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Journal of Physics Condensed Matter

Effect of vertex corrections on the charge and spin responses of the Fermi liquid

Y. M. Malozovsky, J. D. Fan

Published Dec 2, 1996• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/8/49/032

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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.
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.
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.
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.
Using a recently suggested method of bosonization in an arbitrary dimension, we study the anomalous contribution of the low-energy spin and charge excitations to thermodynamic quantities of a two-dimensional (2D) Fermi liquid. The method is slightly modified for the present purpose such that the effective supersymmetric action no longer contains the high-energy degrees of freedom but still accounts for effects of the finite curvature of the Fermi surface. Calculating the anomalous contribution $\ensuremath{\delta}c(T)$ to the specific heat, we show that the leading logarithmic in temperature corrections to $\ensuremath{\delta}c(T)/{T}^{2}$ can be obtained in a scheme combining a summation of ladder diagrams and renormalization group equations. The final result is represented as the sum of two separate terms that can be interpreted as coming from singlet and triplet superconducting excitations. The latter may diverge in certain regions of the coupling constants, which should correspond to the formation of triplet Cooper pairs.
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.
A simple interlayer pair tunneling is solved exactly. We find that in the normal state spin-1/2 particle and hole excitations are gapped. But the state is an unusual metal, characterized by novel fermionic spin zero and charge +2e and -2e excitations that exist about their own Fermi surfaces. The model is consistent with a number of properties of the underdoped cuprates. At finite temperature the Fermi surface appears partially gapped, and at high temperatures the spin gap disappears completely. Superconductivity is induced by an additional intralyer interaction which opens a gap in the charge-fermion spectrum. The symmetry of this charge gap (and hence that of the order parameter) is igenerally different from the symmetry of one-electron or - hole gap. The former can be a d wave, while the latter is more complex.