated pairing, suggesting a unified picture for heavy fermion superconductivity on the threshold of magnetism.

Far away from the threshold of magnetism, however, and close to the lattice density at which a Ce-type volume collapse is observed in pure CeCu2Ge2 by x-ray diffraction at low temperature (12) (Fig. 3A, the vertical line at Δp = 4 GPa), we observe (i) the peak Tc of the second superconducting dome, accompanied by (ii) a linear temperature dependence of the resistivity, (iii) a pronounced maximum of ρ0, and (iv) a steep drop of electronic scattering Δρ with further increasing pressure. These properties of the CeCu2(Si/Ge)2 system point toward a second transition line in this region of the phase diagram, as alluded to in Fig. 1 and noted previously (7, 9, 17, 18). Our study exposes a separate superconducting dome linked to this volume-collapse, high-pressure phase boundary and far removed from the threshold of magnetism, suggesting an unidentified unconventional pairing mechanism. Although first-order phase transitions of the type observed in elemental Ce would not allow the electron/lattice system to grow sufficiently soft to mediate a pair-forming quasiparticle interaction, a more benign, weakly first-order volume collapse with a sufficiently low-lying critical end point could be accompanied by extended and slow density fluctuations, which may induce an attractive quasiparticle interaction in analogy with the role of magnetic fluctuations in the magnetic interaction picture (19). Microscopically, fluctuations of both charge (valence) and spin could induce pairing in high-pressure CeCu2Si2. Both processes may slow down in the cross-over region from the heavy fermion to the intermediate valence state (17, 18), in which two local electronic configurations (one f-electron plus n conduction electrons, and zero f-electrons plus n + 1 conduction electrons) become nearly degenerate. Microscopic theories for the high-pressure superconducting state in CeCu2Si2, in particular those based on widespread and general phenomena such as the transition from heavy fermion to intermediate valence behavior, need to explain the scarcity of other manifestations of this type of superconductivity, which follows naturally from the requirement of the phenomenological picture that the density transition be only weakly first order at low temperature.

The prototype heavy fermion superconductor CeCu2Si2 and its isoelectronic and isostructural partner compound CeCu2Ge2 have long vexed proponents of a magnetic interaction model of superconductivity in 4f electron compounds, because they display an unusually robust superconducting regime with a peak Tc widely separated from the magnetic quantum critical point. The evolution of superconductivity under precise control of both composition and lattice density suggests that, in stoichiometric CeCu2Si2 and CeCu2Ge2, two superconducting domes merge into a single, wide superconducting region. Whereas the low-pressure dome straddles the antiferromagnetic quantum critical point in apparent agreement with a magnetic interaction model, the high-pressure superconducting phase remains enigmatic. The existence of a distinct superconducting state connected to a volume collapse transition should motivate a wider search in Ce-based narrow-band metals and raises the possibility that density fluctuations may have a more general role to play in inducing superconductivity in correlated electron systems, including the high-Tc cuprates.

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