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Excitons and Cooper PairsTwo Composite Bosons in Many-Body Physics$
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Monique Combescot and Shiue-Yuan Shiau

Print publication date: 2015

Print ISBN-13: 9780198753735

Published to Oxford Scholarship Online: March 2016

DOI: 10.1093/acprof:oso/9780198753735.001.0001

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Links Between Cooper Pairs and Excitons

Links Between Cooper Pairs and Excitons

(p.270) 11 Links Between Cooper Pairs and Excitons
Excitons and Cooper Pairs

Monique Combescot

Shiue-Yuan Shiau

Oxford University Press

Chapter 11 compares Wannier excitons, Frenkel excitons, and Cooper pairs, with respect to their potentials, particle degrees of freedom, ground-state energies, wave functions, and many-body parameters. Shiva diagrams for composite boson many-body effects are used to visualize the physics. For these composite particles, it is possible to assign the same physical meaning to the mathematical parameter appearing in the density expansion of their many-body effects. This many-body parameter is N/Nmax, where Nmax is the maximum number of composite bosons the sample can accommodate. Characteristic lengths of Cooper pair wave functions for a single pair and a dense regime of pairs are also discussed. Finally, this chapter discusses the density regimes for excitons and Cooper pairs: excitons exist in the dilute regime, since at high density they dissociate into an electron-hole plasma. By contrast, Cooper pairs can strongly overlap without breaking, owing to the peculiar form of the reduced BCS potential.

Keywords:   many-body parameter, Cooper pair, Wannier exciton, Frenkel exciton, Shiva diagram, pair wave function, potential, degree of freedom, ground-state energy

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