By Monique Combescot, Shiue-Yuan Shiau
This e-book bridges a spot among significant groups of Condensed subject Physics, Semiconductors and Superconductors, that experience thrived independently. utilizing an unique point of view that the main debris of those fabrics, excitons and Cooper pairs, are composite bosons, the authors bring up 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 easy bosons? The authors commence with a superior mathematical and actual beginning to derive excitons and Cooper pairs. They additional introduce Shiva diagrams as a image help to know the many-body physics brought about by means of fermion trade within the absence of fermion-fermion interplay - a singular mechanism now not visualized by means of common Feynman diagrams. complex undergraduate or graduate scholars in physics with out particular historical past will reap the benefits of this e-book. The constructed innovations and formalism must also be worthy for present study on ultracold atomic gases and exciton-polaritons, and quantum information.
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This ebook bridges a spot among significant groups of Condensed subject Physics, Semiconductors and Superconductors, that experience thrived independently. utilizing an unique point of view that the main debris of those fabrics, excitons and Cooper pairs, are composite bosons, the authors elevate primary questions of present curiosity: how does the Pauli exclusion precept wield its strength at the fermionic elements of bosonic debris at a microscopic point and the way this impacts their macroscopic physics?
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Additional info for Excitons and Cooper Pairs : Two Composite Bosons in Many-Body Physics
To understand this dark-bright exciton splitting, let us first consider what happens when a photon is absorbed or emitted in a semiconductor. 11 (a) In photon absorption, one electron is excited from the valence band to the conduction band. (b) Feynman diagram for this process: the initial state has one photon and one valence electron; the final state has one conduction electron. 12 The diagram in (a) is equivalent to the diagram shown in Fig. 11(b): one photon and one valence electron transform into one conduction electron.
10) where Nmax is the maximum number of excitons the sample can accommodate. 11) 28 The Exciton Concept where —of the order of two phonon energies—is the energy extension of the “potential layer” over which the attractive BCS potential acts, while ρ is the density of states taken † † as constant in this layer; so, ρ + 1 is the number of free pair states ak↑ a–k↓ with energy εF0 ≤ εk ≤ εF0 + that participate in the Cooper pair formation. This number also is the maximum number of Cooper pairs that the potential layer can host.
11(a)). In this process, the initial state has one valence electron and one photon, and the final state has one conduction electron (see Fig. 11(b)). The diagram of Fig. 11(b) is equivalent to the diagram of Fig. 12(a) or that of Fig. 12(b) in terms of electron and hole: indeed, photon absorption accompanies the creation of an electron-hole pair, as is obvious from Fig. 11(a). We now consider photon emission. It accompanies the de-excitation of an electron from the conduction band to the valence band, as shown in Fig.