By Monique Combescot, Shiue-Yuan Shiau
This ebook bridges a niche among significant groups of Condensed subject Physics, Semiconductors and Superconductors, that experience thrived independently. utilizing an unique point of view that the most important debris of those fabrics, excitons and Cooper pairs, are composite bosons, the authors elevate basic questions of present curiosity: how does the Pauli exclusion precept wield its energy at the fermionic elements of bosonic debris at a microscopic point and the way this impacts their macroscopic physics? What do we examine from Wannier and Frenkel excitons and from Cooper pairs that is helping us comprehend "bosonic condensation" of composite bosons and its distinction from Bose-Einstein condensation of uncomplicated bosons? The authors start with a great mathematical and actual beginning to derive excitons and Cooper pairs. They extra introduce Shiva diagrams as a photo help to know the many-body physics brought on by way of fermion alternate within the absence of fermion-fermion interplay - a unique mechanism now not visualized by way of normal Feynman diagrams. complicated undergraduate or graduate scholars in physics with out particular historical past will take advantage of this booklet. The built thoughts and formalism must also be valuable for present learn on ultracold atomic gases and exciton-polaritons, and quantum information.
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Additional info for Excitons and Cooper Pairs : Two Composite Bosons in Many-Body Physics
We can also dissociate excitons through thermal excitation by increasing their temperature at constant electron-hole density above a temperature of the order of their binding energy (see Fig. 13). A less obvious way to dissociate excitons is to decrease their density at fixed temperature. Indeed, for a fixed number of particles, here electrons and holes, the equilibrium state for T = 0 is the one having the lowest free energy F = E – TS. 12) The change from bound excitons to electron-hole pairs increases the energy E but also increases the disorder through an increase in particle number.
As Coulomb interaction conserves momentum, the total momentum ke + kh of the electron-hole pair appearing in the ladder diagram of Fig. 6 and entering the sum in Eq. 3) stays constant. This momentum is just the momentum Qi = ke + kh of the i exciton center of mass. 2 Frenkel excitons In the case of Frenkel excitons, the Coulomb processes that delocalize the excitations originally localized on lattice sites n are the intersite interlevel Coulomb processes shown in Fig. 7: the electron excited at lattice site n1 returns to the ground atomic level of the same site while another electron is excited at a different lattice site n2 .
The reason is that the electron and the hole in a quantum dot are forced to stay close to each other by the potential barrier of the dot; Coulomb interaction then plays a minor role even if the energy it induces is very large because, in a small quantum dot, the confinement brings the electron and the hole very close at the Bohr radius scale. By contrast, Coulomb interaction plays a major role in the formation of Wannier excitons in bulk samples, quantum wells, and quantum wires because it provides the mechanism to keep the hole, originally delocalized over the whole sample, close to the electron.
Excitons and Cooper Pairs : Two Composite Bosons in Many-Body Physics by Monique Combescot, Shiue-Yuan Shiau