Combescot M., Shiau S.-Y. Excitons and Cooper Pairs: Two Composite Bosons in Many-Body Physics

Oxford University Press, 2016. — 559 p. — ISBN: 019875373XThis book bridges a gap between two major communities of Condensed Matter Physics, Semiconductors and Superconductors, that have thrived independently. Through an original perspective that their key particles, 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 the 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 start from 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 - a novel mechanism not visualized by standard Feynman diagrams. Advanced undergraduate or graduate students in physics with no prior background will benefit from this book. The developed concepts and methodology should also be useful to present researches on ultracold atomic gases, exciton-polaritons, and quantum information.Excitons
The Exciton Concept
Wannier Excitons
Frenkel Excitons
Elementary Bosons, Wannier Excitons, and Frenkel Excitons
Cooper Pairs
The Cooper Pair Problem
The Bardeen-Cooper-Schrieffer Approach
The Bogoliubov Approach
The Gorkov Approach
Richardson-Gaudin Exact Solution
Links Between Cooper Pairs and Excitons
Particles Related to Excitons
Trions, Biexcitons, and Polaritons
Trions
Biexcitons
Polaritons
Bosonic Condensation
From Elementary to Composite Boson Condensates
Elementary Bosons
Elementary Fermions
Composite Bosons
Appendixes
Some Mathematical Results
Second Quantization Formalism
The Hamiltonian for Wannier Excitons
Valence Electron Operator Versus Hole Operator
“The Coboson Bible”
Direct Coulomb Scatterings for Wannier Excitons
Concerning N Ground-State Wannier Excitons
Photon-Semiconductor Interaction
Photon-Exciton Interaction