Calculation of temperature dependence of electron scattering rate in cadmium due to the electron-phonon interaction
Radio-frequency-size-effect measurements on metal cadmium show a peculiar and unexplained temperature (T) dependence of the electron quasiparticle scattering rate for (1K {le} T {le} 6K): there exists a large anisotropic T{sup 2} term added to the usual T{sup 3} term. In this dissertation, we propose a mechanism in which the umklapp electron-phonon scattering mechanism contributes an anisotropic T{sup 2} term to the orbitally averaged scattering rate for T{sub 1} < T < T{sub 2} where T{sub 1} and T{sub 2} are orbit characteristic temperatures depending strongly on the geometry of the orbit. We conclude that for a particular orbit, if the experimental temperature T falls between T{sub 1} and T{sub 2}, it will be possible to observe such a T{sup 2} term in the scattering rate. We discuss and rule out the possibilities that this T{sub 2} term is due to either the electron-electron interaction or Gantmaker's mechanism of electron-phonon interaction. Detailed numerical calculations of the scattering rate are carried out for temperature between 1 and 10K to verify this conclusion. The calculations are based on realistic model of Cd involving pseudo-potential treatment of the electron band structure, phonon dispersion relations and the electron-phonon interaction. The spin-orbit coupling is incorporated in the model. A Monte-Carlo method is used in the integration over the Fermi surface to determine the scattering rate. The numerical calculations support our proposed mechanism and agree with the experimental observation very well. It shows that for the third zone electron orbits, the scattering rates follow mainly the T{sup 3} rule, representing contributions from the normal scattering processes; only the superthermal umklapp scatterings contribute to the scattering rate because the lower cut off temperature T{sub 1} for the orbits is higher than 10K.
- Research Organization:
- Indiana Univ., Bloomington, IN (USA)
- OSTI ID:
- 5065802
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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