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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Normal and anomalous responses of the Fermi liquid in the charge and spin channels

Y. M. Malozovsky, Jiang-Di Fan

Published Jul 5, 1996• 0 citations
Publisher

Abstract

By means of the perturbative diagram approach the effects of vertex corrections on the charge and spin responses of the Fermi liquid are considered. It is shown that the interaction in the particle-hole channel induces the multipair excitations in both the charge and spin channels. Such excitations lead to the appearance of the anomalous Fermi liquid term Im(chi) approximately - (omega) /T in the charge and spin responses of the Fermi liquid in addition to the normal response approximately - (omega) /vFk. Such a contribution of the anomalous term to the charge and spin responses is in agreement with the marginal Fermi-liquid hypothesis proposed by Varma et al. to explain the universal anomalies in the normal state of the cuprate high-Tc superconductors.

DOI
10.1117/12.250282

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By means of the perturbative diagram approach the effects of vertex corrections on the charge and spin responses of the Fermi liquid are considered. It is shown that the interaction in the particle-hole channel induces the multipair excitations in both the charge and spin channels. Such excitations lead to the appearance of the anomalous Fermi liquid term Im(chi) approximately - (omega) /T in the charge and spin responses of the Fermi liquid in addition to the normal response approximately - (omega) /vFk. Such a contribution of the anomalous term to the charge and spin responses is in agreement with the marginal Fermi-liquid hypothesis proposed by Varma et al. to explain the universal anomalies in the normal state of the cuprate high-Tc superconductors.
The effects of vertex corrections on the charge and spin responses of the Fermi liquid are considered. It is shown that the interaction in the particle - hole channel induces virtual pair excitations (Cooper pair like) in both the charge and the spin channels. It leads to the appearance of an anomalous Fermi-liquid term in both the charge and the spin responses of the Fermi liquid in addition to the normal response . Such a contribution of the anomalous term to the charge and spin responses is in agreement with the marginal Fermi-liquid hypothesis proposed by Varma et al to explain the universal anomalies in the normal state of cuprate high- superconductors.
We have studied in terms of the effective T-matrix the self-energy part for both the attractive (U<0) and repulsive (U>0) Hubbard models. It is shown that the fluctuation pairing for strong coupling at T>T c for the attractive Hubbard model does not cause any pseudogap behavior in the single-particle density of states. We have also identified the origin of the false pseudogap for that case. Meanwhile, the fluctuation pairing significantly affect the density–density and the current–current correlation functions. As a result, there exists a pseudogap in the charge (and current) response for the attractive Hubbard model. In contrast, the pseudogap in the spin response appears to exist for the repulsive Hubbard model only. It is also shown that the contribution from the Hartree–"Cooper" channel gives an anomalous Fermi liquid term, Im χ c ≈-ω/T, to the charge response of the nearly antiferromagnetic Fermi liquid.
We show that there are qualitative differences between the temperature dependence of the spin and charge correlations in the normal state of the 2D attractive Hubbard model using quantum Monte Carlo simulations. The one-particle density of states shows a pseudogap above Tc{T}_{c}Tc​ with a depleted N(0)N\left(0\right)N(0) with decreasing TTT. The susceptibility ${\ensuremath{\chi}}_{s}$ and the low frequency spin spectral weight track N(0)N\left(0\right)N(0), which explains the spin-gap scaling: ${1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}_{s}\left(T\right)$. However, collective excitations contribute to the charge channel, and the compressibility $dn/d\ensuremath{\mu}$ is TTT independent. This anomalous ``spin-charge separation'' is shown to exist even at intermediate ∣U∣|U|∣U∣ where the momentum distribution n(k)n\left(\mathbf{k}\right)n(k) gives evidence for a degenerate Fermi system.
We use Landau's theory of a normal Fermi liquid to derive expressions for the static response of a system with a general tensor interaction that conserves the total spin and the total angular momentum of the quasiparticle-quasihole pair. The magnetic susceptibility is calculated in detail, with the inclusion of the center of mass tensor and cross vector terms in addition to the exchange tensor one. We also introduce a new parametrization of the tensor Landau parameters which significantly reduces the importance of high angular harmonic contributions. For nuclear matter and neutron matter we find that the two most important effects of the tensor interaction are to give a contribution from multipair states and to renormalize the magnetic moments. Response to a weak probe may be calculated using similar methods, replacing the magnetic moments with the matrix elements of the weak charges.
We propose to describe the spin fluctuations in the normal state (spin-pseudogap phase) of underdoped high T(c) cuprates as a manifestation of an algebraic spin liquid. Within the slave boson implementation of spin-charge separation, the normal state is described by massless Dirac fermions, charged bosons, and a gauge field. The gauge interaction, as an exact marginal perturbation, drives the mean-field free-spinon fixed point to a new spin-quantum fixed point-the algebraic spin liquid. Luttinger-liquid-like line shapes for the electron spectral function are obtained in the normal state, and we show how a coherent quasiparticle peak appears as spin and charge recombine.
By means of the Fermi-liquid approach, the effects of exchange and correlations are considered in a layered two-dimensional electron gas. A graphical derivative technique is introduced to obtain the contributions to the interparticle interactions from different channels. It is shown that the interaction in the particle - hole channel can induce the metal - insulator phase transition when the Fermi momentum is comparable with the inverse interlayer spacing, . It is also shown that the Cooper-like scattering processes give rise to the scaling of the Fermi liquid response as Im , which leads to the linear temperature dependence of the quasiparticle damping. The possibility of superconductivity in the region between the insulator and normal metal phases, accounting for the particle - hole excitations, is discussed. The effect of the spin fluctuations on the superconductivity due to the particle - hole excitations is also considered.