Avoided antiferromagnetic order and quantum critical point in CeCoIn5

Stranger than metals

In traditional metals, the temperature ( T ) dependence of electrical resistivity vanishes at low or high T , albeit for different reasons. Here, we review a class of materials, known as “strange” metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T . We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

Are Heavy Fermion Strange Metals Planckian?

Strange metal behavior refers to a linear temperature dependence of the electrical resistivity that is not due to electron–phonon scattering. It is seen in numerous strongly correlated electron systems, from the heavy fermion compounds, via transition metal oxides and iron pnictides, to magic angle twisted bi-layer graphene, frequently in connection with unconventional or “high temperature” superconductivity. To achieve a unified understanding of these phenomena across the different materials classes is a central open problem in condensed matter physics. Tests whether the linear-in-temperature law might be dictated by Planckian dissipation—scattering with the rate ∼kBT/ℏ—are receiving considerable attention. Here we assess the situation for strange metal heavy fermion compounds. They allow to probe the regime of extreme correlation strength, with effective mass or Fermi velocity renormalizations in excess of three orders of magnitude. Adopting the same procedure as done in previous studies, i.e., assuming a simple Drude conductivity with the above scattering rate, we find that for these strongly renormalized quasiparticles, scattering is much weaker than Planckian, implying that the linear temperature dependence should be due to other effects. We discuss implications of this finding and point to directions for further work.

Evidence for a delocalization quantum phase transition without symmetry breaking in CeCoIn5

The study of quantum phase transitions that are not clearly associated with broken symmetry is a major effort in condensed matter physics, particularly in regard to the problem of high-temperature superconductivity, for which such transitions are thought to underlie the mechanism of superconductivity itself. Here we argue that the putative quantum critical point in the prototypical unconventional superconductor CeCoIn₅ is characterized by the delocalization of electrons in a transition that connects two Fermi surfaces of different volumes, with no apparent broken symmetry. Drawing on established theory of f-electron metals, we discuss an interpretation for such a transition that involves the fractionalization of spin and charge, a model that effectively describes the anomalous transport behavior we measured for the Hall effect.

Point-contact spectroscopy of heavy fermion superconductors Ce2PdIn8and Ce3PdIn11in comparison with CeCoIn5

We report point-contact spectroscopy measurements on heavy fermion cousins CeCoIn₅, Ce₂PdIn₈and Ce₃PdIn₁₁to systematically study the hybridization betweenfand conduction electrons. Below a temperatureT*, the spectrum of each compound exhibits an evolving Fano-like conductance shape, superimposed on a sloping background, that suggests the development of hybridization between localfand itinerant conduction electrons in the coherent heavy fermion state belowT*. We present a quantitative analysis of the conductance curves with a two-channel model to compare the tunneling process between normal metallic silver particles in our soft point-contact and heavy-fermion single crystals CeCoIn₅, Ce₂PdIn₈and Ce₃PdIn₁₁.

Interplay of the Spin Density Wave and a Possible Fulde-Ferrell-Larkin-Ovchinnikov State in CeCoIn_{5} in Rotating Magnetic Field

The d-wave superconductor CeCoIn_{5} has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the a-b plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal c axis. It is important to understand the interplay between the SDW and a possible FFLO state in CeCoIn_{5}, as the mere existence of an SDW does not necessarily exclude an FFLO state. Here, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in CeCoIn_{5} is stabilized when the field is directed close to the a-b plane. When the field is rotated toward the c axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the a-b plane and an enhancement of thermal conductivity when field is close to the c axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the c axis.

Pressure Effects on the Magnetic Phase Diagram of the CeNMSb2 (NM: Au and Ag): A DFT Study

We explore the influence of pressure on the magnetic ground state of the heavy-fermion antiferromagnet (ferromagnet) CeAuSb2 (CeAgSb2) using first-principles calculations. The total-energy differences obtained by including the spin-orbit interactions and the on-site Coulomb potential for the Ce-derived 4f-orbitals are necessary to realize the accurate magnetic ground state of CeNMSb2 (NM: Au and Ag). According to our results, the appearance of a new magnetic phase of CeAuSb2 (CeAgSb2) at the pressure of 2.1 GPa (3.5 GPa) is due to the rotation of the magnetic easy axis from the <001> to the <100> direction. Additionally, our data confirm that CeAgSb2 is antiferromagnetic (AFM) above a critical pressure Pc, and such a tendency is expected for CeAuSb2 and remains to be seen. Through the spin-orbit-coupling Hamiltonian and detailed information on the occupation of individual 4f-orbitals of the Ce atom obtained by the electronic-structure calculations, we can deduce the rotation of the magnetic easy axis upon the application of pressure. According to the present and previous studies, the differences among the magnetic properties of CeNMSb2 (NM: Cu, Ag and Au) compounds are not due to the different noble metals, but due to the subtle differences in the relative position of Ce atoms and, in turn, different occupations of Ce 4f-orbitals.

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 C_el/T is strongly peaked at p* (where C_el 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 point^3-5, 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.

Tomonaga-Luttinger liquid behavior and spinon confinement in YbAlO3

Low dimensional quantum magnets are interesting because of the emerging collective behavior arising from strong quantum fluctuations. The one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet is a paradigmatic example, whose low-energy excitations, known as spinons, carry fractional spin S = 1/2. These fractional modes can be reconfined by the application of a staggered magnetic field. Even though considerable progress has been made in the theoretical understanding of such magnets, experimental realizations of this low-dimensional physics are relatively rare. This is particularly true for rare-earth-based magnets because of the large effective spin anisotropy induced by the combination of strong spin-orbit coupling and crystal field splitting. Here, we demonstrate that the rare-earth perovskite YbAlO3 provides a realization of a quantum spin S = 1/2 chain material exhibiting both quantum critical Tomonaga-Luttinger liquid behavior and spinon confinement-deconfinement transitions in different regions of magnetic field-temperature phase diagram.

Anomalous Change in the de Haas-van Alphen Oscillations of CeCoIn_{5} at Ultralow Temperatures

We perform de Haas-van Alphen (dHvA) measurements of the heavy-fermion superconductor CeCoIn_{5} down to 2 mK above the upper critical field. We find that the dHvA amplitudes show an anomalous suppression, concomitantly with a shift of the dHvA frequency, below the transition temperature T_{n}=20  mK. We suggest that the change is owing to magnetic breakdown caused by a field-induced antiferromagnetic (AFM) state emerging below T_{n}, revealing the origin of the field-induced quantum critical point (QCP) in CeCoIn_{5}. The field dependence of T_{n} is found to be very weak for 7-10 T, implying that an enhancement of AFM order by suppressing the critical spin fluctuations near the AFM QCP competes with the field suppression effect on the AFM phase. We suggest that the appearance of a field-induced AFM phase is a generic feature of unconventional superconductors, which emerge near an AFM QCP, including CeCoIn_{5}, CeRhIn_{5}, and high-T_{c} cuprates.

Visualizing heavy fermion confinement and Pauli-limited superconductivity in layered CeCoIn5

Layered material structures play a key role in enhancing electron–electron interactions to create correlated metallic phases that can transform into unconventional superconducting states. The quasi-two-dimensional electronic properties of such compounds are often inferred indirectly through examination of bulk properties. Here we use scanning tunneling microscopy to directly probe in cross-section the quasi-two-dimensional electronic states of the heavy fermion superconductor CeCoIn₅. Our measurements reveal the strong confined nature of quasiparticles, anisotropy of tunneling characteristics, and layer-by-layer modulated behavior of the precursor pseudogap gap phase. In the interlayer coupled superconducting state, the orientation of line defects relative to the d-wave order parameter determines whether in-gap states form due to scattering. Spectroscopic imaging of the anisotropic magnetic vortex cores directly characterizes the short interlayer superconducting coherence length and shows an electronic phase separation near the upper critical in-plane magnetic field, consistent with a Pauli-limited first-order phase transition into a pseudogap phase.

The electronic properties along the out-of-plane direction of layered materials are often inferred indirectly. Here, Gyenis et al. directly probe in cross-section the quasi-two-dimensional correlated electronic states of the heavy fermion superconductor CeCoIn₅.

Universal linear-temperature resistivity: possible quantum diffusion transport in strongly correlated superconductors

The strongly correlated electron fluids in high temperature cuprate superconductors demonstrate an anomalous linear temperature (T) dependent resistivity behavior, which persists to a wide temperature range without exhibiting saturation. As cooling down, those electron fluids lose the resistivity and condense into the superfluid. However, the origin of the linear-T resistivity behavior and its relationship to the strongly correlated superconductivity remain a mystery. Here we report a universal relation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d{\boldsymbol{\rho }}/{\boldsymbol{dT}}=({{\boldsymbol{\mu }}}_{{\bf{0}}}{{\boldsymbol{k}}}_{{\boldsymbol{B}}}/{\boldsymbol{\hslash }})\,{{\boldsymbol{\lambda }}}_{{\boldsymbol{L}}}^{{\bf{2}}}$$\end{document}dρ/dT=(μ0kB/ℏ)λL2, which bridges the slope of the linear-T-dependent resistivity (dρ/dT) to the London penetration depth λ_L at zero temperature among cuprate superconductor Bi₂Sr₂CaCu₂O_8+δ and heavy fermion superconductors CeCoIn₅, where μ₀ is vacuum permeability, k_B is the Boltzmann constant and ħ is the reduced Planck constant. We extend this scaling relation to different systems and found that it holds for other cuprate, pnictide and heavy fermion superconductors as well, regardless of the significant differences in the strength of electronic correlations, transport directions, and doping levels. Our analysis suggests that the scaling relation in strongly correlated superconductors could be described as a hydrodynamic diffusive transport, with the diffusion coefficient (D) approaching the quantum limit D ~ ħ/m*, where m* is the quasi-particle effective mass.

Exotic magnetic states in Pauli-limited superconductors

Magnetism and superconductivity compete or interact in complex and intricate ways. Here we review the special case where novel magnetic phenomena appear due to superconductivity, but do not exist without it. Such states have recently been identified in unconventional superconductors. They are different from the mere coexistence of magnetic order and superconductivity in conventional superconductors, or from competing magnetic and superconducting phases in many materials. We describe the recent progress in the study of such exotic magnetic phases, and articulate the many open questions in this field.

Synthetically tuned structural variations in CePdxGe2−x(x = 0.21, 0.32, 0.69) towards diverse physical properties

Three structural variations of CePd_xGe_2−xwith versatile properties were synthesized by varying the Pd : Ge ratio.

Theory of scanning tunneling spectroscopy: from Kondo impurities to heavy fermion materials

Kondo systems ranging from the single Kondo impurity to heavy fermion materials present us with a plethora of unconventional properties whose theoretical understanding is still one of the major open problems in condensed matter physics. Over the last few years, groundbreaking scanning tunneling spectroscopy (STS) experiments have provided unprecedented new insight into the electronic structure of Kondo systems. Interpreting the results of these experiments-the differential conductance and the quasi-particle interference spectrum-however, has been complicated by the fact that electrons tunneling from the STS tip into the system can tunnel either into the heavy magnetic moment or the light conduction band states. In this article, we briefly review the theoretical progress made in understanding how quantum interference between these two tunneling paths affects the experimental STS results. We show how this theoretical insight has allowed us to interpret the results of STS experiments on a series of heavy fermion materials providing detailed knowledge of their complex electronic structure. It is this knowledge that is a conditio sine qua non for developing a deeper understanding of the fascinating properties exhibited by heavy fermion materials, ranging from unconventional superconductivity to non-Fermi-liquid behavior in the vicinity of quantum critical points.

Super-heavy electron material as metallic refrigerant for adiabatic demagnetization cooling

Low-temperature refrigeration is of crucial importance in fundamental research of condensed matter physics, because the investigations of fascinating quantum phenomena, such as superconductivity, superfluidity, and quantum criticality, often require refrigeration down to very low temperatures. Currently, cryogenic refrigerators with (3)He gas are widely used for cooling below 1 K. However, usage of the gas has been increasingly difficult because of the current worldwide shortage. Therefore, it is important to consider alternative methods of refrigeration. We show that a new type of refrigerant, the super-heavy electron metal YbCo2Zn20, can be used for adiabatic demagnetization refrigeration, which does not require (3)He gas. This method has a number of advantages, including much better metallic thermal conductivity compared to the conventional insulating refrigerants. We also demonstrate that the cooling performance is optimized in Yb1-x Sc x Co2Zn20 by partial Sc substitution, with x ~ 0.19. The substitution induces chemical pressure that drives the materials to a zero-field quantum critical point. This leads to an additional enhancement of the magnetocaloric effect in low fields and low temperatures, enabling final temperatures well below 100 mK. This performance has, up to now, been restricted to insulators. For nearly a century, the same principle of using local magnetic moments has been applied for adiabatic demagnetization cooling. This study opens new possibilities of using itinerant magnetic moments for cryogen-free refrigeration.

Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn_{5}

The thermal conductivity κ of the heavy-fermion metal CeCoIn_{5} was measured in the normal and superconducting states as a function of temperature T and magnetic field H, for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field H_{c2}, κ/T is found to increase as T→0, just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of κ/T with field reveals that the electron-electron scattering (or transport mass m^{⋆}) of those unpaired electrons diverges as H→H_{c2} from below, in the same way that it does in the normal state as H→H_{c2} from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn_{5} at H^{⋆}=H_{c2} even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k-space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations.

From Kondo lattices to Kondo superlattices

The realization of new classes of ground states in strongly correlated electron systems continues to be a major issue in condensed matter physics. Heavy fermion materials, whose electronic structure is essentially three-dimensional, are one of the most suitable systems for obtaining novel electronic states because of their intriguing properties associated with many-body effects. Recently, a state-of-the-art molecular beam epitaxy technique was developed to reduce the dimensionality of heavy electron systems by fabricating artificial superlattices that include heavy fermion compounds; this approach can produce a new type of electronic state in two-dimensional (2D) heavy fermion systems. In artificial superlattices of the antiferromagnetic heavy fermion compound CeIn3 and the conventional metal LaIn3, the magnetic order is suppressed by a reduction in the thickness of the CeIn3 layers. In addition, the 2D confinement of heavy fermions leads to enhancement of the effective electron mass and deviation from the standard Fermi liquid electronic properties, which are both associated with the dimensional tuning of quantum criticality. In the superconducting superlattices of the heavy fermion superconductor CeCoIn5 and nonmagnetic metal YbCoIn5, signatures of superconductivity are observed even at the thickness of one unit-cell layer of CeCoIn5. The most remarkable feature of this 2D heavy fermion superconductor is that the thickness reduction of the CeCoIn5 layers changes the temperature and angular dependencies of the upper critical field significantly. This result is attributed to a substantial suppression of the Pauli pair-breaking effect through the local inversion symmetry breaking at the interfaces of CeCoIn5 block layers. The importance of the inversion symmetry breaking in this system has also been supported by site-selective nuclear magnetic resonance spectroscopy, which can resolve spectroscopic information from each layer separately, even within the same CeCoIn5 block layer. In addition, recent experiments involving CeCoIn5/YbCoIn5 superlattices have shown that the degree of the inversion symmetry breaking and, in turn, the Rashba splitting are controllable, offering the prospect of achieving even more fascinating superconducting states. Thus, these Kondo superlattices pave the way for the exploration of unconventional metallic and superconducting states.

Nodal to nodeless superconducting energy-gap structure change concomitant with fermi-surface reconstruction in the heavy-fermion compound CeCoIn(5)

The London penetration depth λ(T) was measured in single crystals of Ce_{1-x}R_{x}CoIn_{5}, R=La, Nd, and Yb down to T_{min}≈50  mK (T_{c}/T_{min}∼50) using a tunnel-diode resonator. In the cleanest samples Δλ(T) is best described by the power law Δλ(T)∝T^{n}, with n∼1, consistent with the existence of line nodes in the superconducting gap. Substitutions of Ce with La, Nd, and Yb lead to similar monotonic suppressions of T_{c}; however, the effects on Δλ(T) differ. While La and Nd substitution leads to an increase in the exponent n and saturation at n∼2, as expected for a dirty nodal superconductor, Yb substitution leads to n>3, suggesting a change from nodal to nodeless superconductivity. This superconducting gap structure change happens in the same doping range where changes of the Fermi-surface topology were reported, implying that the nodal structure and Fermi-surface topology are closely linked.

Direct evidence for a magnetic f-electron-mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn5

To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high-temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference imaging to reveal quantitatively the momentum space (k-space) structure of the f-electron magnetic interactions of CeCoIn5. Then, by solving the superconducting gap equations on the two heavy-fermion bands Ek(α,β) with these magnetic interactions as mediators of the Cooper pairing, we derive a series of quantitative predictions about the superconductive state. The agreement found between these diverse predictions and the measured characteristics of superconducting CeCoIn5 then provides direct evidence that the heavy-fermion Cooper pairing is indeed mediated by f-electron magnetism.

X-ray photoemission study of CeTIn(5) (T = Co, Rh, Ir)

We investigated CeTIn5 (T = Co, Rh, Ir) using temperature- and angle-dependent x-ray photoemission spectroscopy. The Ce 3d core level has a very similar shape for all three materials and is indicative of weak f-hybridization. The spectra were analyzed using a simplified version of the Anderson impurity model, which yields a Ce 4f occupancy that is larger than 0.9. The temperature dependence shows a continuous, irreversible and exclusive broadening of the Ce 3d peaks, due to oxidation of Ce at the surface.

Zero-field quantum critical point in CeCoIn5

Quantum criticality in the normal and superconducting states of the heavy-fermion metal CeCoIn5 is studied by measurements of the magnetic Grüneisen ratio ΓH and specific heat in different field orientations and temperatures down to 50 mK. A universal temperature over magnetic field scaling of ΓH in the normal state indicates a hidden quantum critical point at zero field. Within the superconducting state, the quasiparticle entropy at constant temperature increases upon reducing the field towards zero, providing additional evidence for zero-field quantum criticality.

Vortex lattice studies in CeCoIn5 with H is orthogonal to c

We present small angle neutron scattering studies of the vortex lattice (VL) in CeCoIn5 with magnetic fields applied parallel (H) to the antinodal [100] and nodal [110] directions. For H is parallel to [100], a single VL orientation is observed, while a 90° reorientation transition is found for H is parallel to [110]. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, Γ=2.0±0.05. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for H is parallel to [001]. At high fields, above which the upper critical field (H(c2)) becomes a first-order transition, an increased disordering of the VL is observed.

Strong magnetic fluctuations in a superconducting state of CeCoIn5

We show results on the vortex core dissipation through current-voltage measurements under applied pressure and magnetic field in the superconducting phase of CeCoIn{5}. We find that as soon as the system becomes superconducting, the vortex core resistivity increases sharply as the temperature and magnetic field decrease. The sharp increase in flux-flow resistivity is due to quasiparticle scattering on critical antiferromagnetic fluctuations. The strength of magnetic fluctuations below the superconducting transition suggests that magnetism is complementary to superconductivity and therefore must be considered in order to fully account for the low-temperature properties of CeCoIn{5}.

Magnetic-field-induced enhancements of nuclear spin-lattice relaxation rates in the heavy-fermion superconductor CeCoIn5 using 59Co nuclear magnetic resonance

(59)Co nuclear spin-lattice relaxation has been measured for the heavy-fermion superconductor CeCoIn(5) in a range of applied fields directed parallel to the c axis. An enhanced normal-state relaxation rate, observed at low temperatures and fields just above H(c2)(0), is taken as a direct measure of the dynamical susceptibility and provides microscopic evidence for an antiferromagnetic instability. The results are well described using the self-consistent renormalized theory for two-dimensional antiferromagnetic spin fluctuations, and parameters obtained in the analysis are applied to previously reported specific heat and thermal expansion data with good agreement.

Antiferromagnetic order in Pauli-limited unconventional superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn(5). We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.

Antiferroquadrupolar ordering in a Pr-based superconductor PrIr(2)Zn(20)

An antiferroquadrupolar ordering at T(Q)=0.11  K has been found in a Pr-based superconductor PrIr(2)Zn(20). The measurements of specific heat and magnetization revealed the non-Kramers Γ(3) doublet ground state with the quadrupolar degrees of freedom. The specific heat exhibits a sharp peak at T(Q)=0.11  K. The increment of T(Q) in magnetic fields and the anisotropic B-T phase diagram are consistent with the antiferroquadrupolar ordered state below T(Q). The entropy release at T(Q) is only 20% of Rln2, suggesting that the quadrupolar fluctuations play a role in the formation of the superconducting pairs below T(c)=0.05  K.

Electronic inhomogeneity in a Kondo lattice

Inhomogeneous electronic states resulting from entangled spin, charge, and lattice degrees of freedom are hallmarks of strongly correlated electron materials; such behavior has been observed in many classes of d -electron materials, including the high-T c copper-oxide superconductors, manganites, and most recently the iron–pnictide superconductors. The complexity generated by competing phases in these materials constitutes a considerable theoretical challenge—one that still defies a complete description. Here, we report a manifestation of electronic inhomogeneity in a strongly correlated f -electron system, using CeCoIn5 as an example. A thermodynamic analysis of its superconductivity, combined with nuclear quadrupole resonance measurements, shows that nonmagnetic impurities (Y, La, Yb, Th, Hg, and Sn) locally suppress unconventional superconductivity, generating an inhomogeneous electronic “Swiss cheese” due to disrupted periodicity of the Kondo lattice. Our analysis may be generalized to include related systems, suggesting that electronic inhomogeneity should be considered broadly in Kondo lattice materials.

Correlated electron state in Ce(1-x)Yb(x)CoIn5 stabilized by cooperative valence fluctuations

X-ray diffraction, electrical resistivity, magnetic susceptibility, and specific heat measurements on Ce(1-x)Yb(x)CoIn5 (0≤x≤1) reveal that many of the characteristic features of the x=0 correlated electron state are stable for x≤0.775 and that phase separation occurs for x>0.775. The stability of the correlated electron state is apparently due to cooperative behavior of the Ce and Yb ions, involving their unstable valences. Low-temperature non-Fermi liquid behavior is observed and varies with x, even though there is no readily identifiable quantum critical point. The superconducting critical temperature T(c) decreases linearly with x towards 0 K as x→1, in contrast with other HF superconductors where T(c) scales with T(coh).

Fluctuations in a superconducting quantum critical point of multi-band metals

In multi-band metals quasi-particles arising from different atomic orbitals coexist at a common Fermi surface. Superconductivity in these materials may appear due to interactions within a band (intra-band) or among the distinct metallic bands (inter-band). Here we consider the suppression of superconductivity in the intra-band case due to hybridization. The fluctuations at the superconducting quantum critical point (SQCP) are obtained by calculating the response of the system to a fictitious space- and time-dependent field, which couples to the superconducting order parameter. The appearance of superconductivity is related to the divergence of a generalized susceptibility. For a single-band superconductor this coincides with the Thouless criterion. For fixed chemical potential and large hybridization, the superconducting state has many features in common with breached pair superconductivity with unpaired electrons at the Fermi surface. The T = 0 phase transition from the superconductor to the normal state is in the universality class of the density-driven Bose-Einstein condensation. For a fixed number of particles and in the strong coupling limit, the system still has an instability to the normal state with increasing hybridization.

Magnetic structure of the antiferromagnetic Fulde-Ferrell-Larkin-Ovchinnikov state

The properties of incommensurate antiferromagnetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are studied by solving the Bogoliubov-de Gennes (BdG) equations. The relationship between the electronic structure and the magnetic structure is clarified. We find that the magnetic structure in the AFM-FFLO state includes three cases. (I) In the strongly localized case, the AFM staggered moment is confined into the FFLO nodal planes where the superconducting order parameter vanishes. (II) In the weakly localized case, the AFM staggered moment appears in the whole spatial region, and its magnitude is enhanced around the FFLO nodal planes. (III) In the extended case, the AFM staggered moment is nearly homogeneous and slightly suppressed in the vicinity of the FFLO nodal planes. The structure of Bragg peaks in the momentum resolved structure factor is studied in each case. We discuss the possibility of an AFM-FFLO state in the heavy fermion superconductor CeCoIn5 by comparing these results with the neutron scattering data of CeCoIn5. Experimentally the magnetic structure and its dependence on the magnetic field orientation in the high-field superconducting phase of CeCoIn5 are consistent with case (II).

Towards the identification of a quantum critical line in the (p, B) phase diagram of CeCoIn5 with thermal-expansion measurements

The low-temperature thermal expansion of CeCoIn(5) single crystals measured parallel and perpendicular to magnetic fields B oriented along the c axis yields the volume thermal-expansion coefficient β. Considerable deviations of β(T) from Fermi-liquid behavior occur already within the superconducting region of the (B, T) phase diagram and become maximal at the upper critical field B(c2)(0). However, β(T) and the Grüneisen parameter Γ are incompatible with a quantum critical point at B(c2)(0), but allow for a quantum criticality shielded by superconductivity and extending to negative pressures for B<B(c2)(0). We construct a tentative (p, B, T) phase diagram of CeCoIn(5) suggesting a quantum critical line in the (p, B) plane.

Quantum criticality in inter-band superconductors

In fermionic systems with different types of quasi-particles, attractive interactions can give rise to exotic superconducting states, such as pair density wave (PDW) superconductivity and breached pairing. In recent years the search for these new types of ground states in cold atoms and in metallic systems has been intense. In the case of metals the different quasi-particles may be the up and down spin bands in an external magnetic field or bands arising from distinct atomic orbitals that coexist at a common Fermi surface. These systems present a complex phase diagram as a function of the difference between the Fermi wavevectors of the different bands. This can be controlled by external means, varying the density in the two-component cold atom system or, in a metal, by applying an external magnetic field or pressure. Here we study the zero temperature instability of the normal system as the Fermi wavevector mismatch of the quasi-particles (bands) is reduced and find a second order quantum phase transition to a PDW superconducting state. From the nature of the quantum critical fluctuations close to the superconducting quantum critical point (SQCP), we obtain its dynamic critical exponent. It turns out to be z = 2 and this allows us to fully characterize the SQCP for dimensions d ≥ 2.

Evidence for a magnetically driven superconducting Q phase of CeCoIn5

We have studied the magnetic order inside the superconducting phase of CeCoIn5 for fields along the [1 0 0] crystallographic direction using neutron diffraction. We find a spin-density wave order with an incommensurate modulation Q=(q,q,1/2) and q=0.45(1), which within our experimental uncertainty is indistinguishable from the spin-density wave found for fields applied along [1 -1 0]. The magnetic order is thus modulated along the lines of nodes of the d{x{2}-y{2}} superconducting order parameter, suggesting that it is driven by the electron nesting along the superconducting line nodes. We postulate that the onset of magnetic order leads to reconstruction of the superconducting gap function and a magnetically induced pair density wave.

Quantum criticality and nodal superconductivity in the FeAs-based superconductor KFe2As2

The in-plane resistivity rho and thermal conductivity kappa of the FeAs-based superconductor KFe2As2 single crystal were measured down to 50 mK. We observe non-Fermi-liquid behavior rho(T) approximately T{1.5} at H{c{2}}=5 T, and the development of a Fermi liquid state with rho(T) approximately T{2} when further increasing the field. This suggests a field-induced quantum critical point, occurring at the superconducting upper critical field H{c{2}}. In zero field, there is a large residual linear term kappa{0}/T, and the field dependence of kappa_{0}/T mimics that in d-wave cuprate superconductors. This indicates that the superconducting gaps in KFe2As2 have nodes, likely d-wave symmetry. Such a nodal superconductivity is attributed to the antiferromagnetic spin fluctuations near the quantum critical point.

Role of f electrons in the Fermi surface of the heavy fermion superconductor beta-YbAlB4

We present a detailed quantum oscillation study of the Fermi surface of the recently discovered Yb-based heavy fermion superconductor beta-YbAlB4. We compare the data, obtained at fields from 10 to 45 T, to band structure calculations performed using the local density approximation. Analysis of the data suggests that f holes participate in the Fermi surface up to the highest magnetic fields studied. We comment on the significance of these findings for the unconventional superconducting properties of this material.

The Nernst effect and the boundaries of the Fermi liquid picture

Following the observation of an anomalous Nernst signal in cuprates, the Nernst effect has been explored in a variety of metals and superconductors during the past few years. This paper reviews the results obtained during this exploration, focusing on the Nernst response of normal quasi-particles as opposed to the one generated by superconducting vortices or by short-lived Cooper pairs. Contrary to what has been often assumed, the so-called Sondheimer cancelation does not imply a negligible Nernst response in a Fermi liquid. In fact, the amplitude of the Nernst response measured in various metals in the low-temperature limit is scattered over six orders of magnitude. According to the data, this amplitude is roughly set by the ratio of electron mobility to Fermi energy, in agreement with the implications of semi-classical transport theory.

Andreev reflection and order parameter symmetry in heavy-fermion superconductors: the case of CeCoIn(5)

We review the current status of Andreev reflection spectroscopy on the heavy fermions, mostly focusing on the case of CeCoIn(5), a heavy-fermion superconductor with a critical temperature of 2.3 K. This is a well-established technique to investigate superconducting order parameters via measurements of the differential conductance from nanoscale metallic junctions. Andreev reflection is clearly observed in CeCoIn(5) as in other heavy-fermion superconductors. Considering the large mismatch in Fermi velocities, this observation seemingly appears to disagree with the Blonder-Tinkham-Klapwijk (BTK) theory. The measured Andreev signal is highly reduced to the order of maximum ∼13% compared to the theoretically predicted value (100%). The background conductance exhibits a systematic evolution in its asymmetry over a wide temperature range from above the heavy-fermion coherence temperature down to well below the superconducting transition temperature. Analysis of the conductance spectra using the extended BTK model provides a qualitative measure for the superconducting order parameter symmetry, which is determined to be the d(x(2)-y(2)) wave in CeCoIn(5). It is found that existing models do not quantitatively account for the data, which we attribute to the intrinsic properties of the heavy fermions. A substantial body of experimental data and extensive theoretical analysis point to the existence of two-fluid components in CeCoIn(5) and other heavy-fermion compounds. A phenomenological model is proposed employing a Fano interference effect between two conductance channels in order to explain both the conductance asymmetry and the reduced Andreev signal. This model appears plausible not only because it provides good fits to the data but also because it is highly likely that the electrical conduction occurs via two channels, one into the heavy-electron liquid and the other into the conduction electron continuum. Further experimental and theoretical investigations will shed new light on the mechanism of how the coherent heavy-electron liquid emerges out of the Kondo lattice, a prototypical strongly correlated electron system. Unresolved issues and future directions are also discussed.

Pressure induced FFLO instability in multi-band superconductors

Multi-band systems such as inter-metallic and heavy fermion compounds have quasi-particles arising from different orbitals at their Fermi surface. Since these quasi-particles have different masses or densities, there is a natural mismatch of the Fermi wavevectors associated with different orbitals. This makes these materials potential candidates to observe exotic superconducting phases as Sarma or FFLO phases, even in the absence of an external magnetic field. The distinct orbitals coexisting at the Fermi surface are generally hybridized and their degree of mixing can be controlled by external pressure. In this work we investigate the existence of an FFLO type of phase in a two-band BCS superconductor controlled by hybridization. At zero temperature, as hybridization (pressure) increases we find that the BCS state becomes unstable with respect to an inhomogeneous superconducting state characterized by a single wavevector q.

Apparent violation of the Wiedemann-Franz law near a magnetic field tuned metal-antiferromagnetic quantum critical point

The temperature dependences of the interlayer electrical and thermal resistivity in a layered metal are calculated for Fermi liquid quasiparticles which are scattered inelastically by two-dimensional antiferromagnetic spin fluctuations. Both resistivities have a linear temperature dependence over a broad temperature range. Extrapolations to zero temperature made from this linear-T range give values that appear to violate the Wiedemann-Franz law. However, below a low-temperature scale, which becomes small close to the critical point, a recovery of this law occurs. Our results describe recent measurements on CeCoIn5 near a magnetic field-induced quantum phase transition. Hence, the experiments do not necessarily imply a non-Fermi liquid ground state.

Multigap superconductivity in the heavy-Fermion system CeCoIn5

New thermal conductivity experiments on the heavy-fermion superconductor CeCoIn5 down to 10 mK rule out the suggested existence of unpaired electrons. Moreover, they reveal strong multigap effects with a remarkably low "critical" field Hc2S for the small gap band, showing that the complexity of heavy-fermion band structure has a direct impact on their response under magnetic field.

Anisotropic effect of Cd and Hg doping on the Pauli limited superconductor CeCoIn5

We studied the effect of impurity on the first order superconducting (SC) transition and the high field-low temperature (HFLT) SC state of CeCoIn5 by measuring the specific heat of CeCo(In1-xCdx)_{5} with x=0.0011, 0.0022, and 0.0033 and CeCo(In1-xHgx)_{5} with x=0.000 16, 0.000 32, and 0.000 48 at temperatures down to 0.1 K and fields up to 14 T. Cd substitution rapidly suppresses the crossover temperature T0, where the SC transition changes from second to first order, to T=0 K with x=0.0022 for H parallel[100], while it remains roughly constant up to x=0.0033 for H parallel[001]. The associated anomaly of the proposed FFLO state in Hg-doped samples is washed out by x=0.000 48, while remaining at the same temperature, indicating high sensitivity of that state to impurities. We interpret these results as supporting the nonmagnetic, possibly FFLO, origin of the HFLT state in CeCoIn5.

Logarithmic Fermi-liquid breakdown in NbFe2

The d-electron low temperature magnet NbFe2 is poised near the threshold of magnetism at ambient pressure, and can be tuned across the associated quantum critical point by adjusting the precise stoichiometry within the Nb1-yFe2+y homogeneity range. In a nearly critical single crystal (y= -0.01), we observe a T3/2 power-law dependence of the resistivity rho on temperature T and a logarithmic temperature dependence of the Sommerfeld coefficient gamma=C/T of the specific heat capacity C over nearly 2 orders of magnitude in temperature, extending down to 0.1 K.

Thermal conductivity evidence for a dx2-y2 pairing symmetry in the heavy-fermion CeIrIn5 superconductor

The phase diagram of the quasi-2D Ce(Ir,Rh)In5 system contains two distinct superconducting domes. By the thermal transport measurements in rotating magnetic fields H, we pinned down the superconducting gap structure of CeIrIn5 in the second dome, located distant from the first dome in proximity to an antiferromagnetic quantum critical point. Clear fourfold oscillation was observed when H is rotated within the ab plane, while no oscillation was observed within the bc plane. In sharp contrast to previous reports, our results are most consistent with dx2-y2 symmetry, implying that the superconductivity in the second phase is also mediated by antiferromagnetic spin fluctuations.

Field-induced quantum critical route to a Fermi liquid in high-temperature superconductors

In high-transition-temperature (T(c)) superconductivity, charge doping is a natural tuning parameter that takes copper oxides from the antiferromagnet to the superconducting region. In the metallic state above T(c), the standard Landau's Fermi-liquid theory of metals as typified by the temperature squared (T(2)) dependence of resistivity appears to break down. Whether the origin of the non-Fermi-liquid behavior is related to physics specific to the cuprates is a fundamental question still under debate. We uncover a transformation from the non-Fermi-liquid state to a standard Fermi-liquid state driven not by doping but by magnetic field in the overdoped high-T(c) superconductor Tl(2)Ba(2)CuO(6+x). From the c-axis resistivity measured up to 45 T, we show that the Fermi-liquid features appear above a sufficiently high field that decreases linearly with temperature and lands at a quantum critical point near the superconductivity's upper critical field-with the Fermi-liquid coefficient of the T(2) dependence showing a power-law diverging behavior on the approach to the critical point. This field-induced quantum criticality bears a striking resemblance to that in quasi-two-dimensional heavy-Fermion superconductors, suggesting a common underlying spin-related physics in these superconductors with strong electron correlations.