Localization-induced Griffiths phase of disordered Anderson lattices

Electronic Griffiths Phase in Disordered Mott-Transition Systems

Solid-state physics and soft-matter physics have been developed independently, with little mutual exchange of the underlying physical concepts. However, after many studies of correlated electron systems, it has been recognized that correlated electrons (especially in Mott-transition systems) in solid matter sometimes show behavior similar to "structured fluids" in soft matter; that is, the electrons exhibit long-length self-organization (but without long-range order) and slow dynamics, which is inevitable for the long-length structures. The essential question is this: what condition causes such behavior in solid matter? We focused on an organic Mott-transition system and demonstrated that the electrons of this system fluctuate very slowly only when the following two factors are met simultaneously: (i) the electronic system is on the metal and Mott-insulator boundary and (ii) the system is subject to quenched disorder. This electronic state with slow dynamics under this condition can be explained by the concept of the "(electronic) Griffiths phase." This concept will potentially be a key in connecting solid-state physics with soft-matter physics.

Non-Fermi Liquid Behavior and Continuously Tunable Resistivity Exponents in the Anderson-Hubbard Model at Finite Temperature

We employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation U and disorder V strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling T^{α} for this metal reveals non-Fermi liquid characteristics. Moreover, a continuous dependence of α on U and V from linear to nearly quadratic is observed. We argue that these exotic results arise from a systematic change with U and V of the "effective" disorder, a combination of quenched disorder and intrinsic localized spins.

Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments

Motivated by the intrinsic non-Fermi-liquid behavior observed in the heavy-fermion quasicrystal Au51Al34Yb15, we study the low-temperature behavior of dilute magnetic impurities placed in metallic quasicrystals. We find that a large fraction of the magnetic moments are not quenched down to very low temperatures T, leading to a power-law distribution of Kondo temperatures P(T(K))∼T(K)(α-1), with a nonuniversal exponent α, in a remarkable similarity to the Kondo-disorder scenario found in disordered heavy-fermion metals. For α<1, the resulting singular P(T(K)) induces non-Fermi-liquid behavior with diverging thermodynamic responses as T→0.

Electronic Griffiths phase in the Te-doped semiconductor FeSb2

We report on the emergence of an electronic Griffiths phase in the doped semiconductor FeSb(2), predicted for disordered insulators with random localized moments in the vicinity of a metal-insulator transition. Magnetic, transport, and thermodynamic measurements of Fe(Sb(1-x)Te(x))(2) single crystals show signatures of disorder-induced non-Fermi liquid behavior and a Wilson ratio expected for strong electronic correlations. The electronic Griffiths phase states are found on the metallic boundary between the insulating state (x = 0) and a long-range albeit weak magnetic order (x ≥ 0.075).

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.

Novel duality in disorder driven local quantum criticality

We find that competition between random Kondo and random magnetic correlations results in a quantum phase transition from a local Fermi liquid to a spin liquid. The local charge susceptibility turns out to have exactly the same critical exponent as the local spin susceptibility, suggesting a novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson symmetry breaking framework. This leads us to propose an enhanced symmetry at the local quantum critical point, described by an O(4) vector for spin and charge. The symmetry enhancement serves as a mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.

Electronic Griffiths phase of the d = 2 Mott transition

We investigate the effects of disorder within the T = 0 Brinkman-Rice scenario for the Mott metal-insulator transition in two dimensions. For sufficiently weak disorder the transition retains the Mott character, as signaled by the vanishing of the local quasiparticle weights Z_{i} and strong screening of the renormalized site energies at criticality. In contrast to the behavior in high dimensions, here the local spatial fluctuations of quasiparticle parameters are strongly enhanced in the critical regime, with a distribution function P(Z) approximately Z;{alpha-1} and alpha --> 0 at the transition. This behavior indicates a robust emergence of an electronic Griffiths phase preceding the metal-insulator transition, in a fashion surprisingly reminiscent of the "infinite randomness fixed point" scenario for disordered quantum magnets.

Universal distribution of Kondo temperatures in dirty metals

Kondo screening of diluted magnetic impurities in a disordered host is studied analytically and numerically in one, two, and three dimensions. It is shown that in the T(K) --> 0 limit the distribution of Kondo temperatures has a universal form P(T(K)) approximately T(K) (-a) that holds in the insulating phase and persists in the metallic phase close to the metal-insulator transition. Moreover, the exponent depends only on the dimensionality. The most important consequence of this result is that the T dependence of thermodynamic properties is smooth across the metal-insulator transition in three dimensional systems.

Spin-liquid behavior in electronic griffiths phases

We examine the interplay of the Kondo effect and the RKKY interactions in electronic Griffiths phases using extended dynamical mean-field theory methods. We find that sub-Ohmic dissipation is generated for sufficiently strong disorder, leading to the suppression of Kondo screening on a finite fraction of spins, and giving rise to universal spin-liquid behavior.

Absence of conventional quantum phase transitions in itinerant systems with disorder

Effects of disorder are examined in itinerant systems close to quantum critical points. We argue that spin fluctuations due to the long-range part of the RKKY interactions generically induce non-Ohmic dissipation due to rare disorder configurations. This dissipative mechanism is found to destabilize quantum Griffiths phase behavior in itinerant systems with arbitrary symmetry of the order parameter, leading to the formation of a "cluster glass" phase preceding uniform ordering.