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arXiv:2404.01534

Strange Sounds

Dmitri V. Khveshchenko

Published Apr 1, 2024• 0 citations
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Abstract

This note addresses the effects of long-ranged and/or retarded interactions on the bosonic collective modes in the so-called 'strange metals'. Recently, there have been conflicting reports on the very existence of such stable collective excitations and their properties. Extending a number of approaches that were previously used in the analyses of the standard Fermi liquid one finds evidence for, both, conventional and novel behaviors of the non-Fermi-liquid counterparts of the zero-, shear-, and other 'sounds'.

DOI
10.48550/arxiv.2404.01534

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This note addresses the effects of long-ranged and/or retarded interactions on the bosonic collective modes in the so-called 'strange metals'. Recently, there have been conflicting reports on the very existence of such stable collective excitations and their properties. Extending a number of approaches that were previously used in the analyses of the standard Fermi liquid one finds evidence for, both, conventional and novel behaviors of the non-Fermi-liquid counterparts of the zero-, shear-, and other 'sounds'.
This note addresses the problem of constructing a proper bosonized description of the collective modes in strongly interacting (non-)Fermi liquids which is specific to two spatial dimensions. Although, in a mild form, this subtlety exists in the Fermi liquid as well, the discussion focuses on the effects of long-ranged and/or retarded interactions which can completely destroy the fermionic quasiparticles. The present analysis also provides a further insight into the nature and properties of the collective bosonic modes in such systems.
This Letter addresses the problem of constructing a proper bosonized description of the collective modes in strongly interacting (non-)Fermi liquids which is specific to two spatial dimensions. Although, in a mild form, this subtlety exists in the Fermi liquid as well, the discussion focuses on the effects of long-ranged and/or retarded interactions which can completely destroy the fermionic quasiparticles. The present analysis provides a further insight into the nature and properties of the collective bosonic modes in such systems.
The experimental discovery of a number of 'strange metals' has reopened the question of the low temperature behavior of interacting Fermi systems. Here we provide a subjective overview of some aspects of the resulting theoretical work. It seems to us that from a theoretical standpoint Landau's Fermi-liquid theory has proven to be a remarkably robust description of clean Fermi systems. The only well documented theoretical examples of non-Fermi-liquid behavior are metals subject to gauge interactions or at quantum critical points. The experimental anomalies which prompted the reexamination of Fermi-liquid theory remain in many cases mysterious.
In a recent paper by Schmeltzer [Phys. Rev. B 52, 7939 (1995)] it is claimed that a non-Fermi liquid behavior arises in a d-dimensional system of fermions interacting through a long-range potential of the form V(q)=g/|q${\mathrm{|}}^{\mathrm{d}+\mathrm{\ensuremath{\epsilon}}\ensuremath{-}|\mathrm{A}\mathrm{x}\mathrm{\ensuremath{-}}1}$ for 0\ensuremath{\leqslant}1. Schmeltzer arrives at this result using both renormalization group (RG) and bosonization. In this Comment we show that a proper application of the bosonization technique to this problem leads instead to a non-Fermi liquid behavior only for \ensuremath{\epsilon}-hat\ensuremath{\geqslant}d-1, in agreement with several previous analyses. We also give a direct physical interpretation of this result. Finally we comment on the application of RG to this problem.
We study the appearance of a sharp collective mode which features transverse current fluctuations within the bosonization approach to interacting two-dimensional Fermi liquids. This mode is analogous to the shear sound modes in elastic media, and, unlike the conventional zero sound mode, it is damped in weakly interacting Fermi liquids and only separates away from the particle-hole continuum when the quasiparticle mass becomes twice the transport mass ${m}^{*}\ensuremath{\gtrsim}2m$. The shear sound should be present in a large class of interacting charged and neutral Fermi liquids especially those proximate to critical points where the quasiparticle mass diverges. In metals this mode remains linearly dispersing in the presence of the long-ranged Coulomb force, unlike the conventional zero sound mode which becomes the plasma mode. We also detail a quick path between bosonization and classical Landau's Fermi liquid theory by constructing a mapping between the solutions of the classical kinetic equation and the quantized bosonic eigenmodes. By further mapping the kinetic equation into a one-dimensional tight-binding model we solve for the entire spectrum of collective and incoherent particle-hole excitations of Fermi liquids with nonzero F0{F}_{0}F0​ and F1{F}_{1}F1​ Landau parameters.