Session L16: Heavy Fermions - Theory and Experiment

$\beta-YbAlB_4$: a critical vortex metal

$\beta-YbAlB_4$ is the first $Yb$ based heavy fermion superconductor and has a non Fermi Liquid behavior in the normal state that develops without external tuning by pressure or doping, making it intrinsically quantum critical [1]. Application of a magnetic field is found to drive the development of a Fermi Liquid in which the Fermi temperature is determined by the Zeeman energy [2]. Here we present a theory for the intrinsic quantum criticality in which the main ingredient is an anisotropic hybridization matrix with line nodes in momentum space that carry a vorticity and resemble topological defects. Our theory predicts that the application of a field induces a novel Lifshitz transition, in which a quasi-two dimensional Fermi Liquid with density of states $N^*(B) \propto 1/\sqrt{B}$ nucleates around the line node in momentum space. We also discuss how the vortex metal picture can account for the ESR anomalies observed in this system [3]. \vskip 0.3truein \noindent[1] S. Nakatsuji \textit{et al.}, Nature Phys. 4, 603 (2008). \noindent[2] Y. Matsumoto \textit{et al.}, Science 21, 316 (2011). \noindent[3] L. M. Holanda \textit{et al.}, Phys Rev. Lett. 107, 026402 (2011).   

Correlated disorder in Kondo lattice

Motivated by recent experiments on Yb-doped CeCoIn$_5$, we study the effect of correlated disorder in Kondo lattice. Correlations between the impurities are considered at the two-particle level. We use mean-field theory approximation for the Anderson lattice model to calculate how the emergence of coherence in the Kondo lattice is impacted by correlations between impurities. We show that the rate at which disorder suppresses coherence temperature depends on the length of impurity correlations. As impurity concentration increases, we generally find that the suppression of coherence temperature is significantly reduced. The results are discussed in the context of available experimental data.   

High-energy dispersion anomalies in actinide compounds

The observation of a prominent peak-dip-hump feature in the spectral weight in number of actinide compounds including Pu-115 superconductors and non-superconducting U-115 remains an unsolved problem. We have developed a first-principles intermediate coupling model to show that most aspects of these strong correlation features can be understood from the spin-fluctuation interaction.[1] The results show that a strong peak in the spin-fluctuation dressed self-energy is present around 0.5 eV in all these materials, which is mostly created by spin-orbit split 5f bands. These fluctuations couple to the single-particle spectrum and give rise to a peak-dip-hump feature, characteristic of the coexistence of itinerant and localized electronic states. Results are in quantitative agreement with photoemission spectra. Finally, we show that the studied actinides can be understood within the rigid-band filling approach, in which the spin-fluctuation coupling constant follows the same materials dependence as the superconducting transition temperature Tc. Work is supported by US DOE. \\[4pt] [1] T. Das. J.-X. Zhu, and M. J. Graf, arXiv:1108.0272   

The Electronic Correlation Strength of Pu

Many materials have strong electron-electron correlation effects that can cause large deviations in electronic structure and materials properties from those predicted by conventional band-structure theory based on the local density approximation. We present a new method or scale to quantify electronic correlations in strongly correlated electron systems and apply it to the different phases of elemental Pu. Using the GW approximation, we show that the f-electron band-width reduction due to correlation effects scales as a function of the initial LDA bandwidth. This relationship is a universal relationship in that it is independent of crystal structure and atomic volume.   

The Role of the Kondo and Phonon Correlations in the Cerium Volume Collapse

We review the most recent experimental and theoretical progress of the $\alpha \leftrightarrow \gamma$ volume collapse occurring in the element cerium. We discuss the experimental results which have been important in differentiating the various electronic and phononic properties of the volume collapse of cerium, these experiments illustrate that drastically different electronic and phononic properties exist between the small volume phase $\alpha$ and large volume phase $\gamma$ of cerium. After interpreting the physical data and realizing that the volume collapse in cerium is primarily the result of different electronic and vibronic correlations in the $\alpha$ and $\gamma$ phases we set up a Hamiltonian which encompasses the physical properties of the collapse. To model the electronic and phononic properties of the $\alpha \leftrightarrow \gamma$ transition of cerium we use the Periodic Anderson Model (PAM) + Holstein Model, with the aim that the Kondo like electronic correlations of the $\alpha$ phase is encoded in the PAM where the large vibronic physics of the $\gamma$ phase is encompassed in the Holstein Model which incorporates a conduction electron-phonon mediated interaction.   

Numerical Study of the Electron-Phonon coupling in the Cerium Volume Collapse

Rare earth elements, for example Cerium, will experience a volume collapse with increasing pressure. Researchers have struggled for six decades to discover the mechanism behind this unusual first order phase transition. Although different models have been proposed that provide some qualitatively correct results, there is no theory that completely captures the volume collapse. Notably, some recent experiments show that lattice oscillations play an important role, contrary to the previous consensus that this phase transition is mainly driven by the contributions from spins and electrons. In this talk, we will discuss our study which employs the DMFA method to explore the role of electron-phonon coupling in the Periodic Anderson Model.   

Lifshitz transition with interactions in high magnetic fields: Application to CeIn$_3$

The N\'eel ordered state of CeIn$_3$ is suppressed by a magnetic field of 61 T at ambient pressure. There is a second transition at $\sim$45 T, which has been associated with a Lifshitz transition [1,2]. Skin depth measurements [2] indicate that the transition is discontinuous as $T \to 0$. Motivated by this transition we study the effects of Landau quantization and interaction among carriers on a Lifshitz transition. The Landau quantization leads to quasi-one-dimensional behavior for the direction parallel to the field. Repulsive Coulomb interactions give rise to a gas of strongly coupled carriers [3]. The density correlation function is calculated for a special long-ranged potential [4]. It is concluded that in CeIn$_3$ a pocket is being emptied as a function of field in a discontinuous fashion in the ground state. This discontinuity is gradually smeared by the temperature [4] in agreement with the skin depth experiments [2]. \vskip 0.05in \par\noindent [1] S.E. Sebastian {\it et al}, PNAS {\bf 106}, 7741 (2009). \par\noindent [2] K.M. Purcell {\it et al}, Phys. Rev. B {\bf 79}, 214428 (2009). \par\noindent [3] P. Schlottmann and R. Gerhardts, Z. Phys. B {\bf 34}, 363 (1979). \par\noindent [4] P. Schlottmann, Phys. Rev. B {\bf 83}, 115133 (2011); J. Appl. Phys., in print.   

Coexistence of antiferromagnetism and superconductivity induced by Pauli-paramagnetic pair breaking

The heavy-fermion material CeCoIn$_5$ is a spin singlet $d$-wave superconductor with a strong Pauli-paramagnetic pair-breaking (PPB) effect. In the case with a magnetic field parallel to the basal plane of this material , there exists a distinct high field and low temperature (HFLT) superconducting (SC) phase in which a Fulde-Ferrell-Larkin-Ovchinnikov vortex lattice may be realized as a result of the strong PPB. Recently, it has been clarified that an antiferromagnetic (AFM) order exists inside the HFLT SC phase in spite of the absence of AFM order in the nonsuperconducting state [1]. Considering that AFM and SC orders are competing with each other in zero field, it is surprising that the AFM ordering is enhanced in the SC state. We theoretically study the stability of an AFM order in a $d$-wave and paramagnetic superconductor. We show that the PPB enhanced strongly by increasing the magnetic field induces an AFM order inside the SC phase and that, in contrast to the competitive nature of AFM and SC orders, the induced AFM order is not localized in vortex cores but coexistent with the SC order [2]. [1] M. Kenzelmann et al., Science 321, 1652 (2008). [2] K. Aoyama and R. Ikeda, arXiv:1107.5577.   

Current-Carrying States in Fulde-Ferrell-Larkin-Ovchinnikov superconductors

Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) superconducting state is believed to be favorable in Pauli-limited heavy-fermion superconductors such as CeCoIn5. Based on Bogliubov de-Gennes equations, we present a theoretical study of current-carrying FFLO states, including the stability and characterization of a superconducting order parameter for a current-carrying FFLO state. Inhomogeneous and anisotropic current density distribution and quasi-particle current contribution related to the order parameter modulation and sign change are found in FFLO state, which are expected to provide an easy way to detect the existence of an FFLO state.   

CeRu2Al2B: A new local moment 4f magnet with a complex T-H phase diagram

There is ongoing interest in the study of Ce-based compounds that are derivatives of certain structure types (e.g., ThCr$_{2}$Si$_{2}$and PbClF), as they are often associated with correlated electron phenomena. We will report results for a new system that falls into this category, CeRu$_{2}$Al$_{2}$B. This compound crystallizes in a filled variant of the layered/tetragonal CeMg$_{2}$Si$_{2}$ structure. Contrary to what is often observed for Ce-based compounds, we find pronounced local moment behavior of the Ce ions, resulting in complicated magnetic ordering at strikingly high temperatures: i.e., antiferromagnetism (AFM) at T$_{N}$ = 14.1 K followed by ferromagnetism (FM) at T$_{C}$ = 12.8 K, which is first order in character. We also find a temperature-magnetic field phase diagram that consists of three distinct ordered phases: (1) AFM, (2) spin reoriented, and (3) FM. Since this type of behavior is unusual for Ce-based compounds, we will discuss prospects for suppressing the ordered state toward T = 0 in order to produce a Doniach-like phase diagram, which may provide a route towards a FM quantum critical point.   

T-P phase diagram for the new local moment 4f ferromagnet CeRu$_{2}$Ga$_{2}$B

We will report results for single crystals of a new Ce-based local moment ferromagnet, CeRu$_{2}$Ga$_{2}$B. Electrical resistivity, magnetization, and magnetic susceptibility measurements reveal ferromagnetism and hysteresis around T$_{C}$ = 16.1 K, while specific heat measurements uncover a huge anomaly at the phase transition, which results in a large discontinuity in the magnetic entropy ($\Delta $S$_{mag }$= 1.7 J/mol-K). Taken together, these data show that CeRu$_{2}$Ga$_{2}$B undergoes a first order ferromagnetic phase transition at a surprisingly high temperature. Since this type of behavior is unusual for Ce-based compounds, we additionally undertook an effort to tune the magnetic state using pressure. We will present electrical resistivity measurements under applied pressures and the resulting temperature-pressure phase diagram, with an emphasis on implications for possible nearness to a ferromagnetic quantum critical point.   

Superconductivity and Magnetic Ordering in $RE$$_2$Pt$_3$Ge$_5$ ($RE$ = La and Pr) Single Crystals

Superconductivity and magnetic properties of rare-earth ternary germanide intermetallic compounds, $RE$$_2$Pt$_3$Ge$_5$ ($RE$ = La and Pr), are investigated. La$_2$Pt$_3$Ge$_5$ and Pr$_2$Pt$_3$Ge$_5$ single crystals were synthesized by high temperature metal flux method with Ge self flux. These two compounds were formed in U$_2$Co$_3$Si$_5$-type orthorhombic structure (space group $Ibam$) and the lattice parameters were determined using XRD of pulverized single crystals. La$_2$Pt$_3$Ge$_5$ exhibits an onset of superconducting phase transition at $T_c$ = 8.1 K, which, to the best of our knowledge, is the highest $T_c$ in U$_2$Co$_3$Si$_5$-type superconductors. Pr$_2$Pt$_3$Ge$_5$ shows both superconducting phase transition at $T_c$ = 7.9 K and antiferromagnetic transition at $T_N$ = 4.4 K. In addition, Pr$_2$Pt$_3$Ge$_5$ reveals strong magnetic anisotropy with an easy magnetic axis perpendicular to the $c$-axis, due to crystalline electric field effect. Including these results, we will discuss the nature of $RE$$_2$Pt$_3$Ge$_5$ single crystals in detail.   

Multi-orbital Kondo physics of Co in Cu hosts

We investigate the electronic structure of cobalt atoms on a copper surface and in a copper host by combining density functional calculations with a numerically exact continuous-time quantum Monte Carlo treatment of the five-orbital impurity problem. In both cases we find low energy resonances in the density of states of all five Co $d$-orbitals. The corresponding self-energies indicate the formation of a Fermi liquid state at low temperatures. Our calculations yield the characteristic energy scale -- the Kondo temperature -- for both systems in good agreement with experiments. We quantify the charge fluctuations in both geometries and suggest that Co in Cu must be described by an Anderson impurity model rather than by a model assuming frozen impurity valency at low energies. We show that fluctuations of the orbital degrees of freedom are crucial for explaining the Kondo temperatures obtained in our calculations and measured in experiments.   

Origin of the Heavy-Fermion behavior in Ca$_{2-x}$Sr$_{x}$RuO$_{4}$

We investigate the electronic states in Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ for $0.5\leq x\leq2.0$ on the basis of the three-orbital Hubbard model in the Gutzwiller approximation. We take the dominant effects of the Ca-substitution into account as the changes of the hybridizations, whose squares are proportional to the nearest-neighbor hopping integrals of the Ru-$t_{2g}$-orbitals, between the Ru-$4d$- and O-$2p$-orbitals. In this presentation, we show the renormalization factors for the Ru $t_{2g}$-orbitals as a function of the intraorbital Coulomb interaction or an angle of the rotation of RuO$_{6}$-octahedra and discuss the origin of the heavy-fermion behavior around $x=0.5$. Our calculation suggests that moderately strong Coulomb interaction and the orbital-dependent modifications of the electronic structures for the Ru-$t_{2g}$-orbitals due to the Ca-substitution cause the heavy-fermion behavior in Ca$_{2-x}$Sr$_{x}$RuO$_{4}$.   

Far-infrared optical properties of pyrochlore heavy fermion superconductor Cd$_2$Re$_2$O$_7$ in the normal and superconducting states

Cd$_2$Re$_2$O$_7$ is a pyrochlore oxide which exhibits superconductivity with a transition temperature \textit{T$_C$} near 1 K. The far-infrared optical properties of Cd$_2$Re$_2$O$_7$ will be presented at temperatures above and below \textit{T$_C$}. Superconductivity induced changes in the phonon structure are observed. Thermal reflectance spectra show two absorption features, near 9.6 and 19.3 cm$^{-1}$ which arise in the superconducting state. Optical conductivity spectra reveal a softening ($\sim$ 1 cm$^{-1}$) of the phonon mode at 35 cm$^{-1}$ in the superconducting state. Analysis of the frequency dependent optical effective mass and scattering rate support the classification of this material as a modest heavy electron system at low temperatures.