Critical quasiparticles in single-impurity and lattice Kondo models (original) (raw)
Related papers
Critical phenomena near the antiferromagnetic quantum critical point of heavy fermions
Physical Review B, 2000
We present a study of the critical phenomena around the quantum critical point in heavy-fermion systems. In the framework of the S = 1/2 Kondo lattice model, we introduce an extended decoupling scheme of the Kondo interaction which allows one to treat the spin fluctuations and the Kondo effect on an equal footing. The calculations, developed in a self-consistent oneloop approximation, lead to the formation of a damped collective mode with a dynamic exponent z = 2 in the case of an antiferromagnetic instability. The system displays a quantum-classical crossover at finite temperature depending how the energy of the mode, on the scale of the magnetic correlation length, compares to k B T. The low temperature behavior, in the different regimes separated by the crossover temperatures, is then discussed for both 2-and 3-dimensional systems.
Quantum criticality in heavy-fermion metals
Nature Physics, 2008
Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy-fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, that use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including the extent to which the quantum criticality in heavy-fermion metals goes beyond the standard theory of order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, the non-Fermi-liquid phenomena that accompany quantum criticality and the interplay between quantum criticality and unconventional superconductivity.
Kondo Destruction and Quantum Criticality in Kondo Lattice Systems
Journal of the Physical Society of Japan, 2014
Considerable efforts have been made in recent years to theoretically understand quantum phase transitions in Kondo lattice systems. A particular focus is on Kondo destruction, which leads to quantum criticality that goes beyond the Landau framework of order-parameter fluctuations. This unconventional quantum criticality has provided an understanding of the unusual dynamical scaling observed experimentally. It also predicted a sudden jump of the Fermi surface and an extra (Kondo destruction) energy scale, both of which have been verified by systematic experiments. Considerations of Kondo destruction have in addition yielded a global phase diagram, which has motivated the current interest in heavy fermion materials with variable dimensionality or geometrical frustration. Here we summarize these developments, and discuss some of the ongoing work and open issues. We also consider the implications of these results for superconductivity. Finally, we address the effect of spin-orbit coupling on the global phase diagram, suggest that SmB 6 under pressure may display unconventional superconductivity in the transition regime between a Kondo insulator phase and an antiferroamgnetic metal phase, and argue that the interfaces of heavy-fermion heterostructures will provide a fertile setting to explore topological properties of both Kondo insulators and heavyfermion superconductors.
Fermiology in a Local Quantum Critical Metal
Recent experimental work has brought the twin issues of the origin of non-Lifshitz-Kosevich scaling in de Haas van Alphen (dHvA) and its precise relation to anomalously broad non-quasiparticle spectral features in "strange" metals, to the forefront. Here, we revisit these issues in the specific context of a "local" quantum critical phase in an extended periodic Anderson model (EPAM). In contrast to the famed Kondo-RKKY scenarios for local quantum criticality, strong local valence fluctuations cause Kondo destruction in the EPAM. We uncover a common underlying element, namely, the Kondo-destruction driven infra-red continuum branch-cut behavior in the one-electron propagator, as the relevant feature that governs both non-Lifshitz-Kosevich scaling in dHvA and anomalously broad non-quasiparticle spectral responses in such a "strange" metal. Employing a non-perturbative scheme to treat effects of non-magnetic disorder in this version of a local strange metal, we propose a modified Dingle scaling that can also be used to test "local" criticality scenarios. Thus, our findings potentially afford an internally consistent description of novel fermiology expected to manifest in strange metals arising as a result of Kondo-destruction arising from an underlying orbital-selective Mott transition. PACS numbers: 71.28+d,71.30+h,72.10-d arXiv:1507.04670v1 [cond-mat.str-el] 16 Jul 2015
arXiv: Strongly Correlated Electrons, 2019
Quantum criticality in certain heavy-fermion metals is believed to go beyond the Landau framework of order-parameter fluctuations. In particular, there is considerable evidence for Kondo destruction: a disappearance of the static Kondo singlet amplitude that results in a sudden reconstruction of Fermi surface across the quantum critical point and an extra critical energy scale. This effect can be analyzed in terms of a dynamical interplay between the Kondo and RKKY interactions. In the Kondo-destroyed phase, a well-defined Kondo resonance is lost, but Kondo singlet correlations remain at nonzero frequencies. This dynamical effect allows for mass enhancement in the Kondo-destroyed phase. Here, we elucidate the dynamical Kondo effect in Bose-Fermi Kondo/Anderson models, which unambiguously exhibit Kondo-destruction quantum critical points. We show that a simple physical quantity---the expectation value langlebfSfcdotbfscrangle\langle {\bf S}_{f} \cdot {\bf s}_{c} \ranglelanglebfSfcdotbfscrangle for the dot product of the local ($...
Two-channel pseudogap Kondo and Anderson models: Quantum phase transitions and non-Fermi liquids
Physical Review B, 2011
We discuss the two-channel Kondo problem with a pseudogap density of states, ρ(ω) ∝ |ω| r , of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi liquid behavior of the metallic r = 0 case, is replaced by a stable particle-hole symmetric intermediate-coupling fixed point for 0 < r < rmax ≈ 0.23. For r > rmax, this non-Fermi liquid phase disappears, and instead a critical fixed point with an emergent spin-channel symmetry appears, controlling the quantum phase transition between two phases with stable spin and channel moments, respectively. We propose lowenergy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ epsilon expansion techniques to calculate critical properties near the critical dimensions r = 0 and r = 1, the latter being potentially relevant for two-channel Kondo impurities in neutral graphene. We find the analytical results to be in excellent agreement with those obtained from applying Wilson's numerical renormalization group technique.
Quantum criticality out of equilibrium in the pseudogap Kondo model
Physical Review B, 2012
We theoretically investigate the non-equilibrium quantum phase transition in a generic setup: the pseudogap Kondo model where a quantum dot couples to two-left (L) and right (R)-voltage-biased fermionic leads with power-law density of states (DOS) with respect to their Fermi levels µ L/R , ρ c,L(R) (ω) ∝ |ω − µ L(R) | r , and 0 < r < 1. In equilibrium (zero bias voltage) and for 0 < r < 1/2, with increasing Kondo correlations, in the presence of particle-hole symmetry this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo phase. Via a controlled frequency-dependent renormalization group (RG) approach, we compute analytically and numerically the non-equilibrium conductance, conduction electron T-matrix and local spin susceptibility at finite bias voltages near criticality. The current-induced decoherence shows distinct nonequilibrium scaling, leading to new universal non-equilibrium quantum critical behaviors in the above observables. Relevance of our results for the experiments is discussed.
Approaching quantum criticality in a partially geometrically frustrated heavy-fermion metal
In the antiferromagnetic (AF) heavy-fermion system CePdAl the magnetic Ce ions form a network of equilateral triangles in the (001) plane, similar to the kagomé lattice, with one third of the Ce moments not participating in the long-range order. The Néel temperature T N = 2.7 K is reduced upon replacing Pd by Ni in CePd 1−x Ni x Al, with T N → 0 for x = 0.144, where the specific heat C exhibits a C/T ∝ − log T dependence. Within the Hertz-Millis-Moriya model of quantum criticality, this behavior might indicate 2D critical antiferromagnetic fluctuations arising from the decoupling of 3D magnetic order by frustration. On the other hand, the simultaneous presence of Kondo effect and geometric frustration might entail a different route to quantum criticality.
Strong coupling theory of heavy fermion criticality
2013
We present a theory of the scaling behavior of the thermodynamic, transport and dynamical properties of a three-dimensional metal at an antiferromagnetic critical point. We show how the critical spin fluctuations at the AFM wavevector q=Q induce energy fluctuations at small q, giving rise to a diverging quasiparticle effective mass over the whole Fermi surface. The coupling of the fermionic and bosonic degrees of freedom leads to a self-consistent relation for the effective mass, which has a strong coupling solution in addition to the well-known weak-coupling, spin-density-wave solution. We thereby use the recently-introduced concept of critical quasiparticles, employing a scale-dependent effective mass ratio m*/m and quasiparticle weight factor Z. As a consequence of the diverging effective mass the Landau Fermi liquid interaction is found to diverge in all channels except the critical one, causing important vertex corrections. The ensuing spin fluctuation spectrum obeys omega/T sc...
Locally critical quantum phase transitions in strongly correlated metals
Nature, 2001
When a metal undergoes a continuous quantum phase transition, non-Fermi-liquid behaviour arises near the critical point. All the low-energy degrees of freedom induced by quantum criticality are usually assumed to be spatially extended, corresponding to long-wavelength¯uctuations of the order parameter. But this picture has been contradicted by the results of recent experiments on a prototype system: heavy fermion metals at a zero-temperature magnetic transition. In particular, neutron scattering from CeCu 6-x Au x has revealed anomalous dynamics at atomic length scales, leading to much debate as to the fate of the local moments in the quantum-critical regime. Here we report our theoretical ®nding of a locally critical quantum phase transition in a model of heavy fermions. The dynamics at the critical point are in agreement with experiment. We propose local criticality to be a phenomenon of general relevance to strongly correlated metals.