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

This 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.

1 - Introduction
2 - The Exciton Concept
3 - Wannier Excitons
4 - Frenkel Excitons
5 - Elementary Bosons, Wannier Excitons, and Frenkel Excitons
6 - The Cooper Pair Problem
7 - The Bardeen-Cooper-Schrieffer Approach
8 - The Bogoliubov Approach
9 - The Gorkov Approach
10 - The Richardson-Gaudin Exact Solution
11 - Links Between Cooper Pairs and Excitons
12 - Trions, Biexcitons, and Polaritons
13 - Trions
14 - Biexcitons
15 - Polaritons
16 - From Elementary to Composite Boson Condensates
17 - Elementary Bosons
18 - Elementary Fermions
19 - Composite Bosons
A.1 - The Kronecker symbol and delta function
A.2 - Fourier transform and series expansion
A.3 - Coulomb scatterings
C.1 - The semiconductor Hamiltonian in first quantization
C.2 - Bloch states
C.3 - The semiconductor Hamiltonian on the Bloch basis
D.1 - Valence electron absence
D.2 - Spin 1/2
D.3 - l=1 orbital momentum
F.1 - Creation potential
F.2 - Direct Coulomb scattering
F.3 - Symmetry properties
G.1 - Normalization factor
G.2 - Hamiltonian mean value
H.1 - Electromagnetic field in vacuum
H.2 - The electron Hamiltonian in a photon field
H.3 - Linear Coupling
H.4 - Quadratic coupling
H.5 - Complex polarization vectors
I.1 - Photon-exciton coupling
I.2 - The sum rule between photon-exciton couplings

M. Combescot is a former student of the Ecole Normale Superieure in Paris, France (Mathematics and Physics majors). In 1973, she obtained her Ph.D. in condensed matter many-body theory from the University of Paris, France (adviser Prof. Ph. Nozières). After two years of postdoc at Cornell University, USA, she returned as a research member at CNRS in Paris, permanently. Yet, she likes teaching very much --- she has been first at the "Aggregation de Physique", a competitive exam for high school teachers. For many years, she taught undergraduate courses at universities and engineering 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. Dr. Shiue-Yuan Shiau obtained his B.S. in 1998 and M.S. in 2002 from National Taiwan University. In 2007, he received his Ph.D in condensed matter physics from the University of Wisconsin-Madison, USA. After postdocs in INAC/SPSM, CEA at Grenoble, France and in RCAS, Academia Sinica at Taipei, Taiwan, he is currently assistant research fellow at National Cheng Kung University, Taiwan.