Heavy-fermion Superconductor Research Articles

Charge Transfer Effect under Odd-Parity Crystalline Electric Field: Divergence of Magnetic Toroidal Fluctuation in β-YbAlB4

A novel property of the quantum critical heavy fermion superconductor $\beta$-YbAlB$_4$ is revealed theoretically. By analyzing the crystalline electronic field (CEF) on the basis of the hybridization picture, odd parity CEF is shown to exist because of sevenfold configuration of B atoms around Yb, which breaks the local inversion symmetry. This allows onsite admixture of 4f and 5d wavefunctions with a pure imaginary coefficient, giving rise to the magnetic toroidal (MT) degree of freedom. By constructing a realistic minimal model for $\beta$-YbAlB$_4$, we show that onsite 4f-5d Coulomb repulsion drives charge transfer between the 4f and 5d states at Yb, which makes the MT fluctuation as well as the electric dipole fluctuation diverge simultaneously with the critical Yb-valence fluctuation at the quantum critical point of the valence transition.

Exotic superconductivity in noncentrosymmetric and magnetic CeNiC2 revealed under high pressure

We have found that magnetically ordered noncentrosymmetric ${\mathrm{CeNiC}}_{2}$ exhibits superconductivity under very high pressures of near 11 GPa. The transition temperature ${T}_{\mathrm{c}}$ is 3.5 K, the highest in all Ce heavy-fermion superconductors, implying quite strong electron pairings with a high-energy scale. Several physical quantities show diverging features of a quantum phase transition, however, its criticality appears in a rather narrow range of pressure. The upper critical field ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}2}(T=0)$ is estimated to be 18 T, much higher than the Pauli paramagnetic limiting field of 6.5 T, indicating spin-triplet electron pairings correlated with its noncentrosymmetric structure.

Unconventional Superconductivity in Heavy Fermion UTe2

We grew single crystals of the recently discovered heavy fermion superconductor UTe2, and measured the resistivity, specific heat and magnetoresistance. Superconductivity (SC) was clearly detected at Tsc=1.65K as sharp drop of the resistivity in a high quality sample of RRR=35. The specific heat shows a large jump at Tsc indicating strong coupling. The large Sommerfeld coefficient, 117mJ K-2mol-1 extrapolated in the normal state and the temperature dependence of C/T below Tsc are the signature of unconventional SC. The discrepancy in the entropy balance at Tsc between SC and normal states points out that hidden features must occur. Surprisingly, a large residual value of the Sommerfeld coefficient seems quite robust (gamma_0/gamma ~ 0.5). The large upper critical field Hc2 along the three principal axes favors spin-triplet SC. For H // b-axis, our experiments do not reproduce the huge upturn of Hc2 reported previously. This discrepancy may reflect that Hc2 is very sensitive to the sample quality. A new perspective in UTe2 is the proximity of a Kondo semiconducting phase predicted by the LDA band structure calculations.

Anisotropic magnetotransport and magnetic phase diagrams of the antiferromagnetic heavy-fermion superconductor Ce3PdIn11

We report the results of our detailed magnetotransport studies on single crystals of the antiferromagnetic heavy-fermion superconductor Ce$_3$PdIn$_{11}$. Electrical resistivity measurements, carried out in different magnetic field orientations with respect to the crystallographic axes, were mainly aimed to amass further insight about the magnetically ordered state. The results manifest a clear metamagnetic transitions in the ordered phase when the applied field is parallel to the tetragonal $c$ axis, while no similar features are seen for the transverse direction, i.e., with the field confined within the $ab$ plane. This finding elucidates the fact that the $c$ axis is the easy magnetic direction in this system. Based on the electrical transport and heat capacity data obtained for Ce$_3$PdIn$_{11}$, magnetic field -- temperature phase diagrams were constructed, which elucidate fairly enigmatic behaviors in this material featuring the existence of both second- and first-order magnetic phase transitions.

Modification of magnetic fluctuations by interfacial interactions in artificially engineered heavy-fermion superlattices

Recent progress in the fabrication techniques of superlattices (SLs) has made it possible to sandwich several-layer-thick block layers (BLs) of heavy-fermion superconductor CeCoIn5 between conventional-metal YbCoIn5 BLs or spin-density-wave-metal CeRhIn5 BLs of a similar thickness. However, the magnetic state in each BL, particularly at the interface, is not yet understood, as experimental techniques applicable to the SL system are limited. Here, we report measurements of 59Co nuclear magnetic resonance, which is a microscopic probe of the magnetic properties inside the target BLs. In the CeCoIn5/YbCoIn5 SL, the low-temperature magnetic fluctuations of the CeCoIn5 BL are weakened as expected from the Rashba spin-orbit effect. However, in the CeCoIn5/CeRhIn5 SL, the fluctuations show an anomalous enhancement below 6 K, highlighting the importance of the magnetic proximity effect occurring near a magnetic-ordering temperature TN ~ 3 K of the CeRhIn5 BL. We suggest that the magnetic properties of the BLs can be altered by the interfacial interaction, which is an alternative route to modify the magnetic properties.

Thermodynamic signatures of quantum criticality in cuprate superconductors

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*-at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram1. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range2 that includes p*. As a function of doping, we find that Cel/T is strongly peaked at p*(where Cel is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point3-5, as observed in heavy-fermion6 and iron-based7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.

Electronic structure and 4f -electron character in Ce2PdIn8 studied by angle-resolved photoemission spectroscopy

The localized-to-itinerant transition of f electrons lies at the heart of heavy-fermion physics, but has only been directly observed in single-layer Ce-based materials. Here, we report a comprehensive study on the electronic structure and nature of the Ce 4f electrons in the heavy-fermion superconductor Ce2PdIn8, a typical n=2 CenMmIn3n+2m compound, using high-resolution and 4d-4f resonance photoemission spectroscopies. The electronic structure of this material has been studied over a wide temperature range, and hybridization between f and conduction electrons can be clearly observed to form a Kondo resonance near the Fermi level at low temperatures. The characteristic temperature of the localized-to-itinerant transition is around 120K, which is much higher than its coherence temperature Tcoh~30K.

UBe13 and U1−xThxBe13: Unconventional Superconductors

UBe13 was the second discovered heavy fermion superconductor, and numerous pieces of evidence exist that imply that it is an unconventional (non-BCS, non-s wave pairing symmetry) superconductor. Exhibiting even more signs of unconventional superconductivity, Th-doped UBe13 is perhaps the most puzzling of any of the unconventional superconductors. This review considers both the parent, undoped compound as well as the more interesting Th-doped UBe13. After summarizing the rather thorough characterization, which because of the interest in these compounds has continued from their discovery in 1983 and 1984 to date, these properties are compared with a recent template for determining whether a superconductor is unconventional. Finally, further experiments are suggested.

Heavy fermion materials and physics

As typical examples of strongly correlated electron systems, heavy fermion materials exhibit diverse quantum ground states such as antiferromagnetic order, ferromagnetic order, non-Fermi-liquid phases, unconventional superconductivity, quantum spin liquids, orbital order and topological order. In contrast to other strongly correlated electron systems, heavy fermion systems have relatively small characteristic energy scales, which allows different quantum states to be tuned continuously by using external parameters such as pressure, magnetic field and chemical doping. Heavy fermion materials thus serve as ideal systems for studying quantum phase transitions, superconductivity and their interplay. In this review, we briefly introduce the history of the field of heavy fermions and the current status both in China and in other countries. The properties of several representative heavy fermion systems are summarized, and some frontier scientific issues in this field are discussed, in particular, concerning heavy fermion superconductors, quantum phase transitions and exotic topological states in strongly correlated electron systems.

Strongly Correlated and Strong Coupled S-Wave Superconductivity of the High Entropy Alloy Ta <sub>1/6</sub>Nb <sub>2/6</sub>Hf <sub>1/6</sub>Zr <sub>1/6</sub>Ti <sub>1/6</sub> Compound

High entropy alloy (HEA) is a random mixture of multiple elements stabilized by a high mixing entropy. We synthesized Ta1/6Nb2/6Hf1/6Zr1/6Ti1/6 bulk HEA compound as a body-centered cubic structure with the lattice parameter a = 3.38 A by arc melting. From the electronic and magnetic properties measurements, we found that it exhibits a superconducting transition at Tc = 7.85 K. From the superconducting properties such as electron-phonon coupling constant λel-ph, electron-phonon potential Vel-ph, density of states at the Fermi level D(EF), superconducting energy gap 2Δ(0)/kBTc, upper-critical field Hc2(0), coherence length ξ, and critical current Jc etc, we found that it is a strong coupled s-wave superconductor in a dirty limit. Meanwhile, the relative sizeable specific heat jump (ΔC/γTc), high effective mass of carrier (29 me), and high Kadowaki-Woods ratio which is close to one of heavy Fermi compounds indicate that it resides in the limit of a strongly correlated system. The vortex pinning force is described by the Dew-Huges double exponential pinning model, implying that there are two types of pinning mechanism. The possible coexistence of strongly correlated behavior in s-wave superconductivity on the HEA compounds is noteworthy because many of the strongly correlated superconductors have a nodal gap symmetry such as heavy fermion and high Tc cuprate superconductors. The HEA compound suggests a different types of superconductivity with the current strongly correlated superconductors as well as metallic superconductors.

Strong Correlation between Ferromagnetic Superconductivity and Pressure-enhanced Ferromagnetic Fluctuations in UGe_{2}.

We have measured magnetization at high pressure in the uranium ferromagnetic superconductor UGe_{2} and analyzed the magnetic data using Takahashi's spin fluctuation theory. There is a peak in the pressure dependence of the width of the spin fluctuation spectrum in the energy space T_{0} at P_{x}, the phase boundary of FM1 and FM2 where the superconducting transition temperature T_{sc} is highest. This suggests a clear correlation between the superconductivity and pressure-enhanced magnetic fluctuations developed at P_{x}. The pressure effect on T_{Curie}/T_{0}, where T_{Curie} is the Curie temperature, suggests that the less itinerant ferromagnetic state FM2 is changed to a more itinerant one FM1 across P_{x}. Peculiar features in relations between T_{0} and T_{sc} in uranium ferromagnetic superconductors UGe_{2}, URhGe, and UCoGe are discussed in comparison with those in high-T_{c} cuprate and heavy fermion superconductors.

Localized 5f2States in UPd5Al2and Valence Crossover in the Vicinity of Heavy-Fermion Superconductivity

Inelastic neutron scattering experiments have been carried out to reveal the 5f electron states of UPd5Al2, an isostructural compound of the heavy-fermion superconductor NpPd5Al2. The tetravalent U...

Magnetic field driven complex phase diagram of antiferromagnetic heavy-fermion superconductor Ce3PtIn11

We present the results of our comprehensive investigation on the antiferromagnetic heavy-fermion superconductor Ce3PtIn11 carried out by means of electrical transport, heat capacity and ac magnetic susceptibility measurements, performed on single-crystalline specimens down to 50 mK in external magnetic fields up to 9 T. Our experimental results elucidate a complex magnetic field – temperature phase diagram which contains both first- and second-order field-induced magnetic transitions and highlights the emergence of field stabilized phases. Remarkably, a prominent metamagnetic transition was found to occur at low temperatures and strong magnetic fields. In turn, the results obtained in the superconducting phase of Ce3PtIn11 corroborate an unconventional nature of Cooper pairs formed by heavy quasiparticles. The compound is an almost unique example of a heavy fermion system in which superconductivity may coexist microscopically with magnetically ordered state.

Breakdown of Fermi liquid theory in topological multi-Weyl semimetals

Fermi liquid theory works very well in most normal metals, but is found violated in many strongly correlated electron systems, such as cuprate and heavy-fermion superconductors. A widely accepted criterion is that, the Fermi liquid theory is valid when the interaction-induced fermion damping rate approaches zero more rapidly than the energy. Otherwise, it is invalid. Here, we demonstrate that this criterion breaks down in topological double-and triple-Weyl semimetals. Renormalization group analysis reveals that, although the damping rate of double- and triple-Weyl fermions induced by the Coulomb interaction approaches zero more rapidly than the energy, the quasiparticle residue vanishes and the Fermi liquid theory is invalid. This behavior indicates a weaker-than-marginal violation of the Fermi liquid theory. Such an unconventional non-Fermi liquid state originates from the special dispersion of double- and triple-Weyl fermions, and is qualitatively different from all the other Fermi-liquid and non-Fermi-liquid states. The predicted properties of the fermion damping rate and the spectral function can be probed by the angle-resolved photoemission spectroscopy. The density of states, specific heat, and conductivities are also calculated and analyzed after incorporating the corrections induced by the Coulomb interaction.

Robustness of magnons near the quantum critical point in the heavy-fermion superconductor CeCu2Si2

Paramagnons are supposed to provide the pairing glue for unconventional superconductors. For the heavy-fermion superconductor ${\mathrm{CeCu}}_{2}{\mathrm{Si}}_{2}$, there is indeed good evidence from inelastic neutron scattering (INS) that spin fluctuations drive the superconductivity. Here, we present the INS measurement of the inelastic response of the antiferromagnetic parent compound, `A-type' ${\mathrm{CeCu}}_{2}{\mathrm{Si}}_{2}$, to probe the relation to the excitations of the superconducting (`S-type') sample. We find that the dispersion is very similar in the antiferromagnetic state and in the normal state of the superconducting sample. Pronounced differences to the response in the superconducting state exist at low energies around the zone center. These findings are in line with observations of other unconventional superconductors.

Gaussian fluctuation corrections to a mean-field theory of complex hidden order in URu2Si2

Hidden-order phase transition in the heavy-fermion superconductor URu$_2$Si$_2$ exhibits the mean-field-like anomaly in temperature dependence of heat capacity. Motivated by this observation, here we explore the impact of the complex order parameter fluctuations on the thermodynamic properties of the hidden order phase. Specifically, we employ the mean-field theory for the hidden order which describes the hidden order parameter by an average of the hexadecapole operator. We compute the gaussian fluctuation corrections to the mean-field theory equations including both the fluctuations due to 'hidden order' as well as antiferromagnetic order parameters. We find that the gaussian fluctuations lead to the smearing of the second-order transition rendering it to become the first-order one. The strength of the first-order transition is weakly dependent on the strength of underlying antiferromagnetic exchange interactions.

The dominant role of critical valence fluctuations on high Tc superconductivity in heavy fermions

Despite almost 40 years of research, the origin of heavy-fermion superconductivity is still strongly debated. Especially, the pressure-induced enhancement of superconductivity in CeCu2Si2 away from the magnetic breakdown is not sufficiently taken into consideration. As recently reported in CeCu2Si2 and several related compounds, optimal superconductivity occurs at the pressure of a valence crossover, which arises from a virtual critical end point at negative temperature Tcr. In this context, we did a meticulous analysis of a vast set of top-quality high-pressure electrical resistivity data of several Ce-based heavy fermion compounds. The key novelty is the salient correlation between the superconducting transition temperature Tc and the valence instability parameter Tcr, which is in line with theory of enhanced valence fluctuations. Moreover, it is found that, in the pressure region of superconductivity, electrical resistivity is governed by the valence crossover, which most often manifests in scaling behavior. We develop the new idea that the optimum superconducting Tc of a given sample is mainly controlled by the compound’s Tcr and limited by non-magnetic disorder. In this regard, the present study provides compelling evidence for the crucial role of critical valence fluctuations in the formation of Cooper pairs in Ce-based heavy fermion superconductors besides the contribution of spin fluctuations near magnetic quantum critical points, and corroborates a plausible superconducting mechanism in strongly correlated electron systems in general.

Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu2Si2 versus YbRh2Si2

ABSTRACTIn this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu2Si2, fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu2Si2. In YbRh2Si2, superconductivity appears to be suppressed at T ⪆ 10 mK by AF order (TN = 70 mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at TA slightly above 2 mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at Tc = 2 mK. Like the pressure – induced QCP in CeRhIn5, the magnetic field – induced one in YbRh2Si2 is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavy – fermion superconductors and other families of unconventional superconductors with higher Tcs, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.

Neutron Inelastic Scattering Study of thef-Electron States in NdPd5Al2

Inelastic neutron scattering experiments were carried out in order to study the f-electron states of NdPd5Al2. This is a Nd based isostructural compound of the heavy-fermion superconductor NpPd5Al2...

NMR studies on antiferromagnetic fluctuation in [formula omitted

We have carried out 195Pt-NMR measurements on a heavy Fermion superconductor UPt3 at H∼1.5−2.0T to investigate the in-plane anisotropy in the normal state. For an applied field parallel to [112¯0] direction, split 195NMR line are observed, which has not been reported previously. Such a line splitting is explained by anisotropic Knight shift tensors associated with the local symmetry of Pt-site in UPt3.