Marginal Fermi Liquid Behavior Research Articles

The Shrinking Fermi Liquid Scenario for Strange-Metal Behavior from Overdamped Optical Phonons

We discuss how the interaction of electrons with an overdamped optical phonon can give rise to a strange-metal behavior over extended temperature and frequency ranges. Although the mode has a finite frequency, an increasing damping shifts spectral weight to progressively lower energies so that despite the ultimate Fermi liquid character of the system at the lowest temperatures and frequencies, the transport and optical properties of the electron system mimic a marginal Fermi liquid behavior. Within this shrinking Fermi liquid scenario, we extensively investigate the electron self-energy in all frequency and temperature ranges, emphasizing similarities and differences with respect to the marginal Fermi liquid scenario.

Quantum critical fluctuations in an Fe-based superconductor

Quantum critical fluctuations may prove to play an instrumental role in the formation of unconventional superconductivity. Here, we show that the characteristic scaling of a marginal Fermi liquid is present in inelastic light scattering data of an Fe-based superconductor tuned through a quantum critical point (QCP) by chemical substitution or doping. From the doping dependence of the imaginary time dynamics we are able to distinguish regions dominated by quantum critical behavior from those having classical critical responses. This dichotomy reveals a connection between the marginal Fermi liquid behavior and quantum criticality. In particular, the overlap between regions of high superconducting transition temperatures and quantum critical scaling suggests a contribution from quantum fluctuations to the formation of superconductivity.

Metallic spin-liquid-like behavior of LiV2O4

LiV$_2$O$_4$ spinel is known to exhibit heavy fermion-like behavior below a characteristic temperature $T_K\simeq 20$ K, while it preserves a paramagnetic state down to $T\sim10^{-2}$ K due to geometrical frustration. Here, it is shown that the dynamical spin susceptibility $\chi({\bf q},\omega)$ in LiV$_2$O$_4$ exhibits anomalous duality which is modeled as a sum of itinerant ($\chi_{\rm F}$) and local ($\chi_{\rm L}$) components,and that the local spin dynamics inferred from $\chi_{\rm L}({\bf q},\omega)$ is qualitatively different from that expected from time-averaged bulk properties. The anomaly coexists with the marginal Fermi liquid behavior inferred from the $-\ln T$ dependence of the electronic specific heat over a wide temperature range below $T_K$. We argue that such unusual properties of LiV$_2$O$_4$ can be attributed to the putative metallic spin liquid state emerging near the quantum critical point between spin glass and Fermi liquid states.

Translationally Invariant Non-Fermi-Liquid Metals with Critical Fermi Surfaces: Solvable Models

We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $d<\infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.

Emergent Non-Fermi-Liquid at the Quantum Critical Point of a Topological Phase Transition in Two Dimensions.

We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and nonrelativistic dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO_{2}/VO_{2} superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-N expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue Z at energy E scales as Z∝E^{a} with a>0, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, Z∝(|logE|)^{-b} with universal b=3/2.

Quantum critical metals ind=3+1dimensions

We study the problem of disorder-free metals in the vicinity of a quantum critical point in $d=3+1$ dimensions. We begin with perturbation theory in the Yukawa coupling between the electrons and undamped bosons (order-parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale, however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the ``marginal Fermi liquid'' phenomenology [Varma et al., Phys. Rev. Lett. 63, 1996 (1989)]. We discuss a large-$N$ theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.

Critical exponents proposed for marginal Fermi liquid

Iqbal, Liu and Mezei (ILM) [1] have proposed critical exponents α, β and δ in terms of a quantity νILM, which gives marginal Fermi liquid behaviour when νILM = 1/2. In particular, this value reproduces in the normal state of high T c cuprates, the electrical resistivity proportional to temperature (T) over a wide range of T, as found experimentally. A consequence shown here is that Griffiths' inequality becomes an equality for all νILM, while Josephson's inequality is also satisfied for all positive values of νILM. The choice νILM = 1/4, on the other hand, reproduces the mean field values of α, β and δ. We propose a specific relation between δ and η for the Ising model by using the ILM family as a guideline.

Anomalous resistivity and the origin of heavy mass in the two-band Hubbard model with one narrow band

We search for marginal Fermi-liquid behavior in the two-band Hubbard model with one narrow band. We consider the limit of low electron densities in the bands and strong intraband and interband Hubbard interactions. We analyze the influence of electron polaron effect and other mechanisms of mass-enhancement (related to momentum dependence of the self-energies) on effective mass and scattering times of light and heavy components in the clean case (electron - electron scattering and no impurities). We find the tendency towards phase-separation (towards negative partial compressibility of heavy particles) in a 3D case for large mismatch between the densities of heavy and light bands in a strong coupling limit. We also observe that for low temperatures and equal densities the resistivity in a homogeneous state R(T) ~ T^2 - behaves in a Fermi-liquid fashion both in 3D and 2D cases. For temperatures higher then effective bandwidth for heavy electrons T > Wh* the coherent behavior of heavy component is totally destroyed. The heavy particles move diffusively in the surrounding of light particles. At the same time the light particles scatter on the heavy ones as if on immobile (static) impurities. In this regime the heavy component is marginal, while the light one is not. The resistivity goes on saturation for T > Wh* in the 3D case. In 2D the resistivity has a maximum and localization tail due to weak - localization corrections of Altshuler - Aronov type. Such behavior of resistivity in 3D could be relevant for some uranium-based heavy-fermion compounds like UNi2Al3 and in 2D for some other mixed-valence compounds possibly including the layered manganites. We also consider briefly the superconductive (SC) instability in the model. The leading instability is towards p-wave pairing and is governed by enhanced Kohn - Luttinger mechanism of SC at low electron density.

Many-body interactions in quasi-freestanding graphene

The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.

Quantum criticality and incipient phase separation in the thermodynamic properties of the Hubbard model

Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t', we find a classical critical point at temperature T(c). This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature T(c) extrapolates to zero as t' vanishes, we conclude that a QCP connects the Fermi liquid to the pseudo-gap region, and that the marginal Fermi-liquid behaviour in its vicinity is the analogue of the supercritical region in the liquid-gas transition.

Anomalous resistivity and superconductivity in the two-band Hubbard model with one narrow band (Review)

We search for marginal Fermi-liquid behavior in the two-band Hubbard model with one narrow band. We consider the limit of low electron densities in the bands and strong intraband and interband Hubbard interactions. We analyze the influence of electron-polaron effects and other mechanisms for mass-enhancement (related to the momentum dependence of the self-energies) on the effective mass and scattering times of light and heavy components in the clean case (electron-electron scattering and no impurities). We find a tendency towards phase separation (towards negative partial compressibility of heavy particles) in the 3D case with a large mismatch between the densities of heavy and light bands in the strong coupling limit. We also find that for low temperatures and equal densities, the resistivity in a homogeneous state R(T)∝T2 behaves as a Fermi-liquid in both 3D and 2D. For temperatures greater than the effective bandwidth for heavy electrons T&amp;gt;Wh*, the coherence of the heavy component breaks down completely. The heavy particles move diffusively in the surrounding light particles. At the same time, light particles scatter on heavy particles as if on immobile (static) impurities. Under these conditions, the heavy component is marginal, while the light component is not. The resistivity approaches saturation for T&amp;gt;Wh* in the 3D case. In 2D the resistivity has a maximum and a localization tail owing to weak-localization corrections of the Altshuler-Aronov type. This behavior of resistivity in 3D could be relevant for some uranium-based heavy-fermion compounds such as UNi2Al3 and in 2D, for some other mixed-valence compounds, possibly including layered manganites. We also consider briefly the superconductive (SC) instability in this model. The leading instability tends to p-wave pairing and is governed by an enhanced Kohn–Luttinger mechanism for SC at low electron densities. The critical temperature corresponds to the pairing of heavy electrons via polarization of the light electrons in 2D.

Electron interactions in bilayer graphene: Marginal Fermi liquid and zero-bias anomaly

We analyze the many-body properties of bilayer graphene (BLG) at charge neutrality, governed by long-range interactions between electrons. Perturbation theory in a large number of flavors is used in which the interactions are described within a random phase approximation, taking account of dynamical screening effect. Crucially, the dynamically screened interaction retains some long-range character, resulting in ${\text{log}}^{2}$ renormalization of key quantities. We carry out the perturbative renormalization group calculations to one loop order and find that BLG behaves to leading order as a marginal Fermi liquid. Interactions produce a log squared renormalization of the quasiparticle residue and the interaction vertex function while all other quantities renormalize only logarithmically. We solve the RG flow equations for the Green's function with logarithmic accuracy and find that the quasiparticle residue flows to zero under RG. At the same time, the gauge-invariant quantities, such as the compressibility, remain finite to ${\text{log}}^{2}$ order, with subleading logarithmic corrections. The key experimental signature of this marginal Fermi liquid behavior is a strong suppression of the tunneling density of states, which manifests itself as a zero bias anomaly in tunneling experiments in a regime where the compressibility is essentially unchanged from the noninteracting value.

Non-Fermi-liquid behavior in the fluctuating gap model: From the pole to a zero of the Green’s function

We analyze the non-Fermi-liquid (NFL) behavior of the fluctuating gap model (FGM) of pseudogap behavior in both one and two dimensions. A detailed discussion of quasiparticle renormalization (Z-factor) is given, demonstrating a kind of marginal Fermi-liquid or Luttinger-liquid behavior and topological stability of the bare Fermi surface (the Luttinger theorem). In the two-dimensional case, we discuss the effective picture of the Fermi surface destruction both in the hot spot model of dielectric (AFM, CDW) pseudogap fluctuations and for the qualitatively different case of superconducting d-wave fluctuations, reflecting the NFL spectral density behavior and similar to that observed in ARPES experiments on copper oxides.

Electron Interactions and Scaling Relations for Optical Excitations in Carbon Nanotubes

Recent fluorescence spectroscopy experiments on single wall carbon nanotubes reveal substantial deviations of observed absorption and emission energies from predictions of noninteracting models of the electronic structure. Nonetheless, the data for nearly armchair nanotubes obey a nonlinear scaling relation as a function of the tube radius R. We show that these effects can be understood in a theory of large radius tubes, derived from the theory of two dimensional graphene where the Coulomb interaction leads to a logarithmic correction to the electronic self-energy and marginal Fermi liquid behavior. Interactions on length scales larger than the tube circumference lead to strong self-energy and excitonic effects that compete and nearly cancel so that the observed optical transitions are dominated by the graphene self-energy effects.

A model of marginal Fermi liquid in d-wave superconductive state

The marginal Fermi liquid (MFL) phenomenology of the cuprates in a normal state is extended to a d-wave superconductive state. We assume that the MFL collective excitation can be factored into a “bare excitation,” P 0( ω, T), and the susceptibility, χ( ω, T), such that the P 0( ω, T) gives rise to, after renormalization, the MFL behavior in the normal state: Im P n( ω, T) ∝ −tanh( ω/2 T). With the P 0 determined this way at a given temperature T, the superconductivity (SC) is incorporated by including the pairing processes in addition to normal ones in the electronic susceptibility. The renormalized excitation spectrum in a SC state is calculated self-consistently together with the renormalization function Z( ω) and pairing function Δ( ω) within the Eliashberg formalism. The following distinctive features of the SC emerging from a MFL, compared with that from a Fermi liquid, are found: (a) the pairing function Δ( ω) of MFL SC does not show any particular bosonic energy scale, and there exist substantial damping and suppression of Δ( ω) in the small frequency region, (b) the renormalized excitation spectrum gets suppressed below ω 0≈2 Δ and shows a hump around ω 0, and (c) the self-energy deviates from the MFL ω/ T-scaling in superconductive state.

Eliashberg Theory of the Superconducting State of Marginal Fermi Liquids

The marginal Fermi liquid (MFL) which describes the anomalous normal state of the cuprates is extended to a d-wave superconductive state. A phenomenological collective excitation, P0(ω,T), is taken such that it gives rise to, after renormalization, the MFL behavior in the normal state. With the P0, the renormalized excitation spectrum and pairing function in superconductive state are calculated self-consistently within the Eliashberg formalism. In the superconductive state, the self-energy deviates from the normal state MFL ω/T-scaling and develops a new energy scale of ω0≈2Δ, where Δ is the pairing amplitude.

Temperature dependence of the collective mode and its influence on the band splitting in bilayer cuprates

The recently observed bilayer splitting in $\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\ensuremath{-}{T}_{\mathrm{c}}$ cuprates is analyzed within a model where the charge carriers are coupled to a phenomenological bosonic spectrum which interpolates between the marginal Fermi liquid structure and collective mode type behavior as a function of temperature. We argue that the origin of the collective mode is associated with dynamic incommensurate charge density waves. Moreover it is shown that the resulting temperature dependence of the self-energy $\ensuremath{\Sigma}$ is in good agreement with that extracted from angle-resolved photoemission data.

Marginal Fermi Liquid Behaviour in the d = 2 Hubbard Model with Cut-Off

We consider the half-filled Hubbard model with a cut-off forbidding momenta close to the angles of the square shaped Fermi surface. By Renormalization Group methods we find a convergent expansion for the Schwinger function up to exponentially small temperatures. We prove that the system is not a Fermi liquid, but on the contrary it behaves like a Marginal Fermi liquid, a behaviour observed in the normal phase of high T_c superconductors.

Crossover from marginal Fermi liquid to Luttinger liquid behavior in carbon nanotubes

We study graphene-based electron systems with long-range Coulomb interaction by performing an analytic continuation in the number of dimensions. We characterize in this way the crossover between the marginal Fermi-liquid behavior of a graphite layer and the Luttinger-liquid behavior at $D=1.$ The former persists for any dimension above $D=1.$ However, the proximity to the $D=1$ fixed-point strongly influences the phenomenology of quasi-one-dimensional systems, giving rise to an effective power-law behavior of observables like the density of states. This applies to nanotubes of a large radius, for which we predict a lower bound of the corresponding exponent that turns out to be very close to the value measured in multiwalled nanotubes.

Marginal Fermi liquid resonance induced by a quantum magnetic impurity in d-wave superconductors.

We consider a model of an Anderson impurity embedded in a d(x(2)-y(2))--wave superconducting state to describe the low-energy excitations of cuprate superconductors doped with a small amount of magnetic impurities. Because of the Dirac-like energy dispersion, a sharp localized resonance above the Fermi energy, showing a marginal Fermi liquid behavior ( omega ln omega as omega-->0), is predicted for the impurity states. The same logarithmic dependence of self-energy and a linear frequency dependence of the relaxation rate are also derived for the conduction electrons, characterizing a new universality class for the strong coupling fixed point. At the resonant energies, the spatial distribution of the electron density of states around the magnetic impurity is also calculated.