This book bridges a gap between two major communities of Condensed Matter Physics, Semiconductors and Superconductors, that have thrived independently. Using an original perspective that the key particles of these materials, excitons and Cooper pairs, are composite bosons, the authors raise fundamental questions of current interest: how does the Pauli exclusion principle wield its power on the fermionic components of bosonic particles at a microscopic level and how this affects their macroscopic physics? What can we learn from Wannier and Frenkel excitons and from Cooper pairs that helps us understand "bosonic condensation" of composite bosons and its difference from Bose-Einstein condensation of elementary bosons? The authors begin with a solid mathematical and physical foundation to derive excitons and Cooper pairs. They further introduce Shiva diagrams as a graphic support to grasp the many-body physics induced by fermion exchange in the absence of fermion-fermion interaction - a novel mechanism not visualized by standard Feynman diagrams. Advanced undergraduate or graduate students in physics with no specific background will benefit from this book. The developed concepts and formalism should also be useful for current research on ultracold atomic gases and exciton-polaritons, and quantum information.
This book connects the two famous fields of Condensed Matter Physics, Semiconductors and Superconductors, through the composite boson nature of their key particles, excitons and Cooper pairs. The goal is to understand through these key particles how composite bosons made of two fermions interact.
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
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. Nozičres). 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 ą l'Energie Atomique de Grenoble, France, and Academia Sinica, Taipei, Taiwan, he is research assistant professor at National Cheng Kung University, Taiwan.
