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

Physics – Condensed Matter – Mesoscale and Nanoscale Physics

Scientific paper

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RevTeX4, 4 pages. Revised version with new results on quantum qots and wires. Published in Phys.Rev.B

Scientific paper

10.1103/PhysRevB.66.153103

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 $\lambda^{2} q^{2}$, where $q$ is a wave vector and $\lambda$ 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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