Ground state energy of N Frenkel excitons |
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Authors: | W Pogosov and M Combescot |
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Institution: | (1) Institut des NanoSciences de Paris, Universite Pierre et Marie Curie, CNRS, Campus Boucicaut, 140 rue de Lourmel, 75015 Paris, France;(2) Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Izhorskaya 13/19, 125412 Moscow, Russia |
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Abstract: | By using the composite many-body theory for Frenkel excitons we have recently developed, we here derive the ground state energy
of N Frenkel excitons in the Born approximation through the Hamiltonian mean value in a state made of N identical Q = 0 excitons. While this quantity reads as a density expansion in the case of Wannier excitons, due to many-body effects induced
by fermion exchanges between N composite particles, we show that the Hamiltonian mean value for N Frenkel excitons only contains
a first order term in density, just as for elementary bosons. Such a simple result comes from a subtle balance, difficult
to guess a priori, between fermion exchanges for two or more Frenkel excitons appearing in Coulomb term and the ones appearing
in the N exciton normalization factor – the cancellation being exact within terms in 1/Ns where Ns is the number of atomic sites in the sample. This result could make us naively believe that, due to the tight binding approximation
on which Frenkel excitons are based, these excitons are just bare elementary bosons while their composite nature definitely
appears at various stages in the precise calculation of the Hamiltonian mean value. |
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Keywords: | PACS" target="_blank">PACS 71 35 -y Excitons and related phenomena 71 35 Aa Frenkel excitons and self-trapped excitons |
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