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 thought of high-frequency phenomena in metals, in paricular the results because of neighborhood good points within the geometry of the Fermi floor. The textual content develops a constant thought of numerous results, resembling cyclotron resonances in magnetic fields basic to the skin. issues lined contain: uncomplicated equations of the Fermi-liquid thought; 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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Its Fourier component equals F: = L g~v,Gv'v(q). 30) The remaining part of the force includes the contribution from a "bare" elasticity of a lattice, and the tenn which originates from the averaging over the local equilibrium. 1-: I I x B]a + lqfJ-(}Y' AafJ}Aqy c 1 y + /i-[Py(-q), nafJ(q)]qfJu q . 31) Here J~ represents the sum of the locally equilibrium contribution to the electron current and the lattice current, -iwQuq(V, A~ = Aq - [uq(V x B]; the last tenns, as well as the first, are averaged over the equilibrium state of the electron liquid.
Other electrons, which move at larger angles to the surface, spend little time in the electric field and therefore they cannot receive a perceptive amount of energy from the field. J is proportional to the angle. 52) According to Pippard we can replace the conductivity 0' by the "effective" conductivity O'eff which contains the extra factor 8/ I. 8. Effective electrons in an anomalous skin effect. 53) where a is a real dimensionless factor of the order of unity. 49) we arrive at the result _(4Jl'Waa)1/3(!
VS) +I 2 . 54) Skin depth 0 is determined by the imaginary part of q. 55) shows that the frequency dependence of the skin depth changes in the nonlocal regime ([ > 0). Under the conditions of the normal skin effect (local regime, [ « 0) the skin depth is proportional to W- 1/2 whereas the skin depth of the anomalous skin effect is proportional to w -1/3. In the order of magnitude the skin depth of the anomalous skin effect is larger than the skin depth of the normal skin effect for the same value of conductivity a.