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Asymptotically exact dispersion relations for collective modes in a confined charged Fermi liquid

I. V. Tokatly·O. Pankratov
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Abstract

Using general local conservations laws we derive dispersion relations for edge modes in a slab of electron liquid confined by a symmetric potential. The dispersion relations are exact up to $λ^{2} q^{2}$, where $q$ is a wave vector and $λ$ is an effective screening length. For a harmonic external potential the dispersion relations are expressed in terms of the {\em exact} static pressure and dynamic shear modulus of a homogeneous liquid with the density taken at the slab core. We also derive a simple expression for the frequency shift of the dipole (Kohn) modes in nearly parabolic quantum dots in a magnetic field.

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I. V. Tokatly, O. Pankratov. 2002-11-13. Asymptotically exact dispersion relations for collective modes in a confined charged Fermi liquid. https://doi.org/10.1103/physrevb.66.153103

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