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arXiv:1904.10467 · Physical review. B./Physical review. B

Two-dimensional Fermi liquid dynamics with density-density and quadrupolar interactions

Rui Aquino, Daniel Gustavo Barci

Published Sep 10, 2019• 9 citations
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Abstract

We consider a Fermi liquid model with density-density as well as quadrupolar forward scattering interactions parametrized by the Landau parameters ${F}_{0}$ and ${F}_{2}$. Using bosonization and a decimation technique, we compute collective modes and spectral functions for a huge range of interactions, ranging from strong repulsion to strong attraction in either angular momentum channel. We present a dynamical phase diagram showing a region of parameters where the collective mode structure changes abruptly, possibly signaling a dynamical phase transition.

DOI
10.1103/physrevb.100.115117

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We consider a Fermi liquid model with density-density as well as quadrupolar forward scattering interactions parametrized by the Landau parameters F0{F}_{0}F0​ and F2{F}_{2}F2​. Using bosonization and a decimation technique, we compute collective modes and spectral functions for a huge range of interactions, ranging from strong repulsion to strong attraction in either angular momentum channel. We present a dynamical phase diagram showing a region of parameters where the collective mode structure changes abruptly, possibly signaling a dynamical phase transition.
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In this paper we use a self-consistent scheme proposed by Singwi, Tosi, Land, and Sjo\ifmmode\ddot\else\textasciidieresis\fi{}lander to study a two-dimensional Fermi liquid whose particles interact via a repulsive hard-core potential with or without an attractive tail. We determine the Landau parameters F0s{\mathit{F}}_{0}^{\mathit{s}}F0s​ and F0a{\mathit{F}}_{0}^{\mathit{a}}F0a​, the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential.
We show the existence of non-Hermitian degeneracies, known as exceptional points, in the collective mode spectrum of Fermi liquids with quadrupolar interactions. Through a careful analysis of the analytic properties of the dynamic quadrupolar susceptibility, we show that, in the weak attractive region, two stable collective modes coalesce to an exceptional point. We completely characterize this singularity, explicitly showing its topological properties. Experimental signatures are also discussed.
The long-wavelength, low-frequency "collisionless" collective oscillations of a superfluid Fermi liquid are studied throughout the region 0<T<Tc0<T<{T}_{c}0<T<Tc​ with the help of a field-theoretic formalism developed in a previous paper. It is found that any collective mode (other than the density fluctuation) that is possible in the normal phase persists below Tc{T}_{c}Tc​ as an oscillation of the normal component, but disappears at some finite temperature which in general depends on the Landau interaction parameters F0{F}_{0}F0​,F1{F}_{1}F1​,Z0{Z}_{0}Z0​, etc. The behavior of the density-fluctuation mode depends critically on F0{F}_{0}F0​, if the latter is negative, there is a well-defined collective oscillation only for $T\ensuremath{\ll}{T}_{c}$, while if it is small and positive, the oscillation is well defined for $T\ensuremath{\ll}{T}_{c}$ and $T\ensuremath{-}{T}_{c}\ensuremath{\ll}{T}_{c}$ but not in the intermediate region. If F0{F}_{0}F0​ is large and positive, the density-fluctuation collective mode exists throughout the whole region 0<T<Tc0<T<{T}_{c}0<T<Tc​ and its velocity is approximately temperature-independent.
In this work, we consider NNN-fold degenerate DDD-dimensional electron gas with spherical Fermi surface and arbitrary forward-scattering density-density interaction transferring small momentum compared to the Fermi momentum kFk_{\mathrm{F}}kF​. The dimensional reduction that is mathematically equivalent to the Haldane patch construction and similar multidimensional bosonization techniques, provides a natural map of two-point DDD-dimensional correlation functions (fermion Green function, susceptibilities etc.) onto effective one-dimensional (1D) correlators with the same diagrammatic structure, which can be evaluated exactly within a 1D bosonizable (Gaussian) theory. We then apply this formalism to evaluate the fermion Green function, pair and charge/flavor susceptibilities, as well as the composite correlation functions for the case of a finite-range interaction, where the interaction range Rs≫1/kFR_{\mathrm{s}} \gg 1/k_{\mathrm{F}}Rs​≫1/kF​ is large compared to the Fermi wavelength. First, we find that the single-particle spectral function remains Fermi-liquid-like which is fully consistent with the previous research. In contrast to the single-particle sector, the many-body channels are efficiently dressed by finite-range interactions, and this dressing is fully equivalent to the one-loop renormalization group (RG), which is also in line with previous multidimensional bosonization results. Within the forward-scattering model, stable long-range order is not possible, and relevant susceptibilities demonstrate singular power-law scaling with temperature TTT at T→0T \to 0T→0. The rest of the abstract is in the PDF.
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.