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Physical Review Letters

Interlayer Josephson tunneling and breakdown of Fermi liquid theory

Sudip Chakravarty, Philip Warren Anderson

Published Jun 13, 1994• 111 citations
Publisher

Abstract

From the single assumption that the spectral density of the single particle excitations in high temperature superconductors obeys a scaling property characterized by a nonvanishing exponent \ensuremath{\alpha}, an interlayer tunneling Hamiltonian is obtained. A nonvanishing value of the exponent \ensuremath{\alpha} implies breakdown of the Fermi liquid theory at sufficiently low energies and low temperatures, consistent with experiments.

DOI
10.1103/physrevlett.72.3859

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From the single assumption that the spectral density of the single particle excitations in high temperature superconductors obeys a scaling property characterized by a nonvanishing exponent \ensuremath{\alpha}, an interlayer tunneling Hamiltonian is obtained. A nonvanishing value of the exponent \ensuremath{\alpha} implies breakdown of the Fermi liquid theory at sufficiently low energies and low temperatures, consistent with experiments.
The superconducting instability in a non-Fermi liquid in dimensions d > 1 is considered. For a particular form of the single particle spectral function with homogeneous scaling A(λk, λ ω) = λα A(k, ω) it is shown that the pair susceptibility is also a scaling function of temperature with power defined by α. We find three different regimes depending on the scaling constant. Bardeen-Cooper-Schrieffer result is recovered for α = − 1 and it corresponds to a marginal scaling of the coupling constant. For α > − 1 the superconducting transition happens above some critical coupling. In the opposite case of α < − 1 for any fixed coupling the system undergoes a transition at low temperatures. Possible implications for theories of high-T c with a superconducting transition driven by interlayer Josephson tunnelling are discussed.
It is widely believed that the t-J model contains some of the key physics of the high-temperature superconductors. It was proposed that the low-energy physics of the t-J model can be described by a gauge theory of fermions and bosons coupled to a gauge field. The normal state of these fermions was assumed to be a Fermi liquid. We show that perturbation theory around the Fermi-liquid state breaks down at low temperature in a wide class of gauge theories of high-temperature superconductors due to the interaction with an overdamped singular mode arising from the gauge field. This breakdown is present even if the coupling to the gauge field is arbitrary small.
We give a Hamiltonian-based interpretation of microscopic Fermi liquid theory within a renormalization group framework. The Fermi liquid fixed-point Hamiltonian with its leading-order corrections is identified and we show that the mean field calculations for this model correspond to the Landau phenomenological approach. This is illustrated first of all for the Kondo and Anderson models of magnetic impurities which display Fermi liquid behaviour at low temperatures. We then show how these results can be deduced by a reorganization of perturbation theory, in close parallel to that for the renormalized φ4 field theory. The Fermi liquid results follow from the two lowest order diagrams of the renormalized perturbation expansion. The calculations for the impurity models are simpler than for the general case because the self-energy depends on frequency only. We show, however, that a similar renormalized expansion can be derived also for the case of a translationally invariant system. The parameters specifying the Fermi liquid fixed-point Hamiltonian are related to the renormalized vertices appearing in the perturbation theory. The collective zero sound modes appear in the quasiparticle-quasihole ladder sum of the renormalized perturbation expansion. The renormalized perturbation expansion can in principle be used beyond the Fermi liquid regime to higher temperatures. This approach should be particularly useful for heavy fermions and other strongly correlated electron systems, where the renormalization of the single-particle excitations are particularly large. We briefly look at the breakdown of Fermi liquid theory from a renormalized perturbation theory point of view. We show how a modified version of the approach can be used in some situations, such as the spinless Luttinger model, where Fermi liquid theory is not applicable. Other examples of systems where the Fermi liquid theory breaks down are also briefly discussed.
Spectral anomaly for interacting fermions is characterized by the spectral function A ([k − k F ], ω) satisfying the scaling relation A (Λy1 [k − k F ], Λy2 ω) =ΛyA A ([k − k F ], ω), where y1, y2, and yA are the exponents defining the universality class. For a Fermi liquid y1 = 1, y2 = 1, yA = −1; all other values of the exponents are termed anomalous. In this paper, an example for which y1 = 1, y2 = 1, but yA = α − 1 is considered in detail. Attractive interaction added to such a critical system leads to a novel superconducting state, which is explored and its relevance to high temperature cuprate superconductors is discussed.
The relations among the critical exponents of condensed Bose liquid are obtained under the assumption of the scaling property for the mean occupation number of particles. Some of these relations are inequalities and may violate the scaling relations of Widom and Kadanoff. This violation is caused by two factors. One is the breakdown of the homogeneity of the one-particle density matrix and the other is nonvanishing condensation density contributing to the total density. The fluctuation of the condensation density is also discussed in connection with the scaling property.
The momentum range about the Fermi momentum in which the concept of ``adiabatic continuity'' is valid is argued to decrease continuously to zero as the Mott transition is approached. This implies that the momentum distribution of occupied single-particle states will not decrease monotonically with momentum if the spectral function for single-particle excitations has no feature other than the quasiparticle peak. The value of the single-particle density of states at the Fermi energy is argued to drop to zero discontinuously at the Mott transition.