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

A high resolution dilatometer using optical fiber interferometer

We introduce a high-performance differential dilatometer based on an all-fiber Michelson interferometer at cryogenic temperature with 10-10 resolution in δL/L. It resolves the linear thermal expansion coefficient by measuring the oscillating changes of sample thickness and sample temperature with the interferometer and in situ thermometer, respectively. By measuring the linear thermal expansion coefficient α near the antiferromagnetic transition region of BaFe2As2 as a demonstration, we show that our dilatometer is able to measure thin samples with sub-pm-level length change resolution and mK-level temperature resolution. Despite the residual background thermal expansion of a few nm/K in the measurement results, our new dilatometer is still a powerful tool for the study of phase transition in condensed matter physics, especially has significant advantages in fragile materials with sub-100 μm thickness and being integrated with multiple synchronous measurements and tuning thanks to its extremely high resolution and contactless nature. The prototype design of this setup can be further improved in many aspects for specific applications.

The scaled-invariant Planckian metal and quantum criticality in Ce1-xNdxCoIn5

The mysterious Planckian metal state, showing perfect T-linear resistivity associated with universal scattering rate, 1/τ = αk_BT/ℏ with α ~ 1, has been observed in the normal state of various strongly correlated superconductors close to a quantum critical point. However, its microscopic origin and link to quantum criticality remains an outstanding open problem. Here, we observe quantum-critical T/B-scaling of the Planckian metal state in resistivity and heat capacity of heavy-electron superconductor Ce_1-xNd_xCoIn₅ in magnetic fields near the edge of antiferromagnetism at the critical doping x_c ~ 0.03. We present clear experimental evidences of Kondo hybridization being quantum critical at x_c. We provide a generic microscopic mechanism to qualitatively account for this quantum critical Planckian state within the quasi-two dimensional Kondo-Heisenberg lattice model near Kondo breakdown transition. We find α is a non-universal constant and depends inversely on the square of Kondo hybridization strength.

A temperature-modulated dilatometer by using a piezobender-based device

We report a new design of a temperature-modulated dilatometer, which obtains the linear thermal expansion coefficient by measuring the oscillating changes of the sample's length and temperature by using a piezobender and a thermocouple, respectively. Using an iron-based superconductor KFe₂As₂ as an example, we show that this device is able to measure thin samples with high resolutions at low temperatures and high magnetic fields. Despite its incapability of giving absolute values, the new dilatometer provides a high-resolution method to study many important physical properties in condensed matter physics, such as thermal and quantum phase transitions and vortex dynamics in the superconducting state. The prototype design of this device can be further improved in many aspects to meet particular requirements.

Hybridization Dynamics in CeCoIn_{5} Revealed by Ultrafast Optical Spectroscopy

We investigate the quasiparticle dynamics in the prototypical heavy fermion CeCoIn_{5} using ultrafast optical pump-probe spectroscopy. Our results indicate that this material system undergoes hybridization fluctuations before the establishment of heavy electron coherence, as the temperature decreases from ∼120  K (T^{†}) to ∼55  K (T^{*}). We reveal that the anomalous coherent phonon softening and damping reduction below T^{*} are directly associated with the emergence of collective hybridization. We also discover a distinct collective mode with an energy of ∼8  meV, which may be experimental evidence of the predicted unconventional density wave. Our findings provide important information for understanding the hybridization dynamics in heavy fermion systems.

Spin-Triplet p-Wave Superconductivity Revealed under High Pressure in UBe_{13}

To unravel the nature of the superconducting symmetry of the enigmatic 5f heavy-fermion UBe_{13}, the pressure dependence of the upper critical field and of the normal state are studied up to 10 GPa. Remarkably, the pressure evolution of the anomalous H_{c2}(T,P) over the entire pressure range up to 5.9 GPa can be successfully explained by the gradual admixture of a field-pressure-induced E_{u} component in an A_{1u} spin-triplet ground state. This result provides strong evidence for parallel-spin pairing in UBe_{13}, which is also supported by the recently observed fully gapped excitation spectrum at ambient pressure. Moreover, we have also found a novel non-Fermi-liquid behavior of the resistivity, ρ(T)∼T^{n} (n≲1), which disappears with the collapse of the negative magnetoresistance behavior and the existence of a superconducting ground state around P=6  GPa, suggesting a close interplay between Kondo scattering and superconductivity.

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.

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.

Quantum critical scaling and fluctuations in Kondo lattice materials

We propose a phenomenological framework for three classes of Kondo lattice materials that incorporates the interplay between the fluctuations associated with the antiferromagnetic quantum critical point and those produced by the hybridization quantum critical point that marks the end of local moment behavior. We show that these fluctuations give rise to two distinct regions of quantum critical scaling: Hybridization fluctuations are responsible for the logarithmic scaling in the density of states of the heavy electron Kondo liquid that emerges below the coherence temperature [Formula: see text], whereas the unconventional power law scaling in the resistivity that emerges at lower temperatures below [Formula: see text] may reflect the combined effects of hybridization and antiferromagnetic quantum critical fluctuations. Our framework is supported by experimental measurements on CeCoIn₅, CeRhIn₅, and other heavy electron materials.

Toward a new microscopic framework for Kondo lattice materials

Understanding the emergence and subsequent behavior of heavy electrons in Kondo lattice materials is one of the grand challenges in condensed matter physics. From this perspective we review the progress that has been made during the past decade and suggest some directions for future research. Our focus will be on developing a new microscopic framework that incorporates the basic concepts that emerge from a phenomenological description of the key experimental findings.

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.

Evidence for Coexistence of Bulk Superconductivity and Itinerant Antiferromagnetism in the Heavy Fermion System CeCo(In(1-x)Cdx)5

In the generic phase diagram of heavy fermion systems, tuning an external parameter such as hydrostatic or chemical pressure modifies the superconducting transition temperature. The superconducting phase forms a dome in the temperature—tuning parameter phase diagram, which is associated with a maximum of the superconducting pairing interaction. Proximity to antiferromagnetism suggests a relation between the disappearance of antiferromagnetic order and superconductivity. We combine muon spin rotation, neutron scattering, and x-ray absorption spectroscopy techniques to gain access to the magnetic and electronic structure of CeCo(In_1−xCd_x)₅ at different time scales. Different magnetic structures are obtained that indicate a magnetic order of itinerant character, coexisting with bulk superconductivity. The suppression of the antiferromagnetic order appears to be driven by a modification of the bandwidth/carrier concentration, implying that the electronic structure and consequently the interplay of superconductivity and magnetism is strongly affected by hydrostatic and chemical pressure.

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}.

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.