Download Local Geometry of the Fermi Surface: And High-Frequency by Natalya A. Zimbovskaya PDF
By Natalya A. Zimbovskaya
A remedy of the Fermi-liquid conception of high-frequency phenomena in metals, in paricular the results because of neighborhood positive aspects within the geometry of the Fermi floor. The textual content develops a constant concept of a number of results, resembling cyclotron resonances in magnetic fields basic to the outside. subject matters lined contain: uncomplicated equations of the Fermi-liquid concept; cyclotron Doppler on waves; neighborhood anomalies within the Fermi floor; cyclotron resonancce in metals; magneto-acoustic oscillations and the neighborhood geometry of the Fermi floor.
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Additional info for Local Geometry of the Fermi Surface: And High-Frequency Phenomena in Metals
Sample text
Using the condition [ > 0 and this estimation we can find the frequency requirements necessary to observe the anomalous skin effect, w > e 2 pF/Ne 2[3. For good metals we have N '" 1022 cm- 3 , PF'" 10- 19 gm cm 20 1. The Electronic Liquid of Metals S-I, which give us w > 10- 2 /- 3 S-1 cm3 . When the mean free path is of the order of 10-4 cm we find w > 1010 S-I. To analyze the behavior of a metal placed in a high-frequency electromagnetic field one can introduce a new quantity-the so-called surface impedance Z.
Supposinguw(r) = u qw exp(iqr), Ew(r) = Eqw exp(iqr), and passing to Fourier trasforms in space variables, we obtain a simple expression for the Fourier component of the correction to a chemical potential of electrons s~ and eliminate it from the kinetic equation. * ( ) = Jvv -q - * ( 37 ) (n, j*) n vv' -q - ( *)' n,n ThequantityPisdefinedsimilarlytoJ, j~v,(-q), n~v'( -q), A~*v'( -q), P~v'( -q)are the Fourier-transfonns of matrix elements of the appropriate operators; the notation (C, D) for arbitrary single-particle operators C and D is defined as follows: (C, D) = - "~ Iv - Iv' Cvv' (q)Dv'v(q).
For a fixed wavelength of the sound the absorption will oscillate as the magnetic field is varied. This phenomenon is known as a geometric resonance. The theory of this effect was proposed by Pippard [15]. Consider an isotropic metal where the projection of a cyclotron path to the plane perpendicular to the magnetic field is a circle. Assume that the transverse ultrasonic wave propagates along the "x" -axis of the chosen coordinate system with a polarization vector along the "y"-axis. The magnetic field as usual is supposed to be directed along the "z" -axis.