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arXiv:2209.05491 · Physical review. B./Physical review. B

Collective density fluctuations of strange metals with critical Fermi surfaces

Xuepeng Wang, Debanjan Chowdhury

Published Mar 28, 2023• 9 citations
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Abstract

A hallmark of a Fermi liquid is a collective excitation associated with fluctuations of the Fermi surface, which evolves into the well-known plasmon in the presence of Coulomb interactions. This paper addresses the fate of the plasmon excitation in non-Fermi liquid metals with a sharply defined Fermi surface, but where long-lived single-electron excitations are absent. The authors use two complementary theoretical techniques to analyze the collective density fluctuations and their decay into the two-particle continuum for three distinct solvable examples of non-Fermi liquids.

DOI
10.1103/physrevb.107.125157

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A hallmark of a Fermi liquid is a collective excitation associated with fluctuations of the Fermi surface, which evolves into the well-known plasmon in the presence of Coulomb interactions. This paper addresses the fate of the plasmon excitation in non-Fermi liquid metals with a sharply defined Fermi surface, but where long-lived single-electron excitations are absent. The authors use two complementary theoretical techniques to analyze the collective density fluctuations and their decay into the two-particle continuum for three distinct solvable examples of non-Fermi liquids.
Interactions in Fermi systems can generate a Pomeranchuk instability leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations and exhibits enhanced collective fluctuations. We analyze fluctuation effects in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. Density correlations with a d-wave form factor and the dynamical forward scattering interaction diverge near the instability. The singular forward scattering leads to large self-energy contributions, which destroy Fermi liquid behavior over the whole Fermi surface except at “cold spots” on the Brillouin zone diagonal. The decay rate of single-particle excitations, which is related to the width of the peaks in the spectral function, exceeds the excitation energy in the low-energy limit. The dispersion of the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots. We discuss the possible relevance of d-wave Fermi surface fluctuations for the “strange metal” behavior observed in the normal phase of cuprates.
Semiholographic models of non-Fermi liquids have been shown to have generically stable generalized quasiparticles on the Fermi surface. Although these excitations are broad and exhibit particle-hole asymmetry, they were argued to be stable from interactions at the Fermi surface. In this work, we use this observation to compute the density response and collective behaviour in these systems. Compared to the Fermi liquid case, we find that the boundaries of the particle-hole continuum are blurred by incoherent contributions. However, there is a region inside this continuum, that we call inner core, within which salient features of the Fermi liquid case are preserved. A particularly striking prediction of our work is that these systems support a plasmonic collective excitation which is well-defined at large momenta, has an approximately linear dispersion relation and is located in the low-energy tail of the particle-hole continuum. Furthermore, the dynamic screening potential shows deep attractive regions as a function of the distance at higher frequencies which might lead to long-lived pair formation depending on the behavior of the pair susceptibility. We also find that Friedel oscillations are present in these systems but are highly suppressed.
The strange metallic regime across a number of high-temperature superconducting materials presents numerous challenges to the classic theory of Fermi liquid metals. Recent measurements of the dynamical charge response of strange metals, including optimally doped cuprates, have revealed a broad, featureless continuum of excitations, extending over much of the Brillouin zone. The collective density oscillations of this strange metal decay into the continuum in a manner that is at odds with the expectations of Fermi liquid theory. Inspired by these observations, we investigate the phenomenology of bosonic collective modes and the particle-hole excitations in a class of strange metals by making an analogy to the phonons of classical lattices falling apart across an unconventional jamming-like transition associated with the onset of rigidity. By making comparisons to the experimentally measured dynamical response functions, we reproduce many of the qualitative features using the above framework. We conjecture that the dynamics of electronic charge density over an intermediate range of energy scales in a class of strongly correlated metals can be at the brink of a jamming-like transition.
At the edge of a phase transition in certain quantum materials, electrons can enter an exotic ``strange metal'' state, where they cease behaving like well-defined quasiparticles. The authors investigate here whether this state, in an isotropic system, is internally stable against perturbations with different angular momenta. By developing a theoretical framework to trace collective electron oscillations through the crossover from a Fermi liquid to a non-Fermi liquid regime, the authors demonstrate that the system remains stable under perturbations with all angular momenta --- including the odd-momentum modes whose stability was previously questioned.
Non-Fermi liquids are unconventional metals whose physical properties deviate qualitatively from those of noninteracting fermions due to strong quantum fluctuations near Fermi surfaces. They arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticles, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. However, it has been difficult to understand their universal low-energy physics due to a lack of theoretical methods that take into account strong quantum fluctuations in the presence of abundant low-energy degrees of freedom. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the codimension of Fermi surface. The second is a nonperturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.