University of Illinois Urbana-Champaign

Many-body effects in metals, modulation doped quantum wells and doped semiconductors

Perakis, Ilias

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https://hdl.handle.net/2142/18905

Description

Title
Many-body effects in metals, modulation doped quantum wells and doped semiconductors
Author(s)
Perakis, Ilias
Issue Date
1992
Doctoral Committee Chair(s)
Chang, Yia-Chung
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • many-body
  • metals
  • quantum wells
  • doped semiconductors
  • semiconductors
  • x-ray edge singularities
Language
en
Abstract
A new approach to the problem of X-ray edge singularities and peaks of many-body origin observed in the optical spectra is presented. We first establish the analogy between a system of one hole interacting with many electrons and the polaron, where one electron interacts with many phonons. We approach both cases as an eigenvalue problem for the time independent Schrodinger equation, obtain expressions for the many-body eigenstate& in a convenient basis and use them to understand the behavior of the system. In the case of a localized hole with infinite mass, we diagonalize the Hamiltonian exactly using first a wavefunction and then a noncanonical transformation. technique. We -use the expressions for the eigenstates to obtain the exact analytic formulas for the optical spectra, accurate over the whole frequency range. We then apply our techniques to the case of a finite mass valence hole, which is realized in modulation doped quantum wells or wires. In this case we approximately diagonalize the Hamiltonian by treating exactly the most important terms leading to nonperturbative behavior. The terms neglected are identified and can be treated in perturbation theory. Our method provides a clear physical picture and valuable insight into the accurate treatment of many-body Hamiltonians.
Type of Resource
text
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http://hdl.handle.net/2142/18905
Copyright and License Information
1992 Ilias Perakis

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