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Excitons and Cooper PairsTwo Composite Bosons in Many-Body Physics$
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Monique Combescot and Shiue-Yuan Shiau

Print publication date: 2015

Print ISBN-13: 9780198753735

Published to Oxford Scholarship Online: March 2016

DOI: 10.1093/acprof:oso/9780198753735.001.0001

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Wannier Excitons

Wannier Excitons

(p.34) 3 Wannier Excitons
Excitons and Cooper Pairs

Monique Combescot

Shiue-Yuan Shiau

Oxford University Press

Chapter 3 deals with Wannier excitons, which are the most commonly studied excitons. Via a phenomenological approach, the formation of a Wannier exciton from a delocalized electron and a delocalized hole, the semiconductor dielectric constant, and photon-exciton coupling are derived. This phenomenology is further supported by a microscopic derivation starting from the crystal Hamiltonian. From it, the hole emerges as a quasiparticle representing an empty state in the full valence band. Excitons interact not only through Coulomb processes between carriers but also through carrier exchanges in the absence of Coulomb processes. Coulomb scattering can be formally derived from commutators involving exciton creation operators and the semiconductor Hamiltonian, while Pauli scattering induced by carrier exchange in the absence of Coulomb interaction can be formally derived from commutators of exciton creation and destruction operators. These two scatterings, visualized by Shiva diagrams, are the fundamental building blocks for Wannier exciton many-body effects.

Keywords:   Wannier exciton, semiconductor Hamiltonian, semiconductor dielectric constant, photon-exciton coupling, Pauli scattering, Coulomb scattering, commutator, exciton creation operator, Shiva diagram, hole

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