Superconductivity In Heavy-fermion Systems Research Articles

Superconductivity in Ce-based heavy-fermion systems under high pressure

In this paper, the possibility of a superconducting state mediated by the valence fluctuations in Ce-based heavy-fermion systems under high pressure is investigated for the extended periodic Anderson model. In this extended version, an additional local Coulomb repulsion between the localized and conduction electrons is included. In the framework of the projector-based renormalization method, we derive self-consistent equations for the superconducting order parameters. Our numerical evaluation for a two-dimensional case specifies that superconductivity in the heavy-fermion systems has a $d$-wave character and is mediated by valence fluctuations. By use of some additional simplifications, a BCS-like equation is found; an effective pairing interaction then is delivered. The interaction depends strongly on momentum and becomes dominant in the valence transition regime.

Fully gapped s -wave superconductivity enhanced by magnetic criticality in heavy-fermion systems

In heavy fermion systems, higher-rank multipole operators are active thanks to the strong spin-orbit interaction (SOI), and the role of diverse multipole fluctuations on the pairing mechanism attracts a lot of attention. Here, we study a mechanism of superconductivity in heavy fermion systems, by focusing on the impact of vertex corrections (VCs) for the pairing interaction going beyond the Migdal approximation. In heavy fermion systems, strong interference between multipole fluctuations cause significant VCs, that represent many-body effects beyond mean-field-type approximations. Especially, the coupling constants between electrons and charged-bosons, including the electron-phonon coupling constant, are strongly magnified by the VCs. For this reason, moderate even-rank (=electric) multipole fluctuations give large attractive interaction, and therefore s-wave superconductivity can emerge in heavy-fermion systems. In particular, phonon-mediated superconductivity is expected to be realized near the magnetic criticality, thanks to the VCs due to magnetic multipole fluctuations. The present mechanism may be responsible for the fully gapped s-wave superconducting state realized in CeCu2Si2.

Strong coupling between localized 5f moments and itinerant quasiparticles in the ferromagnetic superconductor UGe2**Project supported by the National Natural Science Foundation of China (Grant No. 11404297), the Science Challenge Project (Grant No. TZ2016004), and the Science and Technology Foundation of China Academy of Engineering Physics (Grant Nos. 2013B0301050 and 2014A0301013).

The heavy fermion physics arises from the complex interplay of nearly localized 4f/5f electrons and itinerant band-like ones, yielding heavy quasiparticles with an effective mass about 100 times (or more) of the bare electrons. Recently, experimental and theoretical investigations point out a localized and delocalized dual nature in actinide compounds, where itinerant quasiparticles account for the unconventional superconductivity in the vicinity of a magnetic instability. Here we report the strong coupling between localized 5f moments and itinerant quasiparticles in the ferromagnetic superconductor UGe2. The coupling is nearly antiferromagnetic. As embedded in the ferromagnetic matrix of localized 5f moments below , this coupling leads to short-range dynamic correlations of heavy quasiparticles, characterized by fluctuations of magnetic clusters. Those cluster-like spins of itinerant quasiparticles show a broad hump of magnetization at , which is typical for the spin-glass freezing. Thus, our results present the direct observation of itinerant quasiparticles coexisting with localized 5f moments by conventional magnetic measurements, providing a new route into the coexistence between ferromagnetism and superconductivity in heavy fermion systems.

Formation of Cooper pairs between conduction and localized electrons in heavy-fermion superconductors

Cooper pairing between a conduction electron ($c$ electron) and an $f$ electron, referred to as the "$c$-$f$ pairing," is examined to explain s-wave superconductivity in heavy-fermion systems. We first apply the Schrieffer-Wolff transformation to the periodic Anderson model assuming deep $f$ level and strong Coulomb repulsion. The resulting effective Hamiltonian contains direct and spin-exchange interactions between $c$ and $f$ electrons, which are responsible for the formation of the $c$-$f$ Cooper pairs. The mean-field analysis shows that the fully gapped $c$-$f$ pairing phase with anisotropic s-wave symmetry appears in a large region of the phase diagram. We also find two different types of exotic $c$-$f$ pairing phases, the Fulde-Ferrell and breached pairing phases. The formation of the $c$-$f$ Cooper pairs is attributed to the fact that the strong Coulomb repulsion makes a quasiparticle $f$ band near the center of the conduction band.

Superconductivity in heavy fermion systems

The heavy fermion state in the f-electron systems is due to competition between the RKKY interaction and the Kondo effect. The typical compound is CeCu 6 . To understand the electronic state, we studied the Fermi surface properties via the de Haas–van Alphen (dHvA) experiment and energy band calculation for CeSn 3 , CeRu 2 Si 2 , UPt 3 , and nowadays, transuranium compounds. Pressure is also an important technique to control the electronic state. The Néel temperature T N decreases with increasing pressure P and becomes zero at the critical pressure P c : T N → 0 for P → P c . The typical compound is an antiferromagnet CeRhIn 5 , which we studied from the dHvA experiment under pressure. A change of the 4 f-electronic state from localized to itinerant is realized at P c ≃ 2.4 GPa , revealing the first-order phase transition, together with a divergent tendency of the cyclotron mass at P c . It is stressed that appearance of superconductivity in CeRhIn 5 is closely related to the heavy fermion state. It is also noted that the parity-mixed novel superconducting state might be realized in a pressure-induced superconductor CeIrSi 3 without inversion symmetry in the crystal structure.

Magnetotransport in the CeIrIn5 System: The Influence of Antiferromagnetic Fluctuations

We present an overview of magnetotransport measurements on the heavy-fermion superconductor CeIrIn5. Sensitive measurements of the Hall effect and magnetoresistance are used to elucidate the low-temperature phase diagram of this system. The normal-state magnetotransport is highly anomalous, and experimental signatures of a pseudogap-like precursor state to superconductivity, as well as evidence for two distinct scattering times governing the Hall effect and the MR, are observed. Our observations point out the influence of antiferromagnetic fluctuations on the magnetotransport in this class of materials. The implications of these findings, both in the context of unconventional superconductivity in heavy-fermion systems and in relation to the high-temperature superconducting cuprates, are discussed.

Valence Instability and Superconductivity in Heavy Fermion Systems

Many cerium-based heavy fermion (HF) compounds have pressure-temperature phase diagrams in which a superconducting region extends far from a magnetic quantum critical point. In at least two compounds, CeCu2Si2 and CeCu2Ge2, an enhancement of the superconducting transition temperature was found to coincide with an abrupt valence change, with strong circumstantial evidence for pairing mediated by critical valence, or charge transfer, fluctuations. This pairing mechanism, and the valence instability, is a consequence of a f-c Coulomb repulsion term U_fc in the hamiltonian. While some non-superconducting Ce compounds show a clear first order valence instability, analogous to the Ce alpha-gamma transition, we argue that a weakly first order valence transition may be a general feature of Ce-based HF systems, and both magnetic and critical valence fluctuations may be responsible for the superconductivity in these systems.

Quantum effects on the competition between antiferromagnetism and superconductivity in heavy-fermion systems

We study a Ginzburg–Landau theory of two coupled fields describing superconductivity and antiferromagnetism in a metal. A coupling between the two-components superconductor and the antiferromagnetic (AF) field is included in the classical action. The classical results are improved calculating the quantum corrections to one-loop order with the method of the effective potential near the AF phase, but in the paramagnetic side. We discuss the influence of these corrections, including the possibility of fluctuation induced first order transitions. A scaling approach is used to obtain the critical and shift exponents at a quantum bicritical point.

Unconventional superconductivity and magnetism in Sr2RuO4 and related materials

We review the normal and superconducting state properties of the unconventional triplet superconductor Sr$_2$RuO$_4$ with an emphasis on the analysis of the magnetic susceptibility and the role played by strong electronic correlations. In particular, we show that the magnetic activity arises from the itinerant electrons in the Ru $d$-orbitals and a strong magnetic anisotropy occurs ($\chi^{+-} < \chi^{zz}$) due to spin-orbit coupling. The latter results mainly from different values of the $g$-factor for the transverse and longitudinal components of the spin susceptibility (i.e. the matrix elements differ). Most importantly, this anisotropy and the presence of incommensurate antiferromagnetic and ferromagnetic fluctuations have strong consequences for the symmetry of the superconducting order parameter. In particular, reviewing spin fluctuation-induced Cooper-pairing scenario in application to Sr$_2$RuO$_4$ we show how p-wave Cooper-pairing with line nodes between neighboring RuO$_2$-planes may occur. We also discuss the open issues in Sr$_2$RuO$_4$ like the influence of magnetic and non-magnetic impurities on the superconducting and normal state of Sr$_2$RuO$_4$. It is clear that the physics of triplet superconductivity in Sr$_2$RuO$_4$ is still far from being understood completely and remains to be analyzed more in more detail. It is of interest to apply the theory also to superconductivity in heavy-fermion systems exhibiting spin fluctuations.

Coexistence of antiferromagnetism and superconductivity in heavy-fermion systems

We report the novel pressure ( P)–temperature ( T) phase diagrams of antiferromagnetism (AFM) and superconductivity (SC) in CeRhIn 5, CeIn 3, and CeCu 2Si 2 revealed by the nuclear quadrupole resonance measurement. In the itinerant helical magnet CeRhIn 5, we found that the Néel temperature T N is reduced at P≥1.23 GPa with an emergent pseudogap behavior. The coexistence of AFM and SC is found in a narrow P range of 1.63–1.75 GPa, followed by the onset of SC with line-node gap over a wide P window 2.1–5 GPa. In CeIn 3, the localized magnetic character is robust against the application of pressure up to P∼1.9 GPa, beyond which the system evolves into an itinerant regime in which the resistive superconducting phase emerges. We discuss the relationship between the phase diagram and the magnetic fluctuations. In CeCu 2Si 2, the SC and AFM coexist on a microscopic level once its lattice parameter is expanded. We remark that the underlying marginal AFM state is due to collective magnetic excitations in the superconducting state in CeCu 2Si 2. An interplay between AFM and SC is discussed on the SO(5) scenario that unifies AFM and SC. We suggest that the SC and AFM in CeCu 2Si 2 have a common mechanism.

Strong coupling superconductivity in heavy fermion systems

One of the primary interests of heavy fermion superconductivity, besides possible unconventional order parameters, is the possibility of a non-phonon-mediated pairing mechanism. It has proved nevertheless very difficult to find an experimental probe of this hypothesis. The upper critical field, H c 2, of UBe 13 has revealed that this compound was in an extreme strong coupling regime, characterized by a strong coupling constant λ≈15. We present pressure measurements of H c2 in UBe 13, which probe the pressure dependence of λ. The main result is that in this compound, the pairing mechanism is also responsible for a large part of the mass renormalization and cannot arise from electron–phonon interactions. It will be discussed in the framework of the actual interpretations of the heavy masses in heavy fermion systems and UBe 13 will be contrasted with the other heavy fermion superconductors.

Strong coupling superconductivity in heavy-fermion systems

We report measurements under pressure of the upper critical field of the heavy-fermion superconductor UBe 13. An interpretation in the framework of a simple strong coupling model is achieved consistently with only one arbitrary parameter: the strong coupling constant λ. We find that UBe 13 is in an extreme strong coupling regime and that the variation of λ with pressure explains the pressure dependence of the thermodynamic properties of both the normal and superconducting phases, revealing a strong interplay between the mass renormalization and the pairing mechanism.

Muon spin relaxation studies of the interplay between magnetism and superconductivity in heavy fermion systems

The interplay between magnetism and superconductivity in heavy fermion systems is discussed and the role of muon spin relaxation in elucidating these properties is emphasized. Relevant properties of all six heavy fermion superconductors are briefly surveyed and instances where superconductivity and magnetism compete, coexist and couple with one another are pointed out. Current theoretical concepts underlying these phenomena are highlighted.

Magnetism and superconductivity in heavy fermion systems

We discuss some consequences of the interplay between magnetism and superconductivity in the two heavy fermion systems URu2Si2 and UPt3, notably on the temperature dependence of the specific heat, on possible observation of Larkin-OvchinnikovFulde-Ferrel phase, and on the anisotropy of the upper critical field. We demonstrate that in UPt3, a clear double steep superconducting transition can be obtained reversibly.

D-wave superconductivity in heavy fermion systems

The most favored candidate hybrid state (E18) for superconductivity of UPt3 cannot describe the anisotropy in the upper critical field or the tetracritical point in the magnetic phase diagram. We propose here D-axial state (E2g) as the candidate, since this state is unique among the D-wave superconductors to satisfy Garg's condition necessary to have the tetracritical point in the magnetic phase diagram. In addition we find the D-axial state describes extremely well both the anisotropy of the upper critical field and the thermal conductivity in the vortex state of UPt3.

NMR study of weak magnetism and superconductivity in heavy-fermion systems

Using NMR techniques, we have investigated the superconducting and magnetic properties of the heavy-fermion superconductors (HFS), CeCu 2Si 2, and the recently discovered UM 2AL 3 (M = Ni and Pd). The NMR studies have deduced that the nature of the magnetism in HFS is varied, whereas the superconducting property possesses a rather common feature. Namely, the nuclear spin-lattice relaxation rate 1/ T 1 is well described in terms of an anisotropic energy gap model in which the gap vanishes on lines at the Fermi surface with values of 2 Δ/ k B T c = 5.0 and 5.5 for CeCu 2Si 2 and UPd 2Al 3, respectively. The unusual superconductivity coexists with the magnetism, regardless of whether it is in a static or a dynamical regime. In contrast, the NMR experiment detected no signature of an anomaly at the superconducting transition temperature in UNi 2Al 3. The interplay between magnetism and superconductivity is discussed from a comparison with other heavy-fermion superconductors.

Magnetism and superconductivity in heavy fermion systems

The normal and superconducting properties of heavy fermion compounds are reviewed. The discussion is focus on the three uranium compounds : UBe 13, UPt 3 and URu 2Si 2. Special attention is given : 1) to unusual (H.T) superconducting phase diagram as discovered in UPt 3 where two successive superconducting phases seem to occur in zero magnetic field ; 2) to the role of long range ordering as found in URu 2Si 2 and UPt 3.

Magnetism and superconductivity in heavy-fermion systems

The magnetic phase diagrams of Ce(Cu 1- x Ni x ) 2Ge 2 and UCu 4+ x Al 8- x have been explored. Both systems show a transition from local moment antiferromagnetism to a heavy-fermion state upon doping with Ni or controlled changes of stoichiometry, respectively. For UCu 4+ x Al 8- x the results of electronic transport measurements reveal that the transition into a heavy-fermion ground state is accompanied by changes in the underlying bandstructure. The transition into the superconducting state, which completes with some cooperative magnetic state, presumably heavy-fermion band magnetism, is investigated by thermal expansion and specific heat in CeCu 2Si 2.

FLUCTUATION EFFECTS AND ANISOTROPY IN UNCONVENTIONAL SUPERCONDUCTORS

The renormalization group procedure is used to study the interacting-fluctuations regime of an m-component complex order-parameter field with a cubic anisotropy of the type recently discussed group-theoretically in search for an explanation of superconductivity in heavy-fermion systems as well as in high-T c superconductors. The intrinsic magnetic fluctuations are also taken into consideration. The main scaling and the corrections to the scaling laws are completely elucidated. The cross-coupling between the real and the imaginary parts in the cubic term modifies significantly the renormalization-group flow equations in comparison with the real φ4-model with a cubic anisotropy. We find that anisotropy acts to 'stiffen' the first-order character of the transition (the Halperin-Lubensky-Ma effect).

Is there a microscopic foundation for the theory of superconductivity in heavy fermion systems? (abstract)

An attempt is made of collecting reliable information from microscopic models, which may be relevant to the problem of heavy fermion superconductivity. For this purpose direct perturbation theory with respect to hybridization between band states and local states is used to cope with the influence of strong local correlations in lattice periodic systems.1,2 Results taken into account concern the one-particle excitation spectra and the collective behavior, resulting from quasiparticle interactions, of such lattice systems. We discuss the prospects of electronic and phononic mechanisms for superconductivity and the possible resulting symmetry of the order parameter. The particular difficulties found in a microscopic treatment of superconductivity in heavy Fermion systems are pointed out and compared to standard BCS theory.