This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/55616
Description
Title
Field theory of electrons and phonons
Author(s)
Simkin, David Alan
Issue Date
1963
Director of Research (if dissertation) or Advisor (if thesis)
Bardeen, John
Doctoral Committee Chair(s)
Bardeen, John
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D. (doctoral)
Degree Level
Dissertation
Keyword(s)
Electrons
Phonons
Language
en
Abstract
"Electrons in an alkali metal are allowed to interact by multiple processes, including direct coulomb interactions and retarded phonon exchanges, by including in the Hamiltonian both coulomb interaction and electron-phonon interaction terms. Corrections to low temperature one-electron properties are discussed for actual metallic densities by obtaining expressions for the electron self-energy, Sigma(p), in terms of single-particle Green's functions. The phonon terms, including Umklapp processes, are handled by means of Bardeen's matrix elements for the electron-phonon interaction, using longitudinal coupling and subjecting all directionally dependent quantities to a spherical averaging procedure. A criterion is developed to determine when phonon terms are comparable in magnitude to coulomb terms, and when they are negligible. Migdal has shown that phonon processes often contribute small terms proportional to factors of sqrt(m/M) (where m is electron mass and M is ion mass). In fact, phonon terms are of the same size as coulomb terms only for transitions lying within a narrow band of energies about the Fermi surface, whose width is of the order of the longitudinal phonon frequency, omega q. This leads to the general result that physical quantities depending upon Sigma(p), such as correlation energy or paramagnetic susceptibility, should show no phonon contribution to order sqrt(m/M), while quantities such as specific heat, which depend on (dsigma / dp)p = pf (density of states at the Fermi surface), show phonon contributions comparable to the coulomb contributions. A calculation of the phonon contribution to the linear electronic specific heat for sodium is made using the Nozieres-Pines interpolation scheme. Adding this to Silverstein's calculation of the coulomb terms yields a net enhancement over the free-electron value of 21 percent. Actually, for small wave-number vectors q, q less than or equal to sqrt(m/M) pf, it is shown that the electron-phonon interaction becomes just large enough to exactly cancel the divergences in the coulomb interaction perturbation series. This result depends upon the use of ""bare,"" or unrenormalized, quantities, and makes strong use of the longitudinal sum rule for phonon frequencies. A new ""combined"" form of perturbation series is proposed which consists of keeping coulomb and phonon terms together in any integration process, and which depends, for consistency, on a certain contour in the complex energy-transfer plane, chosen to avoid phonon poles. The series does not use any infinite sums (screening) and has the advantage of being consistently defined for all q (no interpolation) in the region of actual metallic densities. A first order specific heat calculation predicts an enhancement of 32 percent over the free-electron value for sodium."
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
