Fermi-liquid Form Research Articles

Non-Fermi Liquid Behavior in the Three-Dimensional Hubbard Model

We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.

Determinant quantum Monte Carlo study of exhaustion in the periodic Anderson model

The Kondo and Periodic Anderson models describe many of the qualitative features of local moments coupled to a conduction band, and thereby the physics of materials such as the heavy fermions. In particular, when the exchange coupling $J$ or hybridization $V$ between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small $J$ or $V$, limit, the moments survive, and the conduction electrons mediate an effective interaction which can trigger long range, often antiferromagnetic, order. In the case of the Kondo model, where the moments are described by local spins, Nozi\`eres considered the possibility that the available conduction electrons within the Kondo temperature of the Fermi surface would be insufficient in number to accomplish the screening. Much effort in the literature has been devoted to the study of the temperature scales in the resulting `exhaustion' problem, and how the `coherence temperature' where a heavy Fermi liquid forms is related to the Kondo temperature. In this paper, we study a version of the Periodic Anderson model in which some of the conduction electrons are removed in a way which avoids the fermion sign problem and hence allows low temperature Quantum Monte Carlo simulations which can access both singlet formation and magnetic ordering temperature scales. We are then able to focus on a somewhat different aspect of exhaustion physics than previously considered: the effect of dilution on the critical $V$ for the singlet-antiferromagnetic transition.

Z2 fractionalized phases of a solvable disordered t−J model

We describe the phases of a solvable $t$-$J$ model of electrons with infinite-range, and random, hopping and exchange interactions, similar to those in the Sachdev-Ye-Kitaev models. The electron fractionalizes, as in an `orthogonal metal', into a fermion $f$ which carries both the electron spin and charge, and a boson $\phi$. Both $f$ and $\phi$ carry emergent $\mathbb{Z}_2$ gauge charges. The model has a phase in which the $\phi$ bosons are gapped, and the $f$ fermions are gapless and critical, and so the electron spectral function is gapped. This phase can be considered as a toy model for the underdoped cuprates. The model also has an extended, critical, `quasi-Higgs' phase where both $\phi$ and $f$ are gapless, and the electron operator $\sim f \phi$ has a Fermi liquid-like $1/\tau$ propagator in imaginary time, $\tau$. So while the electron spectral function has a Fermi liquid form, other properties are controlled by $\mathbb{Z}_2$ fractionalization and the anomalous exponents of the $f$ and $\phi$ excitations. This `quasi-Higgs' phase is proposed as a toy model of the overdoped cuprates. We also describe the critical state separating these two phases.

Nonseparable frequency dependence of the two-particle vertex in interacting fermion systems

We derive functional flow equations for the two-particle vertex and the self-energy in interacting fermion systems which capture the full frequency dependence of both quantities. The equations are applied to the hole-doped two-dimensional Hubbard model as a prototype system with entangled magnetic, charge and pairing fluctuations. Each fluctuation channel acquires substantial dependencies on all three Matsubara frequencies, such that the frequency dependence of the vertex cannot be accurately represented by a channel sum with only one frequency variable in each term. At the temperatures we are able to access, the leading instabilities are mostly antiferromagnetic, with an incommensurate wave vector. However, at large doping, a divergence in the charge channel occurs at a finite frequency transfer, if the vertex flow is computed without self-energy feedback. This enigmatic instability was already observed in a calculation by Husemann et al. [Phys. Rev. B 85, 075121 (2012)], who used an approximate separable ansatz for the frequency dependence of the vertex. We identify a simple mechanism for this instability in terms of a random phase approximation for the charge channel with a frequency dependent effective magnetic interaction as input. In spite of the strong momentum and frequency dependence of the vertex, the self-energy has a Fermi liquid form. At the moderate interaction strength where our approach is applicable, we obtain a moderate reduction of the quasi-particle weight and a sizable decay rate with a pronounced momentum dependence. Nevertheless, the self-energy feedback into the vertex flow turns out to be crucial, as it suppresses the unphysical finite frequency charge instability.

Quantum Phase Transitions and Multicriticality in Ta(Fe1−xVx)2

We present a comprehensive study of synthesis, structure analysis, transport and thermodynamic properties of the C14 Laves phase Ta(Fe1-xVx)2. Our measurements confirm the appearance of spin-density wave (SDW) order within a dome-like region of the x - T phase diagram with vanadium content 0.02 < x < 0.3. Our results indicate that on approaching TaFe2 from the vanadium-rich side, ferromagnetic (FM) correlations increase faster than the antiferromagnetic (AFM) ones. This results in an exchange-enhanced susceptibility and in the suppression of the SDW transition temperature for x < 0.13 forming the dome-like shape of the phase diagram. This effect is strictly related to a significant lattice distortion of the crystal structure manifested in the c/a ratio. At x = 0.02 both FM and AFM energy scales have similar strength and the system remains paramagnetic down to 2 K with an extremely large Stoner enhancement factor of about 400. Here, spin fluctuations dominate the temperature dependence of the resistivity \rho ~ T ^ 3/2 and of the specific heat C/T ~ - log(T) which deviate from their conventional Fermi liquid forms, inferring the presence of a quantum critical point of dual nature.

Shear viscosity of strongly interacting fermionic quantum fluids

Eighty years ago, Eyring proposed that the shear viscosity of a liquid η has a quantum limit η≳nℏ where n is the density of the fluid. Using holographic duality and the anti–de Sitter/conformal field theory correspondence in string theory, Kovtun, Son, and Starinets (KSS) conjectured a universal bound ηs≥ℏ4πkB for the ratio between the shear viscosity and the entropy density s. Using dynamical mean-field theory, we calculate the shear viscosity and entropy density for a fermionic fluid described by a single-band Hubbard model at half-filling. Our calculated shear viscosity as a function of temperature is compared with experimental data for liquid He3. At low temperature, the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid 1/T2 dependence, where T is the temperature. With increasing temperature and interaction strength U, there is significant deviation from the Fermi liquid form. Also, the shear viscosity violates the quantum limit near the crossover from coherent quasiparticle-based transport to incoherent transport (the bad metal regime). Finally, the ratio of the shear viscosity to the entropy density is found to be comparable to the KSS bound for parameters appropriate to liquid He3. However, this bound is found to be strongly violated in the bad metal regime for parameters appropriate to lattice electronic systems such as organic charge-transfer salts.Received 3 June 2015Revised 17 August 2015DOI:https://doi.org/10.1103/PhysRevB.92.125103©2015 American Physical Society

Magnetic exchange inα-iron fromab initiocalculations in the paramagnetic phase

Applying the local density approximation (LDA) and dynamical mean field theory (DMFT) to paramagnetic $\alpha $-iron, we revisit a problem of theoretical description of its magnetic properties. The analysis of local magnetic susceptibility shows that at sufficiently low temperatures $T<1500K$, both, $e_{g}$ and $t_{2g}$ states equally contribute to the formation of the effective magnetic moment with spin S=1. The self-energy of t_{2g} states shows sizable deviations from Fermi-liquid form, which accompanies earlier found non-quasiparticle form of e_{g} states. By considering the non-uniform magnetic susceptibility we find that the non-quasiparticle form of $e_{g}$ states is crucial for obtaining ferromagnetic instability in $\alpha $-iron. The main contribution to the exchange interaction, renormalized by the effects of electron interaction, comes from the hybridization between $t_{2g}$ and $e_{g}$ states. We furthermore suggest the effective spin-fermion model for $\alpha $-iron, which allows us to estimate the exchange interaction from paramagnetic phase, which is in agreement with previous calculations in the ordered state within the LDA approaches.

Extremely correlated Fermi liquid theory meets dynamical mean-field theory: Analytical insights into the doping-driven Mott transition

We consider a doped Mott insulator in the large dimensionality limit within both the recently developed extremely correlated Fermi liquid (ECFL) theory and the dynamical mean-field theory (DMFT). We show that the general structure of the ECFL sheds light on the rich frequency dependence of the DMFT self-energy. Using the leading Fermi liquid form of the two key auxiliary functions introduced in the ECFL theory, we obtain an analytical ansatz, which provides a good quantitative description of the DMFT self-energy down to hole doping level $\ensuremath{\delta}\ensuremath{\simeq}0.2$. In particular, the deviation from Fermi liquid behavior and the corresponding particle-hole asymmetry developing at a low-energy scale are well reproduced by this ansatz. The DMFT being exact at large dimensionality, our study also provides a benchmark of the ECFL in this limit. We find that the main features of the self-energy and spectral line shape are well reproduced by the ECFL calculations in the $O({\ensuremath{\lambda}}^{2})$ minimal scheme, for not too low doping level $\ensuremath{\delta}\ensuremath{\gtrsim}0.3$. The DMFT calculations reported here are performed using a state-of-the-art numerical renormalization-group impurity solver, which yields accurate results down to an unprecedentedly small doping level $\ensuremath{\delta}\ensuremath{\lesssim}0.001$.

Quantum-critical pairing in electron-doped cuprates

We revisit the problem of spin-mediated superconducting pairing at the antiferromagnetic quantum-critical point with the ordering momentum ({\pi},{\pi}) = 2k_F. The problem has been previously considered by one of the authors. However, it was later pointed out that that analysis neglected umklapp processes for the spin polarization operator. We incorporate umklapp terms and re-evaluate the normal state self-energy and the critical temperature of the pairing instability. We show that the self-energy has a Fermi-liquid form and obtain the renormalization of the quasiparticle residue Z, the Fermi velocity, and the curvature of the Fermi surface. We argue that the pairing is a BCS-type problem, but go one step beyond the BCS theory and calculate the critical temperature T_c with the prefactor. We apply the results to electron-doped cuprates near optimal doping and obtain T_c \geq 10 K, which matches the experimental results quite well.

Magnetism inNb1−yFe2+y: Composition and magnetic field dependence

We present a systematic study of transport and thermodynamic properties of the Laves phase system ${\text{Nb}}_{1\ensuremath{-}y}{\text{Fe}}_{2+y}$. Our measurements confirm that Fe-rich samples, as well as those rich in Nb (for $|y|\ensuremath{\ge}0.02$), show bulk ferromagnetism at low temperature. For stoichiometric ${\text{NbFe}}_{2}$, on the other hand, magnetization, magnetic susceptibility, and magnetoresistance results point toward spin-density wave (SDW) order, possibly helical, with a small ordering wave vector $Q\ensuremath{\sim}0.05\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$. Our results suggest that on approaching the stoichiometric composition from the iron-rich side, ferromagnetism changes into long-wavelength SDW order. In this scenario, $Q$ changes continuously from 0 to small, finite values at a Lifshitz point in the phase diagram, which is located near $y=+0.02$. Further reducing the Fe content suppresses the SDW transition temperature, which extrapolates to zero at $y\ensuremath{\approx}\ensuremath{-}0.015$. Around this Fe content magnetic fluctuations dominate the temperature dependence of the resistivity and of the heat capacity which deviate from their conventional Fermi-liquid forms, inferring the presence of a quantum critical point. Because the critical point is located between the SDW phase associated with stoichiometric ${\text{NbFe}}_{2}$ and the ferromagnetic order which reemerges for very Nb-rich ${\text{NbFe}}_{2}$, the observed temperature dependences could be attributed both to proximity to SDW order or to ferromagnetism.

Quasiparticle anisotropy and pseudogap formation: A weak-coupling renormalization-group analysis

Abstract We calculate the self-energy at weak-coupling for the t – t ′ Hubbard model within the one-loop functional RG approach. At van Hove (vH) band fillings the quasiparticle (qp) concept is found invalid at k F =( π , 0). At low temperature the qp weight along the Fermi surface continuously vanishes from a finite value at the zone diagonal towards the ( π , 0) point. Away from vH band fillings the qp peak is formed inside a pseudogap of size Δ, and within a finite frequency window | ω |≪ Δ around the Fermi energy the electronic self-energy has the conventional Fermi-liquid form. With increasing separation between Fermi level and vHs the spectral anomalies gradually disappear.

Spin-fluctuation-dominated electrical transport ofNi3Alat high pressure

We present the first study of a magnetic quantum phase transition in the itinerant-electron ferromagnet Ni3Al at high pressures. Electrical resistivity measurements in a diamond anvil cell at hydrostatic pressures up to 100 kbar and temperatures as low as 50 mK indicate that the Curie temperature collapses towards absolute zero at a critical pressure pc=82(2) kbar. Over wide ranges in pressure and temperature, both in the ferromagnetic and paramagnetic states, the temperature variation of the resistivity is found to deviate from the conventional Fermi-liquid form. We consider the extent to which this deviation can be understood in terms of a mean-field model of enhanced spin fluctuations on the border of ferromagnetism in three dimensions.

Nonanalytic corrections to the Fermi-liquid behavior

The issue of non-analytic corrections to the Fermi-liquid behavior is revisited. Previous studies have indicated that the corrections to the Fermi-liquid forms of the specific heat and the static spin susceptibility scale as $T^{D}$ and $T^{D-1}$, respectively (with extra logarithms for $D=1,3$). In addition, the non-uniform spin susceptibility is expected to depend on the bosonic momentum $Q$ in a non-analytic way, i.e., as $Q^{D-1}$ (again with extra logarithms for $D=1,3$). It is shown that these non-analytic corrections originate from the universal singularities in the dynamical bosonic response functions of a generic Fermi liquid. In contrast to the leading, Fermi-liquid forms which depend on the interaction averaged over the Fermi surface, the non-analytic corrections are parameterized by only two coupling constants, which are the components of the interaction potential at momentum transfers $q=0$ and $q=2k_F$. For 3D systems, a recent result of Belitz, Kirkpatrick and Vojta for the spin susceptibility is reproduced and the issue why a non-analytic momentum dependence of the non-uniform spin susceptibility ($Q^{2}\ln |Q|$) is \emph{not}paralleled by a non-analyticity in the $T-$ dependence ($T^2$) is clarified. For the case of a 2D system with a finite-range interaction, explicit forms of the corrections to the specific heat ($\propto T^2$), uniform ($\propto T$) and non-uniform ($\propto |Q|$) spin susceptibilities are obtained. It is shown that previous calculations of the temperature dependences of these quantities in 2D were incomplete. Some of the results and conclusions of this paper have recently been announced in a short communication [A. V. Chubukov and D. L. Maslov, cond-mat/0304381].

Heat capacity of 3He in aerogel.

The heat capacity of pure 3He in low density aerogel is measured at 22.5 bars. The superfluid response is simultaneously monitored with a torsional oscillator. A slightly rounded heat capacity peak, 65 microK in width, is observed at the 3He-aerogel superfluid transition, T(ca). Subtracting the bulk 3He contribution, the heat capacity shows a Fermi-liquid form above T(ca). We can fit the heat capacity attributed to superfluid within the aerogel with a rounded BCS form accounting for 0.30 of the nonbulk fluid in the aerogel, or by assuming a substantial reduction in the superfluid order parameter. Both approaches are consistent with earlier superfluid density measurements.

Instability of the non-Fermi-liquid state in a metal with d or f impurities

It is shown that the non-Fermi-liquid state is unstable with respect to scattering of multiparticle excitations with different quantum numbers by one another. As a result of the scattering, a multiparticle Fermi-liquid resonance forms at the Fermi level. An anomalous increase in the conductivity occurs as a result of a transition between the non-Fermi-liquid and Fermi-liquid states.

Unconventional properties of superconducting cuprates

We present an explanation of the unusual peak/dip/hump features observed in photoemission experiments on Bi2212 at T⪡ T c. We argue that the strong spin-fermion interaction combined with the feedback effect on the spin damping due to superconductivity yields a Fermi liquid form of the fermionic spectral function for ω<2 Δ where Δ is the maximum value of the superconducting gap, and a nonFermi liquid form for ω>2 Δ. In the Fermi liquid regime, the spectral function A(k F , ω) displays a quasiparticle peak at ω= Δ; in the nonFermi liquid regime it possesses a broad maximum at ω⪢ Δ. In between the two regimes, the spectral function has a dip at ω∼2 Δ.

Anomalous Resonance of the Symmetric Single-Impurity Anderson Model in the Presence of Pairing Fluctuations

We consider the symmetric single-impurity Anderson model in the presence of pairing fluctuations. In the isotropic limit, the degrees of freedom of the local impurity are separated into hybridizing and non-hybridizing modes. The self-energy for the hybridizing modes can be obtained exactly, leading to two subbands centered at $\pm U/2$. For the non-hybridizing modes, the second order perturbation yields a singular resonance of the marginal Fermi liquid form. By multiplicative renomalization, the self-energy is derived exactly, showing the resonance is pinned at the Fermi level, while its strength is weakened by renormalization.

Tunneling through point contacts in the quantum Hall effect

We study tunneling through gated point contacts on GaAs/AlGaAs heterojunctions in the regime of the integer (IQHE) and fractional (FQHE) quantum Hall effects. The off-resonant conductance data at bulk filling factor ν= 1 3 has a steep temperature dependence that is roughly consistent with the predictions of Luttinger liquid theory for edge states. In the IQHE, we find only weak temperature dependence at ν=1 in the bulk. However, the line shape of tunneling resonances at ν=1 is not well fit by a Fermi-liquid form, perhaps indicating that complex edge structure affects resonant transmission.

Theory of the optical conductivity in the cuprate superconductors

We present a study of the normal state optical conductivity in the cuprate superconductors using the nearly antiferromagnetic Fermi liquid (NAFL) description of the magnetic interaction between their planar quasiparticles. We find that the highly anisotropic scattering rate in different regions of the Brillouin zone, both as a function of frequency and temperature, a benchmark of NAFL theory, leads to an average relaxation rate of the Marginal Fermi Liquid form for overdoped and optimally doped systems, as well as for underdoped systems at high temperatures. We carry out numerical calculations of the optical conductivity for several compounds for which the input spin fluctuation parameters are known. Our results, which are in agreement with experiment on both overdoped and optimally doped systems, show that NAFL theory explains the anomalous optical behavior found in these cuprate superconductors.

Spectral properties of the planar t- J model

Results for the single-particle spectral function A( k, ω) in the planar t- J model, obtained by the numerical finite-temperature method for small systems, are presented. At intermediate doping and at low temperatures spectra show strong asymmetry between the hole and electron part, and near the Fermi surface reveal the marginal Fermi-liquid form. An analytical approach, based on the equations of motion for projected Green's functions and the decoupling approximation, reproduces reasonably these features.