Probing the quantum critical behavior of CeCoIn5 via Hall effect measurements

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∼ k B T / 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.

Foundations of heavy-fermion superconductivity: lattice Kondo effect and Mott physics

This article overviews the development of heavy-fermion superconductivity, notably in such rare-earth-based intermetallic compounds which behave as Kondo-lattice systems. Heavy-fermion superconductivity is of unconventional nature in the sense that it is not mediated by electron-phonon coupling. Rather, in most cases the attractive interaction between charge carriers is apparently magnetic in origin. Fluctuations associated with an antiferromagnetic (AF) quantum critical point (QCP) play a major role. The first heavy-fermion superconductor CeCu2Si2 turned out to be the prototype of a larger group of materials for which the underlying, often pressure-induced, AF QCP is likely to be of a three-dimensional (3D) spin-density-wave (SDW) variety. For UBe13, the second heavy-fermion superconductor, a magnetic-field-induced 3D SDW QCP inside the superconducting phase can be conjectured. Such a 'conventional', itinerant QCP can be well understood within Landau's paradigm of order-parameter fluctuations. In contrast, the low-temperature normal-state properties of a few heavy-fermion superconductors are at odds with the Landau framework. They are characterized by an 'unconventional', local QCP which may be considered a zero-temperature 4 f-orbital selective Mott transition. Here, as concluded for YbRh2Si2, the breakdown of the Kondo effect concurring with the AF instability gives rise to an abrupt change of the Fermi surface. Very recently, superconductivity was discovered for this compound at ultra-low temperatures. Therefore, YbRh2Si2 along with CeRhIn5 under pressure provide a natural link between the large group of about fifty low-temperature heavy-fermion superconductors and other families of unconventional superconductors with substantially higher T c, e.g. the doped Mott insulators of the perovskite-type cuprates and the organic charge-transfer salts.

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.

Two-fluid model for heavy electron physics

The two-fluid model is a phenomenological description of the gradual change of the itinerant and local characters of f-electrons with temperature and other tuning parameters and has been quite successful in explaining many unusual and puzzling experimental observations in heavy electron materials. We review some of these results and discuss possible implications of the two-fluid model in understanding the microscopic origin of heavy electron physics.

Quantum critical behavior in heavy electron materials

Quantum critical behavior in heavy electron materials is typically brought about by changes in pressure or magnetic field. In this paper, we develop a simple unified model for the combined influence of pressure and magnetic field on the effectiveness of the hybridization that plays a central role in the two-fluid description of heavy electron emergence. We show that it leads to quantum critical and delocalization lines that accord well with those measured for CeCoIn5, yields a quantitative explanation of the field and pressure-induced changes in antiferromagnetic ordering and quantum critical behavior measured for YbRh2Si2, and provides a valuable framework for describing the role of magnetic fields in bringing about quantum critical behavior in other heavy electron materials.

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.

Non-Fermi liquid regimes with and without quantum criticality in Ce(1-x)Yb(x)CoIn5

One of the greatest challenges to Landau's Fermi liquid theory--the standard theory of metals--is presented by complex materials with strong electronic correlations. In these materials, non-Fermi liquid transport and thermodynamic properties are often explained by the presence of a continuous quantum phase transition that happens at a quantum critical point (QCP). A QCP can be revealed by applying pressure, magnetic field, or changing the chemical composition. In the heavy-fermion compound CeCoIn5, the QCP is assumed to play a decisive role in defining the microscopic structure of both normal and superconducting states. However, the question of whether a QCP must be present in the material's phase diagram to induce non-Fermi liquid behavior and trigger superconductivity remains open. Here, we show that the full suppression of the field-induced QCP in CeCoIn5 by doping with Yb has surprisingly little impact on both unconventional superconductivity and non-Fermi liquid behavior. This implies that the non-Fermi liquid metallic behavior could be a new state of matter in its own right rather than a consequence of the underlying quantum phase transition.

Quasiparticle entropy in the high-field superconducting phase of CeCoIn(5)

The heavy-fermion superconductor CeCoIn(5) displays an additional transition within its superconducting (SC) state, whose nature is characterized by high-precision studies of the isothermal field dependence of the entropy, derived from combined specific heat and magnetocaloric effect measurements at temperatures T≥100  mK and fields H≤12  T aligned along different directions. For any of these conditions, we do not observe an additional entropy contribution upon tuning at constant temperature by magnetic field from the homogeneous SC into the presumed Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) SC state. By contrast, for H∥[100] a reduction of entropy was found that quantitatively agrees with the expectation for spin-density-wave order without FFLO superconductivity. Our data exclude the formation of a FFLO state in CeCoIn(5) for out-of-plane field directions, where no spin-density-wave order exists.

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}.

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.

Superconductivity versus quantum criticality: what can we learn from heavy fermions?

Two quantum critical point (QCP) scenarios are being discussed for different classes of antiferromagnetic (AF) heavy-fermion (HF) systems. In the itinerant one, where AF order is of the spin-density wave (SDW) type, the heavy 'composite' charge carriers keep their integrity at the QCP. The second one implies a breakdown of the Kondo effect and a disintegration of the composite fermions at the AF QCP. We discuss two isostructural compounds as exemplary materials for these two different scenarios: CeCu(2)Si(2) exhibits a three-dimensional (3D) SDW QCP and superconductivity, presumably mediated by SDW fluctuations, as strongly suggested by recent inelastic neutron scattering experiments. In Y bRh(2)Si(2), the AF QCP is found to coincide with a Kondo-destroying one. However, in the latter compound these two QCPs can be detached by varying the average unit-cell volume, e.g. through the application of chemical pressure, as realized by partial substitution of either Ir or Co for Rh. A comparison of CeCu(2)Si(2) and Y bRh(2)Si(2) indicates that the apparent differences in quantum critical behaviour go along with disparate behaviour concerning the (non-) existence of superconductivity (SC). No sign of SC could be detected in Y bRh(2)Si(2) down to mK temperatures. A potential correlation between the specific nature of the QCP and the occurrence of SC, however, requires detailed studies on further quantum critical HF superconductors, e.g. on β-Y bAlB(4), UBe(13), CeCoIn(5) and CeRhIn(5).

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.

Dimensional crossover of quantum critical behavior in CeCoIn5

The nature of quantum criticality in CeCoIn5 is studied by low-temperature thermal expansion alpha(T). At the field-induced quantum critical point at H = 5 T a crossover scale T* approximately 0.3 K is observed, separating alpha(T)/T proportional, variant T(-1) from a weaker T(-1/2) divergence. We ascribe this change to a crossover in the dimensionality of the critical fluctuations which may be coupled to a change from unconventional to conventional quantum criticality. Disorder, whose effect on quantum criticality is studied in CeCoIn(5-x)Sn(x) (0 < or = x < or = 0.18), shifts T* towards higher temperatures.

Precursor State to Unconventional Superconductivity in CeIrIn5

We present Hall effect and magnetoresistance measurements in the heavy fermion superconductor CeIrIn(5). At low temperature, a Kondo coherent state is established. Deviations from Kohler's rule and a quadratic temperature dependence of the cotangent of the Hall angle are reminiscent of properties observed in the high-temperature superconducting cuprates. A striking observation pertains to the presence of a precursor state--characterized by a change in the Hall mobility--that precedes the superconductivity in this material, in similarity to the pseudogap in the cuprate superconductors.

Thermoelectric response near a quantum critical point: the case of CeCoIn5

We present a study of thermoelectric coefficients in CeCoIn5 down to 0.1 K and up to 16 T in order to probe the thermoelectric signatures of quantum criticality. In the vicinity of the field-induced quantum critical point, the Nernst coefficient nu exhibits a dramatic enhancement without saturation down to the lowest measured temperature. The dimensionless ratio of the Seebeck coefficient to the electronic specific heat shows a minimum at a temperature close to threshold of the quasiparticle formation. Close to Tc(H), in the vortex-liquid state, the Nernst coefficient behaves anomalously in puzzling contrast with other superconductors and standard vortex dynamics.