Excitons and Cooper Pairs Two Composite Bosons in Many-Body Physics

Monique Combescot, Directeur de Recherche CNRS Emeritus, Institute de NanoSciences de Paris, Universite Pierre-et-Marie-Curie, Shiue-Yuan Shiau, Assistant Research Fellow, Department of Physics and National Center for Theoretical Sciences, National Cheng Kung University

Monique Combescot is a former student from the École Normale Supérieure in Paris, France, (Maths and Physics major). In 1973, she obtained a PhD in many-body theory from the University of Paris, France (adviser Prof. Ph. Nozières). After a 2-year postdoc at Cornell University, USA, she returned as a research member of the CNRS in Paris, permanently. She likes teaching very much — she has been first at the "Aggregation de Physique". She has taught many undergraduate courses at the University and at Engineer Schools in Paris. Over the last two decades, she also gave various courses at the graduate level, in Paris and in many other places in the world. This book is based on one of these lectures.

Shiue-Yuan Shiau obtained B.S. in 1998 and M.S. in 2002 from National Taiwan University. He received his PhD in physics in 2007 from the University of Wisconsin-Madison. After postdoctoral positions in INAC/SPSM Commissariat à l'Energie Atomique de Grenoble, France, and Academia Sinica, Taipei, Taiwan, he is research assistant professor at National Cheng Kung University, Taiwan.

1. IntroductionPart I: Excitons2. The Exciton Concept3. Wannier Excitons4. Frenkel Excitons5. Elementary Bosons, Wannier and Frenkel Excitons, and Frenkel ExcitonsPart II: Cooper Pairs6. The Cooper Pair Problem7. The Bardeen-Cooper-Schrieffer Approach8. The Bogoliubov Approach9. The Gorkov Approach10. Richardsib-Gaudin Exact Solution11. Links Between Cooper Pairs and ExcitonsPart III: Particles Related to Excitons12. Trions, Biexcitons and Polaritons13. Trions14. Biexcitons15. PolaritonsPart IV: Bosonic Condensation16. From Elementary Composite Boson Condensates17. Elementary Bosons18. Composite Fermions19. Composite BosonsAppendix A : Some Mathematical ResultsA.1. The Kronecker symbol and delta functionA.2. Fourier transform and series expansionA.3. Coulomb scatteringsAppendix B : The Second Quantization FormalismAppendix C : The Hamiltonian for Wannier ExcitonsC.1. The semiconductor Hamiltonian in first quantizationC.2. Bloch statesC.3. The semiconductor Hamiltonian on the Bloch basisAppendix D : The Valence Electron Operator Versus the Hole OperatorD.1. Valence electron absenceD.2. Spin 1/2D.3. l=1 orbital momentumAppendix E : "The Coboson Bible"Appendix F : Direct Coulomb Scattering for Wannier ExcitonsF.1. Creation potentialF.2. Direct Coulomb scatteringF.3. Symmetry propertiesAppendix G : Concerning N Ground-State Wannier ExcitonsG.1. Normalization factorG.2. Hamiltonian mean valueAppendix H : Photon-Semiconductor InteractionH.1. Electromagnetic field in vacuumH.2. The electron Hamiltonian in a photon fieldH.3. Linear CouplingH.4. Quadratic couplingH.5. Complex polarization vectorsAppendix I : Photon-Exciton InteractionI.1. Photon-exciton couplingI.2. The sum rule between photon-exciton couplingsReferencesIndex