Issue |
Europhys. Lett.
Volume 55, Number 3, August 2001
|
|
---|---|---|
Page(s) | 390 - 396 | |
Section | Condensed matter: electronic structure, electrical, magnetic, and optical properties | |
DOI | https://doi.org/10.1209/epl/i2001-00427-7 | |
Published online | 01 December 2003 |
New criteria for bosonic behavior of excitons
1
Groupe de Physique des Solides, Université
Denis Diderot and Université Pierre et Marie Curie,
CNRS - Tour 23, 2 place Jussieu, 75251 Paris
Cedex 05, France
2
France Telecom R& D RTA/CDP - 196 avenue
Henri Ravera 92225 Bagneux Cedex, France
Received:
17
April
2001
Accepted:
18
May
2001
Dimensional arguments lead to say that N excitons in a sample
of volume V behave as bosons for ,
ax being the exciton radius and λ a dimensionless
factor. The Mott criterion, which is based on the disappearance
of all exciton bound states because of screening, gives
. Since excitons feel each other through both Coulomb
interaction and Pauli exclusion between their electrons and
holes, criteria based on the underlying fermionic character of
the exciton should be even more relevant. Two significant
quantities are the boson departure
and boson
number
, where
is the exciton
creation operator. Their expectation values in the N-exciton
state are close to their boson values for
and
, respectively. By contrast, the expectation
value of
in the vacuum state is close to
N! for
only. This surprising N2-dependence
comes from the intrinsic N-body character of Pauli
exclusion. Consequences of these new criteria on the Bose
condensation of excitons are discussed.
PACS: 71.35.Lk – Collective effects (Bose effects, phase space filling, and excitonic phase transitions)
© EDP Sciences, 2001
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