Session G22: Heavy Fermions: Theory and Experiment

Entanglement entropy near Kondo-destruction quantum critical points

We study the impurity entanglement entropy $S_e$ in quantum impurity models that feature a Kondo-destruction quantum critical point (QCP) arising from a pseudogap in the conduction-band density of states and/or from an additional coupling of the impurity to a bosonic bath. On the local-moment (Kondo-destroyed) side of the QCP, the entanglement entropy contains a critical component that can be related to the order parameter characterizing the phase transition. In Kondo models describing a spin-$S$ impurity, $S_e$ assumes its maximal value $\ln(2S+1)$ at the QCP and throughout the Kondo phase, independent of particle-hole (a)symmetry and irrespective of whether the Kondo phase features exact, over-, or under-screening of the impurity spin. In Anderson models, by contast, $S_e$ takes a nonuniversal value at the QCP. At particle-hole symmmetry, $S_e$ rises monotonically on passage from the local-moment phase to the Kondo phase, while breaking this symmetry can lead to a cusp peak in $S_e$ due to a divergent charge susceptibility at the QCP. Implications of these results for quantum-critical systems and quantum dots are discussed.   

Low temperature phases of the periodic Anderson model with electron-phonon correlation

We study the periodic Anderson model with the conduction electrons coupled to phonons. It has been shown by using the dynamical mean field theory that the model contains two disordered phases, the Kondo singlet phase for strong hybridization and the local moment phase for weak hybridization. In the hybridization-temperature plane, these two phases are separated by a first order phase transition line which terminates at a second order phase transition point. At low temperature the entropy in the Kondo singlet phase is quenched by the formation of a Fermi liquid, while the local moment phase will have residual entropy unless it is quenched by ordering. We calculate the lattice charge susceptibility to demonstrate that the conduction electrons form a charge density wave ordering below a critical temperature.   

Kondo-Heisenberg Lattice: Majorana fermions Mean field approach

we study Kondo lattice model including direct antiferromagnetic Heisenberg exchange interaction using Majorana fermions representation at half filling. An O(3)-symmetric Mean field Hamiltonian is derived on bipartite lattice. All different kind of possible spin-spin correlations functions between conduction band spins, c-electrons, and localized spin, f-electron, in both on site and different sublattices are calculated in translationally invariant solution of the mean field Theory. Finite temperature behavior of Majoranas pairs correlations are investigated for some special limit of some of the mean filed parameters.   

Magnetic Excitons in Heavy Fermion SemiMetals

A magnetic exciton is a precursor magnetic exciton, similar to an antiparamagnon in a metal, which exists in strongly correlated semiconductors. The magnetic exciton has a spectrum which resembles the broadened dispersion relation of an antiparamagnon for excitation energies greater than the semi-conducting gap, but becomes sharp for energies less than the semi-conducting gap. The narrowness of the spectral feature is due to the absence of decay channels into the continuum of electron-hole pairs. Such excitations have been observed by inelastic neutron scattering experiments on the heavy-fermion semiconductors SmB6 and YbB12. However, magnetic excitons have not been observed in cerium based heavy-fermion semiconductors nor has their occurrence been linked to the vicinity of a quantum critical point. Recently, magnetic excitons have been observed in a class of heavy-fermion semimetals, which are defined as having a non-zero density of states within the gap. The identification of the excitations as precursor excitations has been confirmed by the discovery of related materials that have an antiferromagnetically ordered state. We examine, theoretically, the spectral features of a model of a heavy fermion semi-metal and discuss the effects of doping.   

Superconductivity deep inside the hidden-order phase of URu2Si2: a phenomenological model

Recent magnetic torque and x-ray experiments have revealed that the tetragonal symmetry is broken in the hidden-order phase of URu$_2$Si$_2$. An important issue is how this symmetry breaking affects the superconducting state that develops deep inside the hidden-order state. Here we investigate this problem using a phenomenological model for both the ``nematic'' (i.e. tetragonal symmetry-broken) and superconducting phases. Based on recent field-angle-dependent heat capacity and thermal conductivity data, as well as Kerr effect measurements, we consider a chiral $d+id$ superconducting state that also breaks time-reversal symmetry. We find that in the presence of an orthorhombic/nematic order parameter, the system displays two sequential superconducting transitions: in the first, at $T_c$, the system enters a superconducting phase whereas in the second, at $T^* < T_c$, time-reversal symmetry is broken. Near the second transition, a ``soft'' but damped collective mode related to gap amplitude fluctuations emerges, which could be manifested in Raman scattering data. Between these two transitions, we find an unusual $\omega \log(\omega)$ dependence of the low-energy density of states, and show how it impacts the properties of several thermodynamic quantities in the $T^* < T < T_c$ regime.   

Crossover from non-Fermi liquid to Fermi liquid behavior and the superconducting dome in heavy electron systems

A nested Fermi surface and the remaining interaction between the carriers after the heavy particles are formed give rise to itinerant antiferromagnetism. We consider an electron and a hole pocket, separated by a wave vector ${\bf Q}$, and Fermi momenta $k_{F1}$ and $k_{F2}$, respectively.\footnote{P. Schlottmann, Phys. Rev. B {\bf 59}, 12379 (1999). } The order is gradually suppressed by increasing the mismatch of the two Fermi momenta and a QCP is obtained as $T_N \to 0$. For critical mismatch of the Fermi vectors (tuned QCP) the specific heat over $T$ increases as $-\ln(T)$ as $T$ is lowered$^{1,2}$ and the linewidth of the quasi-particles is linear in $T$ and $\omega$. With increasing nesting mismatch and decreasing temperature the specific heat and the linewidth display a crossover from non-Fermi liquid ($\sim T$) to Fermi liquid ($\sim T^2$) behavior. If in addition the vector ${\bf Q}$ is commensurate with the lattice (Umklapp with ${\bf Q} = {\bf G}/2$), pairs of electrons can be transferred between the pockets. To avoid the QCP this process may lead to superconductivity and a superconducting dome above the quantum critical point. We investigate the conditions under which such a dome arises.\footnote{P. Schlottmann, Phys. Rev. B {\bf 89}, 014511 (2014).}   

Temperature-dependent behavior of mixed-valent SmS : a DFT+DMFT study

We have investigated temperature-dependent behaviors of electronic structure and resistivity in a mixed-valent golden phase of SmS (g-SmS), based on the dynamical mean-field theory band structure calculations. Upon cooling, the coherent Sm 4f bands are formed to produce the hybridization-induced pseudo-gap near the Fermi level, and accordingly the topology of Fermi surface is changed. Also we have discussed the topological nature in g-SmS. From the analysis of anomalous resistivity behavior in SmS, we have identified universal energy scales, which characterize the Kondo/mixed-valent semimetallic systems.   

The Ising-Anisotropic Kondo Lattice in a transverse field: EDMFT study and implications for the global phase diagram

Heavy-fermion materials exhibit a rich variety of phase transitions. Of particular interest are quantum phase transitions and the associated breakdown of the Fermi liquid picture. A theoretical example of this is the Kondo destruction effect in the context of local quantum criticality [1]. To capture this effect and others, a zero-temperature global phase diagram for heavy-fermion materials has been proposed [1]. It incorporates the competition between the Kondo effect (promoted by exchange coupling $J_K$) and the variable quantum fluctuations of the local-moment magnetism (parameterized by $G$). We investigate this competition in the Ising-anisotropic Kondo lattice with a transverse magnetic field, where the field serves to tune $G$. We determine a zero-temperature phase diagram of this model within the extended dynamical mean-field theory (EDMFT), and discuss the implications of our results for the global phase diagram of heavy-fermion systems. \\[4pt] [1] Q. Si et al., J. Phys. Soc. Jpn. \textbf{83}, 061005 (2014).   

Super-Symplectic spin and heavy fermion systems

Heavy fermion materials are systems in which the presence of local moments leads to new physics. The phase diagram of these systems is very rich, usually presenting an antiferromagnetic (AFM) phase, a heavy Fermi liquid regime (HFL), and non Fermi-liquid behavior above the AFM quantum critical point (QCP). Our understanding of what happens to the local moments in different extremes of this phase diagram is based in two different representation for the spin: a Schwinger boson representation, appropriate for the description of AFM, and an Abrikosov fermion representation, suitable for the understanding of the HFL development. The theoretical approaches to this problem so far have been restricted to describe only extremes of this phase diagram, and are not reliable for the description of the more interesting region of the diagram, around the QCP. In this region the magnetic and Kondo energy scales interplay and can lead to dramatic changes in the character of the quantum phase transition. Here we use supersymmetric symplectic spins in order to investigate this intermediate regime.   

Enhanced Pairing Correlations near a Quantum Critical Point in Two Impurity Anderson Model with a Pseudogap

Significant progress has been made on the understanding of quantum critical heavy fermion metals. In addition to the spin density wave quantum critical point (QCP), a Kondo destruction QCP beyond the Landau framework has been discovered. However, its implications on the formation of unconventional superconductivity remain unclear. Motivated by a cluster-EDMFT approach [1], we address this question in simplified models for Kondo destruction QCP, as arising in the two impurity pseudogap Anderson model. We study the model using the continuous time quantum Monte-Carlo method, with either an Ising or Heisenberg inter-impurity RKKY interaction. For each case we have found a QCP distinct from both the Kondo destruction criticality of a single impurity pseudogap Anderson model and the quantum criticality of the conventional two impurity model. We observe critical local moment fluctuations with a power-law divergence in the staggered spin susceptibility, and show that the single-particle spectral function obey energy over temperature scaling. We find that the singlet pairing susceptibility is significantly enhanced near the QCP. Implications for unconventional superconductivity in quantum critical heavy fermion systems will be discussed. [1] J.H.Pixley, A. Cai, Q. Si, arXiv:1409.1090   

Numerical study of the periodic Anderson model with a quarter-filled conduction band

Using the dynamical cluster approximation with continuous-time quantum Monte Carlo as the cluster solver and the recently introduced dual-fermion method, we study the underlying physics of the periodic Anderson model where the conduction band is near quarter-filling while the f-band electron band is half filled. For these parameters, the RKKY coupling changes its nature from ferromagnetic to anti-ferromagnetic, yielding an interesting phase-diagram. Especially, we find the charge ordering of the conduction band is strongly enhanced, which could be due to the proximity to a quantum critical point.   

Unconventional Superconductivity in the Vicinity of the Local Quantum Critical Point

Unconventional superconductivity and its relationship with quantum criticality remains a central question in strongly correlated electron systems. In the case of heavy fermion metals, the existence of antiferromagnetic quantum critical points (QCPs) is well established. Theoretical work has identified the existence of a local QCP where the Kondo effect is driven critical concomitant with the vanishing of the magnetic order parameter. Experiments on the heavy fermion compound CeRhIn$_{\mathrm{5}}$ and other materials have provided strong evidence that such a QCP drives unconventional superconductivity. With this in mind we solve the periodic Anderson model using a cluster extended dynamical mean field theory. We show that the Kondo energy scale is continuously suppressed at the antiferromagnetic QCP, and we determine the scaling form of the order parameter susceptibility and find remarkable agreement with well-established experiments in the related heavy fermion system CeCu$_{\mathrm{6-x}}$Au$_{\mathrm{x}}$. Most importantly, we find that the singlet pairing susceptibility is strongly enhanced at the QCP, which points towards a new pairing mechanism associated with both magnetic and local critical fluctuations.   

Metamagnetism in CeCoIn$_{5}$ and the Single Energy Scale Model

The anisotropic linear and nonlinear magnetic response of the non-ordering heavy electron compound CeCoIn$_{5}$ will be presented. Many heavy electron materials exhibit a a peak in the linear susceptibility at a temperature T$_{1}$ which correlates with the metamagnetic critical field, H$_{\mathrm{c}}$. There is also a peak in the nonlinear susceptibility $\chi_{3}$, at T$_{3}$ = 0.5T$_{1}$ in many materials and this feature has been explained recently with a single energy scale model. In CeCoIn$_{5}$ however, a plateau rather than a peak is observed in the linear susceptibility which evolves into a paramagnetic type divergence upon further cooling. This apparent violation of the ``ideal'' metamagnetic behavior is resolved here. The single energy scale model augmented with a paramagnetic contribution successfully accounts for the observed linear and nonlinear anisotropic magnetic response in CeCoIn$_{5}$.   

Quantum criticality driven by geometrical frustration

Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids which cannot be classified by conventional order parameter theory and display emergent excitations. Whether geometrical frustration of magnetic moments in metals can induce unconventional quantum critical points is an active area of research. We focus on the heavy-fermion metal CeRhSn with twodimensional triangular configuration of the Kondo ion. Low-temperature thermodynamic experiments prove zero-field quantum criticality. A striking anisotropy of the linear thermal expansion, displaying critical and non-critical behavior along and perpendicular to the basal plane, respectively, is ascribed to the effect of strong geometrical frustration. We further find evidence of fluctuating local 4f moments, implying a novel quantum critical spin liquid state with fractionalized quasiparticles.   

Many-body instabilities and mass generation in slow Dirac materials

Some Kondo insulators are expected to possess topologically protected surface states with linear Dirac spectrum, the topological Kondo insulators. Because the bulk states of these systems typically have heavy effective electron masses, the surface states may exhibit extraordinarily small Fermi velocities that could force the effective fine structure constant of the surface states into the strong coupling regime. Using a tight-binding model we study the many-body instabilities of these systems and identify regions of parameter space for which antiferromagnetic, ferromagnetic and charge density wave instabilities occur.