Superconductor CeCu Research Articles

Revealing sign-reversal s+− -wave pairing by quasiparticle interference in the heavy-fermion superconductor CeCu2Si2

Recent observations of two nodeless gaps in superconducting CeCu$_2$Si$_2$ have raised intensive debates as to its exact gap structure of either sign-reversal ($s^{+-}$) or sign-preserving ($s^{++}$) pairing. Here we investigate the quasiparticle interference (QPI) using realistic Fermi surface topology for both weak and strong interband impurity scatterings. Our calculations of the QPI and integrated antisymmetrized local density of states reveal qualitative distinctions between $s^{+-}$ and $s^{++}$ pairing states, which include the intragap impurity resonance and a significant energy-dependence difference between two gap energies. Our predictions provide a guide for phase-sensitive QPI measurements to uncover decisively the true pairing symmetry in the heavy-fermion superconductor CeCu$_2$Si$_2$.

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.

Full-Gap Superconductivity Robust against Disorder in Heavy-Fermion CeCu_{2}Si_{2}.

A key aspect of unconventional pairing by the antiferromagnetic spin-fluctuation mechanism is that the superconducting energy gap must have the opposite sign on different parts of the Fermi surface. Recent observations of non-nodal gap structure in the heavy-fermion superconductor CeCu_{2}Si_{2} were then very surprising, given that this material has long been considered a prototypical example of a superconductor where the Cooper pairing is magnetically mediated. Here we present a study of the effect of controlled point defects, introduced by electron irradiation, on the temperature-dependent magnetic penetration depth λ(T) in CeCu_{2}Si_{2}. We find that the fully gapped state is robust against disorder, demonstrating that low-energy bound states, expected for sign-changing gap structures, are not induced by nonmagnetic impurities. This provides bulk evidence for s_{++}-wave superconductivity without sign reversal.

Thermodynamic study of gap structure and pair-breaking effect by magnetic field in the heavy-fermion superconductorCeCu2Si2

This paper presents the results of specific-heat and magnetization measurements, in particular their field-orientation dependence, on the first discovered heavy-fermion superconductor CeCu$_2$Si$_2$ ($T_{\rm c} \sim 0.6$ K). We discuss the superconducting gap structure and the origin of the anomalous pair-breaking phenomena, leading e.g., to the suppression of the upper critical field $H_{\rm c2}$, found in the high-field region. The data show that the anomalous pair breaking becomes prominent below about 0.15 K in any field direction, but occurs closer to $H_{\rm c2}$ for $H \parallel c$. The presence of this anomaly is confirmed by the fact that the specific-heat and magnetization data satisfy standard thermodynamic relations. Concerning the gap structure, field-angle dependences of the low-temperature specific heat within the $ab$ and $ac$ planes do not show any evidence for gap nodes. From microscopic calculations in the framework of a two-band full-gap model, the power-law-like temperature dependences of $C$ and $1/T_1$, reminiscent of nodal superconductivity, have been reproduced reasonably. These facts further support multiband full-gap superconductivity in CeCu$_2$Si$_2$.

Superconducting gap and vortex lattice of the heavy-fermion compoundCeCu2Si2

The order parameter and pairing mechanism for superconductivity in heavy fermion compounds are still poorly understood. Scanning tunneling microscopy and spectroscopy at ultra-low temperatures can yield important information about the superconducting order parameter and the gap structure. Here, we study the first heavy fermion superconductor, CeCu_2Si_2. Our data show the superconducting gap which is not fully formed and exhibits features that point to a multi-gap order parameter. Spatial mapping of the zero bias conductance in magnetic field reveals the vortex lattice, which allows us to unequivocally link the observed conductance gap to superconductivity in CeCu_2Si_2. The vortex lattice is found to be predominantly triangular with distortions at fields close to \sim 0.7 H_{c2}.

Broadband Corbino spectroscopy and stripline resonators to study the microwave properties of superconductors

<p>Superconducting materials are of great interest both for the fundamental understanding of electrons in solids as well as for a range of different applications. Studying superconductors with microwaves offers a direct experimental access to the electrodynamic response of these materials, which in turn can reveal fundamental material properties such as the superconducting penetration depth. Here we describe two different techniques to study superconductors at microwave frequencies: the broadband Corbino approach can cover frequencies from the MHz range up to 50 GHz continuously but is limited to thin-film samples whereas the stripline resonators are sensitive enough to study low-loss single crystals but reveal data only at a set of roughly equidistant resonant frequencies. We document the applicability of these two techniques with data taken on an ultrathin TaN film and a single crystal of the heavy-fermion superconductor CeCu<sub>2</sub>Si<sub>2</sub>, respectively.</p>

Emergent Loop-Nodals±-Wave Superconductivity inCeCu2Si2: 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.

Heavy fermion superconductor CeCu2Si2under high pressure: Multiprobing the valence crossover

The first heavy fermion superconductor CeCu${}_{2}$Si${}_{2}$ has not revealed all its striking mysteries yet. At high pressures, superconductivity is supposed to be mediated by valence fluctuations, in contrast to ambient pressure, where spin fluctuations most likely act as pairing glue. We have carried out a multiprobe (electric transport, thermopower, ac specific heat, Hall and Nernst effects) experiment up to $7\phantom{\rule{4.pt}{0ex}}\text{GPa}$ on a high-quality CeCu${}_{2}$Si${}_{2}$ single crystal. For the first time, the resistivity data make it possible quantitatively to draw the valence crossover line within the $p\ensuremath{-}T$ plane and to locate the critical end point at $4.5\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{4.pt}{0ex}}\text{GPa}$ and a slightly negative temperature. In the same pressure region, remarkable features have also been detected in the other physical properties, presumably acting as further signatures of the Ce valence crossover and the associated critical fluctuations: We observe maxima in the Hall and Nernst effects and a sign change and a strong sensitivity on magnetic field in the thermopower signal.

NQR study of pressure induced superconductivity in CeCu2Si2

AbstractWe have measured nuclear quadrupole resonance (NQR) for 63Cu nuclei under high pressure up to 4.8 GPa. A linear increase in NQR frequency $^{63} \nu _{\rm Q}$ of 63Cu nuclei was observed below 3 GPa. However, $^{63} \nu _{\rm Q}$ deviates gradually from the linear relation above 3.5 GPa. The downward deviation is associated with a change of valence and consistent with the results of band calculations with the structural parameters under pressure. Antiferromagnetic (AFM) spin fluctuations are drastically suppressed with increasing pressure, whereas Tc increases from 0.7 K at ambient pressure to 1.64 K at 4.2 GPa. We have found that bulk superconductivity suddenly disappears at 4.8 GPa accompanied with a rapid decrease in the density of states at the Fermi level. magnified image These are indenter pressure cells for NQR measurements.

The de Haas–van Alphen Oscillation and Fermi Surface Properties of YCu2Si2

We have succeeded in growing a high-quality single crystal of a non-4 f reference compound YCu 2 Si 2 for a heavy-fermion superconductor CeCu 2 Si 2 , and observed the de Haas–van Alphen (dHvA) oscillation. The detected dHvA branches in YCu 2 Si 2 indicate that the Fermi surfaces are multiply connected, and the dHvA frequencies are in the range from 9×10 6 to 2×10 8 Oe. These dHvA branches are found to be well explained by the results of energy band calculations. The corresponding cyclotron masses are light, ranging from 0.4 to 1.5 m 0 , and are consistent with the electronic specific heat coefficient of 2.2 mJ/(K 2 ·mol).

Magnetism and superconductivity in the heavy-fermion compound CeCu 2Si 2 studied by neutron scattering

We report on inelastic neutron scattering experiments on the heavy-fermion superconductor CeCu 2Si 2 to study the magnetic excitation spectrum in single crystals. Elastic short-range magnetic correlations have been observed in the superconducting state. While the low-energy magnetic response seems to be quasielastic in the normal state above T c ≈ 600 mK , a truly inelastic response is detected in the superconducting state well below T c . This inelastic response is discussed in connection to the properties of the superconducting state.

Non-Fermi Liquid States in the PressurizedCeCu2(Si1−xGex)2System: Two Critical Points

In the archetypal strongly correlated electron superconductor CeCu2Si2 and its Ge-substituted alloys CeCu2(Si1-xGex)2 two quantum phase transitions--one magnetic and one of so far unknown origin-can be crossed as a function of pressure. We examine the associated anomalous normal state by detailed measurements of the low temperature resistivity (rho) power-law exponent alpha. At the lower critical point (at pcl, 1<or=alpha<or=1.5) alpha depends strongly on Ge concentration x and thereby on disorder level, consistent with a Hlubina-Rice-Rosch scenario of critical scattering off antiferromagnetic fluctuations. By contrast, alpha is independent of x at the upper quantum phase transition (at pc2, alpha approximately equal to 1), suggesting critical scattering from local or q=0 modes, in agreement with a density- or valence-fluctuation approach.

Spin and valence-fluctuation mediated superconductivity in pressurised Fe and CeCu 2(Si/Ge) 2

We review the evidence supporting valence-fluctuation-mediated superconductivity in CeCu 2Si 2 and CeCu 2Ge 2, where T c reaches 2.4 K at high pressure. In these systems the valence and magnetic critical points, at p v and p c, respectively, are well separated. Characteristic signatures associated with both are distinct. In contrast, the valence and spin fluctuation regions appear much closer in most Ce-based compounds. Concerning d-transition metals, superconductivity in pure iron emerges in the pressure window 15–30 GPa with the onset of T c up to almost 3 K. All relevant observations point to unconventional superconductivity, likely mediated by ferromagnetic spin fluctuations.

Twenty-five years of heavy-fermion superconductivity

We discuss first the physical properties of the prototypical heavy-fermion superconductor CeCu 2Si 2 and, second, the relationship of its superconductivity with both a spin-density-wave-type quantum phase transition and a weak valence transition of Ce that occurs at high pressure. We, then, briefly address the isostructural heavy-fermion compound YbRh 2Si 2, displaying a local type of quantum critical behavior which appears to be detrimental to superconductivity.

Superconductivity and Magnetism in Heavy-Fermion Compounds

In this contribution we recall some of the early work devoted to Ce-based Kondo alloys which subsequently lead to thorough investigations on so-called “Kondo-lattice” systems like CeAl 2 , CeAl 3 and CeCu 2 Si 2 , subsequently referred to as heavy-fermion metals. We then address the physical properties of the first heavy-fermion superconductor CeCu 2 Si 2 and discuss the relationship of its superconductivity with both a spin-density-wave-type quantum critical point and a weak valence transition of Ce that occurs at high pressure. Finally, we introduce the isostructural Kondo-lattice system YbRh 2 Si 2 , displaying a novel type of quantum critical behavior which appears to be detrimental to superconductivity.

Exotic Superconductivity in the Coexistent Phase of Antiferromagnetism and Superconductivity in CeCu2(Si0.98Ge0.02)2: A Cu-NQR Study under Hydrostatic Pressure

We report a pressure ($P$) effect on CeCu$_2$(Si$_{0.98}$Ge$_{0.02}$)$_2$ where an antiferromagnetic (AFM) order at $T_N \sim$ 0.75 K coexists with superconductivity below $T_c \sim$ 0.4 K\@. At pressures exceeding $P = 0.19$ GPa, the AFM order is suppressed, which demonstrates that the sudden emergence of AFM order due to the Ge doping is ascribed to the intrinsic lattice expansion. The exotic superconductivity at $P = 0$ GPa is found to evolve into a typical heavy-fermion one with a line-node gap above $P = 0.91$ GPa\@. We highlight that the anomalous enhancement in nuclear spin-lattice relaxation rate $1/T_1$ that follows a $T_1T$ = const. behavior well below $T_c$ at $P$ = 0 GPa is characterized by the persistence of low-lying magnetic excitations, which may be inherent to the coexistent state of antiferromagnetism and superconductivity.

Magnetism and Superconductivity on the Border of Magnetic Phase: Cu-NQR Study of Ge-Substituted CeCu2Si2

We report Cu-NQR result on Ge-doped heavy-fermion superconductor CeCu 2 (Si 1- x Ge x ) 2 (0 < x ≤0.2). The main effect of the Ge doping is considered to be a negative pressure from the temperature dependence of the relaxation rate 1/ T 1 . We found the broadening of the Cu-NQR spectra originating from an internal field at the Cu site, and the distinct hump in 1/ T 1 at T N even in the sample with x =0.02. By the Ge doping, the T N increases and the superconducting transition temperature T c decreases from the same temperature of 0.65 K, implying that the magnetic and the superconducting phases are nearly degenerate in undoped CeCu 2 Si 2 . With increasing x , dynamical characteristics of magnetic order at x =0 change to more static ones which are suggested to be in a localized regime above x ∼0.25. The 1/ T 1 does not show significant reduction below T c , This result is not consistent with a line-node-gap model, but reveals that low-energy magnetic excitations survive persistently even in the supercondu...

Exotic magnetic and superconducting phases in CeCu 2Si 2 close to magnetically ordered state : Cu-NQR study

We report Cu-NQR results under pressure on heavy-fermion (HF) superconductor CeCu 2Si 2 close to a magnetic phase, Ce 0.99Cu 2.02Si 2 and CeCu 2(Si 0.98Ge 0.02) 2. It is found that an application of a minute pressure exceeding 0.3 GPa markedly suppresses low-energy magnetic fluctuations observed at ambient pressure ( P=0) in Ce 0.99Cu 2.02Si 2. Correspondingly, anomalous superconducting (SC) characteristics evolve into conventional HF-SC ones with increasing pressure. In the latter, the Ge substitution works as a negative chemical pressure. CeCu 2(Si 0.98Ge 0.02) 2 reveals a magnetic phase transition at T N=0.75 K followed by the SC phase transition at T c∼0.4 K at P=0. It is suggested experimentally that the magnetic fluctuations seen in Ce 0.99Cu 2.02Si 2 at P=0 possesses a quantum critical character of both SC and magnetically ordered states.

Magnetism and Superconductivity in CeCu2(Si1-xGex)2 Probed by Cu NQR

We report Cu-NQR results on Ge-doped heavy-fermion superconductor CeCu2(Si1−x Ge x )2 (0<x≤0.2) and undoped Ce0.99Cu2.02Si2. The main effect of the Ge doping is considered to be a negative pressure, since the strength of hybridization decreases by the Ge doping. With increasing x, the dynamical characteristics of the magnetic order at x=0 change to more static ones which suggests a localized regime above x∼0.25. From the derived T–x phase diagram, it is suggested that the magnetic and the superconducting phases are almost degenerate in undoped CeCu2Si2. An exotic interplay between the magnetism characterized by the slow fluctuations and the superconductivity is implied in the region of small x.

Unconventional normal-state properties and superconductivity in heavy-fermion metals

We discuss (i) UPd 2Al 3, for which local-moment antiferromagnetism ( T N = 14.3 K) coexists with heavy-fermion (HF) superconductivity below T c ≈ 2 K, (ii) the HF superconductor CeCu 2Si 2 ( T c ≈ 0.6 K) which, for B > B c2, shows pronounced “non-Fermi-liquid” (NFL) effects near a quantum-critical point at which the spin-density-wave “phase A” disappears, and (iii) the NFL CeNi 2Ge 2, a “clean-limit” HF superconductor below T c ≈ 0.1 K.