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arXiv:1103.6179

Marginal Fermi Liquid from a Partially Nested Fermi Surface and Impurity Scattering in a Two Dimensional Metal

Eliot Kapit

Published Mar 31, 2011• 0 citations
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Abstract

The electron-electron scattering rate of low-energy quasiparticles is computed perturbatively for a two-dimensional metal with a partially nested Fermi surface, a weak electron-electron interaction and an energy-independent impurity scattering rate. We show that even when the nested section comprises only a small fraction of the Fermi surface, the low energy quasiparticle decay rates throughout the Fermi surface gain a term which is linear in energy $ω$. The coefficient of this linear contribution is largest along the nested regions but remains finite elsewhere, and is strongly dependent on the impurity scattering rate $δ$. We discuss the possible relevance of this result to unconventional superconductors (such as the cuprates) and to the normal state of charge density wave materials such as the rare Earth tellurides.

DOI
10.48550/arxiv.1103.6179

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The electron-electron scattering rate of low-energy quasiparticles is computed perturbatively for a two-dimensional metal with a partially nested Fermi surface, a weak electron-electron interaction and an energy-independent impurity scattering rate. We show that even when the nested section comprises only a small fraction of the Fermi surface, the low energy quasiparticle decay rates throughout the Fermi surface gain a term which is linear in energy ωωω. The coefficient of this linear contribution is largest along the nested regions but remains finite elsewhere, and is strongly dependent on the impurity scattering rate δδδ. We discuss the possible relevance of this result to unconventional superconductors (such as the cuprates) and to the normal state of charge density wave materials such as the rare Earth tellurides.
An unusual scaling of the spin susceptibility, as a function of frequency/temperature, was discovered for noninteracting electrons on a nested Fermi surface. This scaling has been confirmed by neutron-scattering experiments on high-temperature superconductors, and it can explain the anomalous quasiparticle damping in cuprates if electron collisions are dominant. The present work proves that self-energy and vertex corrections preserve the scaling features of the susceptibility to leading order in the Hubbard on-site Coulomb repulsion U. Analytic results for the static susceptibility show how self-energy and vertex terms modify the traditional random-phase approximation results for a spin-density-wave instability and suppress the charge susceptibility. These results are relevant to d-wave superconductors, organic metals, and chromium.
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.
We study the temperature dependence of the electrical resistivity of interacting two-dimensional Fermi liquids. We perform a numerical simulation of the nonequilibrium state based on semiclassical Boltzmann transport theory. A two-dimensional system of quasiparticles on a square lattice serves as a model system. We use a single-orbital tight-binding model of the dispersion. For conceptual purposes, we choose a simple repulsive onsite interaction that leads to quasiparticle scattering and delta-potential scatterers as a model of nonmagnetic impurity scattering. Through our simulation, we demonstrate that deviations from the predictions of standard Fermi-liquid theory can arise due to the nontrivial scattering geometry of umklapp processes, in special cases even in the ultralow-temperature limit. We show through qualitative arguments how these unconventional scaling properties of the electrical resistivity, which are often interpreted as indication of a non-Fermi-liquid state, can arise due to special geometric conditions of the Fermi surface. The appearance of robust deviations from the predictions of Fermi-liquid theory within our simple model presents a viewpoint in order to interpret unconventional transport properties in electron-electron scattering dominated metallic systems.
We analyze quantum fluctuation effects at the onset of charge or spin-density wave order in two-dimensional metals with an incommensurate nesting (2kF2{k}_{F}2kF​) wave vector connecting two pairs of hot spots on the Fermi surface. We first compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a perturbation expansion (one loop). Non-Fermi liquid behavior with a linear (in energy) quasiparticle decay rate and a logarithmically vanishing quasiparticle weight is obtained. The momentum dependence of the self-energy entails only finite renormalizations of the Fermi velocity and the Fermi-surface curvature at the hot spots. The perturbative one-loop result is not self-consistent and casts doubt on the stability of the 2kF2{k}_{F}2kF​ quantum critical point. We construct a self-consistent solution of the one-loop equations with self-energy feedback, where the quantum critical point is stabilized rather than being destroyed by fluctuations, while the non-Fermi liquid behavior as found in the perturbative one-loop calculation is confirmed.
We use a diagrammatic approach to study low-energy physics of a two-dimensional electron system where the Fermi level is near van Hove singularities in the energy spectrum. We find that in most regions of the ${\ensuremath{\epsilon}}_{F}\ensuremath{-}T$ phase diagram the system behaves as a normal Fermi liquid rather than a marginal Fermi liquid. Particularly, the imaginary part of the self-energy is much smaller than the excitation energy, which implies well-defined quasiparticle excitations, and single-particle properties are only weakly affected by the presence of the van Hove singularities. The relevance to high-temperature superconductivity is also discussed.
When a van Hove singularity is located in the vicinity of the Fermi level, the electronic scattering rate acquires a nonanalytic contribution. This invalidates basic assumptions of Fermi liquid theory and within treatments based on perturbation theory leads to a non-Fermi liquid self-energy and transport properties. Such anomalies are shown to also occur in the strongly correlated metallic state within dynamical mean-field theory. We consider the Hubbard model on a two-dimensional square lattice with nearest- and next-nearest-neighbor hoppings within the single-site dynamical mean-field theory. At temperatures on the order of the low-energy scale T0{T}_{0}T0​ an unusual maximum emerges in the imaginary part of the self-energy which is renormalized toward the Fermi level for finite doping. At zero temperature this double-well structure is suppressed but an anomalous energy dependence of the self-energy remains. For the frustrated Hubbard model on the square lattice with next-nearest-neighbor hopping, the presence of the van Hove singularity changes the asymptotic low-temperature behavior of the resistivity from a Fermi liquid to non-Fermi liquid dependency as function of doping. The results of this work are discussed regarding their relevance for high-temperature cuprate superconductors.