Heavy-fermion CeCoIn5 Research Articles

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.

Unconventional superconductivity in the strong-coupling limit for the heavy fermion system CeCoIn5

We present scanning tunneling spectroscopy measurements of the local quasiparticles' excitation spectra of the heavy fermion CeCoIn5 between 440mK and 3K in samples with a bulk Tc=2.25K. The spectral shape of our low-temperature tunneling data, quite textbook nodal-Δ conductance, allow us to confidently fit the spectra with a d-wave density of states considering also a shortening of quasiparticles' lifetime term Γ. The Δ(0) value obtained from the fits yields a BCS ratio 2Δ/kTc=7.73 suggesting that CeCoIn5 is an unconventional superconductor in the strong coupling limit. The fits also reveal that the height of coherence peaks in CeCoIn5 is reduced with respect to a pure BCS spectra and therefore the coupling of quasiparticles with spin excitations should play a relevant role. The tunneling conductance shows a depletion at energies smaller than Δ for temperatures larger than the bulk Tc, giving further support to the existence of a pseudogap phase that in our samples span up to T*∼1.2Tc. The phenomenological scaling of the pseudogap temperature observed in various families of cuprates, 2Δ/kT*∼4.3, is not fulfilled in our measurements. This suggests that in CeCoIn5 the strong magnetic fluctuations might conspire to close the local superconducting gap at a smaller pesudogap temperature-scale than in cuprates.

Multi-band Eilenberger Theory of Superconductivity: Systematic Low-Energy Projection

We propose the general multi-band quasiclassical Eilenberger theory of superconductivity to describe quasiparticle excitations in inhomogeneous systems. With the use of low-energy projection matrix, the $M$-band quasiclassical Eilenberger equations are systematically obtained from $N$-band Gor'kov equations. Here $M$ is the internal degrees of freedom in the bands crossing the Fermi energy and $N$ is the degree of freedom in a model. Our framework naturally includes inter-band off-diagonal elements of Green's functions, which have usually been neglected in previous multi-band quasiclassical frameworks. The resultant multi-band Eilenberger and Andreev equations are similar to the single-band ones, except for multi-band effects. The multi-band effects can exhibit the non-locality and the anisotropy in the mapped systems. Our framework can be applied to an arbitrary Hamiltonian (e.g. a tight-binding Hamiltonian derived by the first-principle calculation). As examples, we use our framework in various kinds of systems, such as noncentrosymmetric superconductor CePt$_{3}$Si, three-orbital model for Sr$_{2}$RuO$_{4}$, heavy fermion CeCoIn$_{5}$/YbCoIn$_{5}$ superlattice, a topological superconductor with the strong spin-orbit coupling Cu$_{x}$Bi$_{2}$Se$_{3}$, and a surface system on a topological insulator.

Impurity-induced antiferromagnetic order in Pauli-limited nodal superconductors: Application to heavy-fermionCeCoIn5

We investigate the properties of the coexistence phase of itinerant antiferromagnetism and nodal $d$-wave superconductivity (Q-phase) discovered in heavy fermion CeCoIn5 under applied magnetic field. We solve the minimal model that includes $d$-wave superconductivity and underlying magnetic correlations in real space to elucidate the structure of the $Q$-phase in the presence of an externally applied magnetic field. We further focus on the role of magnetic impurities, and show that they nucleate the Q-phase at lower magnetic fields. Our most crucial finding is that, even at zero applied field, dilute magnetic impurities cooperate via RKKY-like exchange interactions to generate a long-range ordered coexistence state identical to the Q-phase. This result is in agreement with recent neutron scattering measurements [S. Raymond et al., J. Phys. Soc. Jpn. {\bf 83}, 013707 (2014)].

Enhancement of electronic spin susceptibility in Pauli-limited unconventional superconductors

We calculate the wave-vector dependent electronic spin susceptibility $\chi_{\alpha\beta}(\mathbf q, \mathbf H_0)$ of a d-wave superconductor in uniform magnetic field $\mathbf{H}_0$ with Pauli pair-breaking. We find that the transverse component of the susceptibility tensor can be greater than its normal state value; the longitudinal component also slightly increases but in a very limited range of $q$s. We identify several wave vectors $\{\mathbf q_\perp,\mathbf q_\parallel\}$, that correspond to the maxima of either $\chi_\perp$ or $\chi_\parallel$. We compare our results with available data on the high-field phase in heavy-fermion CeCoIn$_5$.

Growth, Characterization and Fermi Surface of Heavy Fermion CeCoIn5 Superconductor

High quality single crystals of heavy Fermion CeCoIn5 superconductor have been grown by flux method with a typical size of (1 − 2) × (1 − 2) × (∼ 0.1) mm3. The single crystals are characterized by structural analysis from x-ray diffraction and Laue diffraction, as well as compositional analysis. Magnetic and electrical measurements on the single crystals show a sharp superconducting transition with a transition temperature at Tc,onset ∼2.3 K and a transition width of ∼0.15K. The resistivity of the CeCoIn5 crystal exhibits a hump at ∼45 K, which is typical of a heavy Fermion system. High resolution angle-resolved photoemission spectroscopy (ARPES) measurements of CeCoIn5 reveal clear Fermi surface sheets that are consistent with the band structure calculations when assuming itinerant Ce 4f electrons at low temperature. This work provides important information on the electronic structure of heavy Fermion CeCoIn5 superconductor. It also lays a foundation for further studies on the physical properties and superconducting mechanism of the heavy Fermion superconductors.

Multigap superconductivity in heavy fermion systems

Heavy fermion superconductors are largely studied for their unconventional ground states. We present results on the skutterudite compound PrOs4Sb12 (Tc ≈ 1.8K), and on the heavy-fermion CeCoIn5 (Tc ≈ 2.3K), where both the low field and the low temperature behaviour of their thermal conductivity yield evidence for multigap superconductivity.

Unconventional superconductors under a rotating magnetic field. I. Density of states and specific heat

We develop a fully microscopic theory for the calculations of the angle-dependent properties of unconventional superconductors under a rotated magnetic field. We employ the quasiclassical Eilenberger equations, and use a variation of the Brandt-Pesch-Tewordt (BPT) method to obtain a closed form solution for the Green's function. The equations are solved self-consistently for quasi-two-dimensional $d_{x^2-y^2}$ ($d_{xy}$) superconductors with the field rotated in the basal plane. The solution is used to determine the density of states and the specific heat. We find that applying the field along the gap nodes may result in minima or maxima in the angle-dependent specific heat, depending on the location in the T-H plane. This variation is attributed to the scattering of the quasiparticles on vortices, which depends on both the field and the quasiparticle energy, and is beyond the reach of the semiclassical approximation. We investigate the anisotropy across the T-H phase diagram, and compare our results with the experiments on heavy fermion CeCoIn$_5$.

Unconventional superconductors under a rotating magnetic field. II. Thermal transport

We present a microscopic approach to the calculations of thermal conductivity in unconventional superconductors for a wide range of temperatures and magnetic fields. Our work employs the non-equilibrium Keldysh formulation of the quasiclassical theory. We solve the transport equations using a variation of the Brandt-Pesch-Tewordt (BPT) method, that accounts for the quasiparticle scattering on vortices. We focus on the dependence of the thermal conductivity on the direction of the field with the respect to the nodes of the order parameter, and discuss it in the context of experiments aiming to determine the shape of the gap from such anisotropy measurements. We consider quasi-two dimensional Fermi surfaces with vertical line nodes and use our analysis to establish the location of gap nodes in heavy fermion CeCoIn$_5$ and organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$.

Fulde-Ferrell-Larkin-Ovchinnikov State in a Perpendicular Field of Quasi-Two-DimensionalCeCoIn5

A Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state was previously reported in the quasi-2D heavy fermion CeCoIn5 when a magnetic field was applied parallel to the ab plane. Here, we conduct 115In NMR studies of this material in a perpendicular field, and provide strong evidence for FFLO in this case as well. Although the topology of the phase transition lines in the H-T phase diagram is identical for both configurations, there are several remarkable differences between them. Compared to H parallelab, the FFLO phase for H perpendicularab is confined in a much narrower region at the low-T-high-H corner in the H-T plane, and the critical field separating the FFLO and non-FFLO superconducting states almost ceases to have a temperature dependence. Moreover, directing H perpendicularab results in a notable change in the quasiparticle excitation spectrum within the planar node associated with the FFLO transition.

NMR study of the novel superconducting state in [formula omitted

A Fulde–Ferrell–Larkin–Ovchinnkov (FFLO) state is investigated in the quasi-2D heavy fermion CeCoIn 5 by a 115In NMR study in both perpendicular and parallel field to the ab-plane. Although the topology of the phase transition lines in the H – T phase diagram of the FFLO state is identical for both configurations, there are several remarkable differences between them.

Anomalous transport phenomena in [formula omitted] close to quantum critical point

Various transport coefficients show striking deviations from conventional Fermi-liquid behaviors in many electron systems which are close to antiferromagnetic (AF) quantum critical points (QCP). For example, Hall coefficients and Nernst coefficients in three-dimensional heavy fermion CeCoIn 5 and CeCu 6 - x Au x increase remarkably at low temperatures. These temperature dependences are too strong to explain in terms of the relaxation time approximation. To elucidate the origin of these anomalous transport phenomena in three-dimensional systems, we study the role of current vertex corrections (CVC) based on the fluctuation exchange (FLEX) approximation. We find that the Hall coefficient and the Nernst coefficient strongly increase due to the CVC in the vicinity of the AF QCP, even in three-dimensional systems.

Transport phenomena in a three-dimensional system close to the magnetic quantum critical point: The conserving approximation with current vertex corrections

It is known that various transport coefficients strongly deviate from conventional Fermi-liquid behaviors in many electron systems which are close to antiferromagnetic (AF) quantum critical points (QCP). For example, Hall coefficients and Nernst coefficients in three-dimensional heavy fermion CeCoIn5 and CeCu6-xAux increase strikingly at low temperatures, whose overall behaviors are similar to those in high-Tc cuprates. These temperature dependences are too strong to explain in terms of the relaxation time approximation. To elucidate the origin of these anomalous transport phenomena in three-dimensional systems, we study the current vertex corrections (CVC) based on the fluctuation exchange (FLEX) approximation, and find out decisive role of the CVC. The main finding of the present paper is that the Hall coefficient and the Nernst coefficient strongly increase thanks to the CVC in the vicinity of the AF QCP, irrespective of dimensionality. We also study the relaxation time of quasi-particles, and find that "hot points" and "cold lines" are formed in general three-dimensional systems due to strong AF fluctuations.

Fulde–Ferrell–Larkin–Ovchinnikov superconductivity in heavy fermion CeCoIn 5

We report angular dependent heat capacity, RF penetration depth, and magnetization studies on CeCoIn 5, a clean quasi-2D strongly correlated superconductor in the paramagnetic limit. At temperatures below 350 mK and magnetic field applied parallel to the conducting planes, we find evidence for the inhomogeneous FFLO superconducting state close to the upper critical field. For small tilt angles, where both orbital and paramagnetic pair-breaking becomes important, the superconducting order parameter assumes higher Landau level states within the FFLO state. For applied field at an angle greater than 15° no FFLO signature is observed and a BCS-type superconducting state emerges.

Evolution of Hall Coefficient in Two-Dimensional Heavy Fermion CeCoIn5

We report on the pressure dependence of the Hall coefficient $R_H$ in quasi-2D heavy fermion CeCoIn$_5$. At ambient pressure, below a temperature associated with the emergence of non-Fermi liquid properties, $R_H$ is anomalously enhanced. We found that the restoration of the Fermi liquid state with applied pressure leads to a gradual suppression of this dramatic enhancement. Moreover, the enhancement in $R_H$ was found to be confined to an intermediate temperature window, where inelastic electron-electron scattering is dominant. Our results strongly support the presence of cold and hot spots on the Fermi surface probably due to anisotropic scattering by antiferromagnetic fluctuations, which may also prove relevant for the debate on the anomalous normal-state properties of high-$T_c$ cuprates.

Avoided antiferromagnetic order and QCP in [formula omitted

We measured the specific heat and resistivity of heavy fermion CeCoIn 5 between the superconducting critical field H c 2 = 4.95 and 9 T, with the field in the [0 0 1] direction, and at temperatures down to 50 mK. These results show that this compound has a quantum critical point (QCP) with the magnetic field as the tuning parameter. For a field of 5 T just above H c 2 the temperature dependence of both specific heat C p ( T ) and resistivity ρ ( T ) show non-Fermi liquid (NFL) behavior down to the lowest temperatures with C p ( T ) ∝ - log ( T ) and ρ ( T ) - ρ ( T = 0 ) ∝ T . For fields above 8 T the data exhibit a crossover from a NFL to a Fermi liquid behavior. Specific heat and resistivity data show behavior predicted by spin-fluctuation theory, suggesting that the NFL behavior is due to incipient antiferromagnetism (AFM) in CeCoIn 5 with the quantum critical point in the vicinity of H c 2 . For fields below H c 2 the AFM phase separated by a QCP from the paramagnetic ground state is not observed, as the system becomes first superconducting.

Possible Fulde–Ferrell–Larkin–Ovchinnikov superconducting state in CeCoIn 5

We report observation of the specific heat anomaly within the superconducting state of the heavy fermion CeCoIn 5. It appears in the vicinity of the superconducting critical field H c2, where the superconducting transition changes from second to first order, above 10 T for H || [1 1 0] and H || [1 0 0] , and above 4.7 T for H || [0 0 1] , and at temperatures on the order of 0.1 T c. We interpret the anomaly within the superconducting state as a signature of a Fulde–Ferrell–Larkin–Ovchinnikov FFLO inhomogeneous superconducting state.

Normal-state Hall Angle and Magnetoresistance in Quasi-2D Heavy Fermion CeCoIn5near a Quantum Critical Point

The normal-state Hall effect and magnetoresisitance (MR) have been measured in the quasi-2D heavy fermion superconductor CeCoIn_5. In the non-Fermi liquid region where the reistivity rho_xx exhibits an almost perfect T-linear dependence, the Hall angle varies as cot theta_H propto T^2 and the MR displays a strong violation of Kohler's rule. We demonstrate a novel relation between the MR and the Hall conductivity, Delta rho_xx/rho_xx propto (sigma_xy rho_xx)^2. These results bear a striking resemblance to the normal-state properties of high-T_c cuprates, indicating universal transport properties in the presence of quasi-2D antiferromagnetic fluctuations near a quantum critical point.

Avoided antiferromagnetic order and quantum critical point in CeCoIn5.

We measured the specific heat and resistivity of heavy fermion CeCoIn5 between the superconducting critical field H(c2)=5 T and 9 T, with the field in the [001] direction, and at temperatures down to 50 mK. At 5 T the data show a non-Fermi liquid (NFL) behavior down to the lowest temperatures. At the field above 8 T the data exhibit a crossover from the Fermi liquid to a non-Fermi liquid behavior. We analyzed the scaling properties of the specific heat and compared both the resistivity and the specific heat with the predictions of a spin-fluctuation theory. Our analysis leads us to suggest that the NFL behavior is due to incipient antiferromagnetism (AFM) in CeCoIn5 with the quantum critical point in the vicinity of H(c2). Below H(c2) the AFM phase which competes with the paramagnetic ground state is superseded by the superconducting transition.

Determination of the directions of gap nodes in exotic superconductors

The superconducting gap structure, especially the direction of the nodes, is an unresolved issue in most unconventional superconductors. Recently it has been demonstrated that the thermal conductivity κ is a powerful tool for probing the nodal structure. Here measuring κ in H rotating within the basal plane, we discuss the nodal structure of the unconventional superconductors, 2D spin-triplet Sr2RuO4, 2D heavy fermion CeCoIn5, 2D organic κ-(BEDT-TTF)2Cu(NCS)2, and 3D borocarbide YNi2B2C.