Fermi-liquid theory for thin arbitrarily polarized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow /><mml:mn>3</mml:mn></mml:msup></mml:math>He films

Li, David Z.; Anderson, R. H.; Miller, Michael David

doi:10.1103/physrevb.85.224511

Cited by 4 publications

(16 citation statements)

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“…In Ref. 10, we pointed out that there exists a single measurement of a zero-sound speed for a 3 He film at zero polarization by Godfrin, Meschke, Lauter, Böhm, Krotscheck, and Panholzer. 25 Their substrate was graphite, the 3 He areal density was n = 0.049Å −2 , the wave vector was q = 5.5 nm −1 , and the energy transfer was ω = 0.68 ± 0.05 meV.…”

Section: Discussionmentioning

confidence: 97%

“…9 of Ref. 10. At the lowest density shown (0.0132Å −2 ), the Fermi velocity ranges from approximately 50 m/s at zero polarization up to about 100 m/s at full polarization.…”

Section: B Quasiparticle-phonon Collisionsmentioning

confidence: 95%

“…In the usual manner, [9][10][11] we can introduce a Fourier representation: W σ σ (cos θ ) = ∞ =0 α T (cos θ )W σ σ . In the following, we shall restrict ourselves to including only the = 0 term.…”

Section: A Quasiparticle-quasiparticle Collisionsmentioning

confidence: 99%

“…2 Thin films of normal 3 He have been studied experimentally for many years as prototypical two-dimensional Fermi liquids. [3][4][5][6][7][8] In a recent series of papers [9][10][11] [Li, Anderson, and Miller (LAM)], we have utilized a perturbation-theory-based approach to study the properties of thin, arbitrarily polarized Fermi-liquid films. Perturbation theory was applied to the low-density Fermi gas in three dimensions by Khalatnikov and Abrikosov (KA).…”

Section: Introductionmentioning

confidence: 99%

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Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Anderson

Miller

2013

Phys. Rev. B

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We study the propagation and attenuation of zero sound and first sound in thin, arbitrarily polarized Fermi-liquid films. Following Khalatnikov and Abrikosov, we solve Landau's linearized kinetic equation in the relaxation-time approximation for a complex speed of sound. Analytic solutions are obtained in the hydrodynamic and ballistic limits for arbitrary polarization. By solving the collision integral in two dimensions, we find the well-known result that quasiparticle-quasiparticle collisions contribute to the collision frequencies 1/τ σ , with a low-temperature term proportional to T 2 ln (T F σ /T ), where σ = ↑, ↓ is the spin state. If the films are adsorbed to a dynamic substrate, we find additional possible contributions to the collision frequency that come from quasiparticle-phonon interactions. We show, however, that for 3 He thin films, the mismatch between possible maximum values of the Fermi velocity and the substrate speed of sound freezes this contribution out at usual experimental temperatures. Thus, we can conclude that zero sound propagates at absolute zero in this type of adsorbed Fermi-liquid film. By utilizing previous results for the Landau parameters of an arbitrarily polarized 3 He film, we compute numerical solutions for the sound speeds and attenuation in the hydrodynamic and ballistic regimes, thereby studying the transition from first sound to zero sound as a function of temperature.

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Section: Discussionmentioning

confidence: 97%

“…9 of Ref. 10. At the lowest density shown (0.0132Å −2 ), the Fermi velocity ranges from approximately 50 m/s at zero polarization up to about 100 m/s at full polarization.…”

Section: B Quasiparticle-phonon Collisionsmentioning

confidence: 95%

Section: A Quasiparticle-quasiparticle Collisionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Anderson

Miller

2013

Phys. Rev. B

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“…The behavior of the full susceptibility is then determined entirely by the quasiparticle χ c(s) qp,l (q, ω). Although the calculations are straightforward and some of the results have appeared before, 26,28,[30][31][32][33][34][35][36][37][38][39][40] we include below the details of the derivation of χ c(s) qp,l (q, ω) in 2D, as we will be interested in the pole structure of the susceptibility not only near a Pomeranchuk transition but also away from it. In what follows we consider separately the cases of l = 0, 1, 2, and then analyze the case of arbitrary l. In these calculations we assume that a single Landau parameter F c(s) l is much larger than the rest and compute χ c(s) qp,l (q, ω) using Eq.…”

Section: A Quasiparticle Susceptibilitymentioning

confidence: 99%

Collective modes near a Pomeranchuk instability in two dimensions

Klein

Maslov

Pitaevskiĭ

et al. 2019

Phys. Rev. Research

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Competing solutions of Landau’s kinetic equation for zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Li¹,

Anderson²,

Miller³

et al. 2014

J. Stat. Mech.

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We examine in detail the method introduced by Sanchez-Castro, Bedell, and Wiegers (SBW) to solve Landau's linearized kinetic equation, and compare it with the well-known standard method introduced by Abrikosov and Khalatnikov (AK). The SBW approach, hardly known, differs from AK in the way that moments are taken with respect to the angular functions of the Fourier transformed kinetic equation. We compare the SBW and AK solutions for zero-sound and firstsound propagation speeds and attenuation both analytically in the zero and full polarization limits, and numerically at arbitrary polarization using Landau parameters appropriate for thin 3 He films.We find that the lesser known method not only yields results in close agreement with the standard method, but in most cases does so with far less analytic and computational effort.

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Fermi-liquid theory for thin arbitrarily polarized3He films

Cited by 4 publications

References 50 publications

Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Collective modes near a Pomeranchuk instability in two dimensions

Competing solutions of Landau’s kinetic equation for zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

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