Fractionalized fermi liquids

Antiferromagnetism in metals: from the cuprate superconductors to the heavy fermion materials

The critical theory of the onset of antiferromagnetism in metals, with concomitant Fermi surface reconstruction, has recently been shown to be strongly coupled in two spatial dimensions. The onset of unconventional superconductivity near this critical point is reviewed: it involves a subtle interplay between the breakdown of fermionic quasiparticle excitations on the Fermi surface and the strong pairing glue provided by the antiferromagnetic fluctuations. The net result is a logarithm-squared enhancement of the pairing vertex for generic Fermi surfaces, with a universal dimensionless coefficient independent of the strength of interactions, which is expected to lead to superconductivity at the scale of the Fermi energy. We also discuss the possibility that the antiferromagnetic critical point can be replaced by an intermediate 'fractionalized Fermi liquid' phase, in which there is Fermi surface reconstruction but no long-range antiferromagnetic order. We discuss the relevance of this phase to the underdoped cuprates and the heavy fermion materials.

Quantum critical phase and Lifshitz transition in an extended periodic Anderson model

We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of 'strange' metal phases in quantum matter.

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson paradigm. The Landau-Ginzburg-Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.

Defects in heavy-fermion materials: unveiling strong correlations in real space

Defects provide important insight into the complex electronic and magnetic structure of heavy-fermion materials by inducing qualitatively different real-space perturbations in the electronic and magnetic correlations of the system. These perturbations possess direct experimental signatures in the local density of states, such as an impurity bound state, and the nonlocal spin susceptibility. Moreover, highly nonlinear quantum interference between defect-induced perturbations can drive the system through a first-order phase transition to a novel inhomogeneous ground state.

Spin fluctuations in normal state CeCu2Si2 on approaching the quantum critical point

We report on the magnetic excitation spectrum in the normal state of the heavy-fermion superconductor CeCu92)Si(2) on approaching the quantum critical point (QCP). The magnetic response in the superconducting state is characterized by a transfer of spectral weight to energies above a spin excitation gap. In the normal state, a slowing-down of the quasielastic magnetic response is observed, which conforms to the scaling expected for a QCP of spin-density-wave type. This interpretation is substantiated by an analysis of specific heat data and the momentum dependence of the magnetic excitation spectrum. Our study represents the first direct observation of an almost critical slowing-down of the normal state magnetic response at a QCP when suppressing superconductivity. The results strongly imply that the coupling of Cooper pairs in CeCu(2)Si(2) is mediated by overdamped spin fluctuations.

Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice

We present measurements of the basic properties of Ce(2)Ge(2)Mg, Yb(2)Pt(2)Pb and Ce(2)Pt(2)Pb, which are members of a new class of geometrically frustrated magnets R(2)T(2)X (R = rare earth, T = transition metal, X = main group). Here, the moment-bearing R atoms are confined to layers where they are arranged in the Shastry-Sutherland lattice. Magnetic susceptibility and specific heat measurements indicate that Ce(2)Ge(2)Mg orders antiferromagnetically at 9.4 K and Yb(2)Pt(2)Pb at 2.07 K. No long ranged order is observed in Ce(2)Pt(2)Pb above 0.05 K. Analysis of Schottky peaks in the specific heat indicates that all three compounds have doublet ground states that are well separated in energy from the excited states of the crystal-field-split manifold. Electrical resistivity measurements show that Ce(2)Ge(2)Mg and Yb(2)Pt(2)Pb are excellent metals with small residual resistivities. However, the measured resistivity of Ce(2)Pt(2)Pb is large and almost temperature-independent, suggesting that strong disorder or perhaps strong quantum critical fluctuations saturate the quasiparticle scattering in this compound. The magnetic entropy develops very slowly above the onset of antiferromagnetic order and we discuss the possibility that a nonordered fluid of dimerized moments exists above T(N) in Ce(2)Ge(2)Mg and Yb(2)Pt(2)Pb, and for a wide range of temperatures in Ce(2)Pt(2)Pb, which appears to be close to a frustration-driven quantum critical point.

Zeeman-driven Lifshitz transition: a model for the experimentally observed Fermi-surface reconstruction in YbRh2Si2

The heavy-fermion metal YbRh(2)Si(2) displays a field-driven quantum phase transition where signatures of a Fermi-surface reconstruction have been identified, often interpreted as a breakdown of the Kondo effect. We argue that instead many properties of the material can be consistently described by assuming a Zeeman-driven Lifshitz transition of narrow heavy-fermion bands. Using a suitable quasiparticle model, we find a smeared jump in the Hall constant and lines of maxima in susceptibility and specific heat, very similar to experimental data. An intermediate non-Fermi-liquid regime emerges due to the small effective Fermi energy near the transition. Further experiments to discriminate the different scenarios are proposed.

Modulated spin liquid: a new paradigm for URu2Si2

We argue that near a Kondo breakdown critical point, a spin liquid with spatial modulations can form. Unlike its uniform counterpart, we find that this occurs via a second order phase transition. The amount of entropy quenched when ordering is of the same magnitude as for an antiferromagnet. Moreover, the two states are competitive, and at low temperatures are separated by a first order phase transition. The modulated spin liquid we find breaks Z4 symmetry, as recently seen in the hidden order phase of URu2Si2. Based on this, we suggest that the modulated spin liquid is a viable candidate for this unique phase of matter.

Discontinuous Hall coefficient at the quantum critical point in YbRh₂Si₂

YbRh2Si2 is a model system for quantum criticality. In particular, Hall effect measurements helped identify the unconventional nature of its quantum critical point. Here, we present a high-resolution study of the Hall effect and magnetoresistivity on samples of different quality. We find a robust crossover on top of a sample dependent linear background contribution. Our detailed analysis provides a complete characterization of the crossover in terms of its position, width, and height. Importantly, we find in the extrapolation to zero temperature a discontinuity of the Hall coefficient occurring at the quantum critical point for all samples. In particular, the height of the jump in the Hall coefficient remains finite in the limit of zero temperature. Hence, our data solidify the conclusion of a collapsing Fermi surface. Finally, we contrast our results to the smooth Hall effect evolution seen in chromium, the prototype system for a spin-density-wave quantum critical point.

Tandem pairing in heavy-fermion superconductors

We consider the internal structure of a d-wave heavy-fermion superconducting condensate, showing that it necessarily contains two components condensed in tandem: pairs of quasiparticles on neighboring sites and composite pairs consisting of two electrons bound to a single local moment. These two components draw upon the antiferromagnetic and Kondo interactions to cooperatively enhance the superconducting transition temperature. This tandem condensate is electrostatically active, with an electric quadrupole moment predicted to lead to a superconducting shift in the nuclear quadrupole resonance frequency.

Tunneling into clean heavy fermion compounds: origin of the Fano line shape

Recently observed tunneling spectra on clean heavy-fermion compounds show a lattice periodic Fano line shape similar to what is observed in the case of tunneling to a Kondo ion adsorbed at the surface. We show that the translation symmetry of a clean surface in the case of weakly correlated metals leads to a tunneling spectrum which shows a hybridization gap but does not have a Fano line shape. By contrast, in a strongly correlated heavy-fermion metal the heavy quasiparticle states will be broadened by interaction effects. The hybridization gap is completely filled in this way, and an ideal Fano line shape of width ∼2TK results. In addition, we discuss the possible influence of the tunneling tip on the surface, in (i) leading to additional broadening of the Fano line and (ii) enhancing the hybridization locally, hence adding to the impurity type behavior. The latter effects depend on the tip-surface distance.

Holographic metals and the fractionalized fermi liquid

We show that there is a close correspondence between the physical properties of holographic metals near charged black holes in anti-de Sitter (AdS) space, and the fractionalized Fermi liquid phase of the lattice Anderson model. The latter phase has a "small" Fermi surface of conduction electrons, along with a spin liquid of local moments. This correspondence implies that certain mean-field gapless spin liquids are states of matter at nonzero density realizing the near-horizon, AdS₂ × R² physics of Reissner-Nordström black holes.

Majorana liquids: the complete fractionalization of the electron

We describe ground states of correlated electron systems in which the electron fractionalizes into separate quasiparticles which carry its spin and its charge, and into real Majorana fermions which carry its Fermi statistics. Such parent states provide a unified theory of previously studied fractionalized states: their descendants include insulating and conducting states with neutral spin S=1/2 fermionic spinons, and states with spinless fermionic charge carriers. We illustrate these ideas on the honeycomb lattice, with field theories of such states and their phase transitions.

Differential conductance and quantum interference in Kondo systems

We present a large-N theory for the differential conductance, dI/dV, in Kondo systems measured via scanning tunneling spectroscopy. We demonstrate that quantum interference between tunneling processes into the conduction band and into the magnetic f-electron states is crucial in determining the experimental Fano line shape of dI/dV. This allows one to uniquely extract the Kondo coupling and the ratio of the tunneling amplitudes from the experimental dI/dV curve. Finally, we show that dI/dV directly reflects the strength of the antiferromagnetic interaction in Kondo lattice systems.

Analysis of the antiferromagnetic phase transitions of the 2D Kondo lattice

We study the antiferromagnetic quantum phase transition of a 2D Kondo-Heisenberg square lattice using the nonlinear sigma model. A renormalization group analysis of the competing Kondo-RKKY interaction is carried out to one-loop order in the expansion, and a new quantum critical point (QCP) strongly affected by Kondo fluctuations is found. Near this QCP, the spin-wave velocity scales logarithmically, i.e., breakdown of hydrodynamic behavior, and the spin wave is logarithmically frozen out. The renormalization group results also allow us to propose a new phase diagram near the antiferromagnetic fixed point of this 2D Kondo lattice model.

Layered Kondo lattice model for quantum critical beta-YbAlB4

We analyze the magnetic and electronic properties of the quantum critical heavy fermion superconductor beta-YbAlB4, calculating the Fermi surface and the angular dependence of the extremal orbits relevant to the de Haas-van Alphen measurements. Using a combination of the realistic materials modeling and single-ion crystal field analysis, we are led to propose a layered Kondo lattice model for this system, in which two-dimensional boron layers are Kondo coupled via interlayer Yb moments in a Jz=+/-5/2 state. This model fits the measured single-ion magnetic susceptibility and predicts a substantial change in the electronic anisotropy as the system is pressure tuned through the quantum critical point.

Evolution of a large Fermi surface in the Kondo lattice

The single-particle spectrum of the Kondo lattice model is derived with the use of the continuous-time quantum Monte Carlo method, combined with the dynamical mean-field theory. Crossover behavior is traced quantitatively either to a heavy Fermi-liquid state or to a magnetically ordered state from the local-moment state at high temperatures. The momentum distribution in the low-temperature limit acquires a discontinuity at the location that involves the local-spin degrees of freedom. Even without the charge degrees of freedom for local electrons, the excitation spectra exhibit hybridized bands similar to those in the Anderson lattice. Temperature dependence in the zero-energy component of the self-energy is crucial in forming the Fermi-liquid state with the large Fermi surface.

Kondo stripes in an Anderson-Heisenberg model of heavy fermion systems

We study the interplay between the spin-liquid and Kondo physics, as related to the nonmagnetic part of the phase diagram of heavy fermion materials. Within the unrestricted mean-field treatment of the infinite-U 2D Anderson-Heisenberg model, we find that there are two topologically distinct nondegenerate uniform heavy Fermi liquid states that may form as a consequence of the Kondo coupling between spinons and conduction electrons. For certain carrier concentrations, the uniform Fermi liquid becomes unstable with respect to the formation of a new kind of anharmonic "Kondo stripe" state with inhomogeneous Kondo screening strength and the charge density modulation. These features are experimentally measurable and thus may help to establish the relevance of the spin-liquid correlations to heavy fermion materials.

Model of quantum criticality in He3 bilayers adsorbed on graphite

Recent experiments on He3 bilayers adsorbed on graphite have shown striking quantum critical properties at the point where the first layer localizes. We model this system with the Anderson lattice plus interlayer Coulomb repulsion in two dimensions. Assuming that quantum critical fluctuations come from a vanishing of the effective hybridization, we can reproduce several features of the system, including the apparent occurrence of two quantum critical points, the variation of the effective mass and coherence temperature with coverage.

Kondo breakdown as a selective Mott transition in the Anderson lattice

We show within the slave-boson technique that the Anderson lattice model exhibits a Kondo breakdown quantum critical point where the hybridization goes to zero at zero temperature. At this fixed point, the f electrons experience as well a selective Mott transition separating a local-moment phase from a Kondo-screened phase. The presence of a multiscale quantum critical point in the Anderson lattice in the absence of magnetism is discussed in the context of heavy fermion compounds. This study is the first evidence for a selective Mott transition in the Anderson lattice.

Kondo breakdown and hybridization fluctuations in the kondo-heisenberg lattice

We study the deconfined quantum critical point of the Kondo-Heisenberg lattice in three dimensions using a fermionic representation for the localized spins. The mean-field phase diagram exhibits a zero temperature quantum critical point separating a spin liquid phase where the hybridization vanishes and a Kondo phase where it does not. Two solutions can be stabilized in the Kondo phase: namely, a uniform hybridization when the band masses of the conduction electrons and the spinons have the same sign, and a modulated one when they have opposite sign. For the uniform case, we show that above a very small temperature scale, the critical fluctuations associated with the vanishing hybridization have dynamical exponent z=3, giving rise to a resistivity that has a TlogT behavior. We also find that the specific heat coefficient diverges logarithmically in temperature, as observed in a number of heavy fermion metals.

Fractionalization, topological order, and quasiparticle statistics

We argue, based on general principles, that topological order is essential to realize fractionalization in gapped insulating phases in dimensions d > or = 2. In d = 2 with genus g, we derive the existence of the minimum topological degeneracy q(g) if the charge is fractionalized in units of 1/q, irrespective of microscopic model or effective theory. Furthermore, if the quasiparticle is either boson or fermion, it must be at least q(2g).

Hidden Caldeira-Leggett dissipation in a Bose-Fermi Kondo model

We show that the Bose-Fermi Kondo model (BFKM), which may find applicability both to certain dissipative mesoscopic qubit devices and to heavy-fermion systems described by the Kondo lattice model, can be mapped exactly onto the Caldeira-Leggett model. This mapping requires an ohmic bosonic bath and an Ising-type coupling between the latter and the impurity spin. This allows us to conclude unambiguously that there is an emergent Kosterlitz-Thouless quantum phase transition in the BFKM with an ohmic bosonic bath. By applying a bosonic numerical renormalization group approach, we thoroughly probe physical quantities close to the quantum phase transition.

Understanding the heavy fermion phenomenology from a microscopic model

We solve the 3D periodic Anderson model using a two impurity cluster dynamical mean field theory. We obtain the temperature versus hybridization phase diagram. Approaching the quantum critical point (QCP) both the Néel and lattice Kondo temperatures decrease and they do not cross at the lowest temperature we reached. While strong ferromagnetic spin fluctuation on the Kondo side is observed, our result suggests the critical static spin susceptibility is local in space at the QCP. We observe in the crossover region a logarithmic temperature dependence in the specific heat coefficient and spin susceptibility.

Fractionalization and Fermi-surface volume in heavy-fermion compounds: the case of YbRh2Si2

We establish an effective theory for heavy-fermion compounds close to a zero temperature antiferromagnetic (AFM) transition. Coming from the heavy Fermi liquid phase across to the AFM phase, the heavy electron fractionalizes into a light electron, a bosonic spinon, and a new excitation: a spinless fermionic field. Assuming this field acquires dynamics and dispersion when one integrates out the high energy degrees of freedom, we give a scenario for the volume of its Fermi surface through the phase diagram. We apply our theory to the special case of YbRh2(Si1-xGex)2 where we recover, within experimental resolution, several low temperature exponents for transport and thermodynamics.

Quantum critical properties of the Bose-Fermi Kondo model in a large-N limit

Studies of non-Fermi-liquid properties in heavy fermions have led to the current interest in the Bose-Fermi Kondo model. Here we use a dynamical large-N approach to analyze an SU(N)xSU(kappaN) generalization of the model. We establish the existence in this limit of an unstable fixed point when the bosonic bath has a sub-Ohmic spectrum (/omega/(1-epsilon)sgnomega, with 0<epsilon<1). At the quantum-critical point, the Kondo scale vanishes and the local spin susceptibility (which is finite on the Kondo side for kappa<1) diverges. We also find an omega/T scaling for an extended range (15 decades) of omega/T. This scaling violates (for epsilon> or =1/2) the expectation of a naive mapping to certain classical models in an extra dimension; it reflects the inherent quantum nature of the critical point.

Nexus between quantum criticality and phase formation in U(Ru1-xRhx)2Si2

Simplification of the magnetic field-versus-temperature phase diagram and quantum criticality in URu2Si2 dilutely doped with Rh are studied by measuring the magnetization and resistivity in magnetic fields of up to 45 T. For x=4%, the hidden order is completely destroyed, leaving a single field-induced phase II. A correlation between the field dependence of this phase and that of the quantum critical point, combined with the suppression of the T2 coefficient of the resistivity within it, implicates field-tuned quantum criticality as an important factor in phase formation.