An exciton is a bound pair of an electron and a hole. At low densities
(*na*_{B}^{D} << 1, where *a*_{B}
is the exciton Bohr radius, *n*
the density, and *D* the dimensionality), excitons are hydrogen-like Bose-particles.
Because the exciton mass is small—even smaller than the free electron mass—exciton
Bose-Einstein condensation (BEC) is expected to occur at relatively high temperatures, about 1 K,
for experimentally accessible exciton densities. In a dense e-h system
(*na*_{B}^{D} << 1),
excitons are Cooper-pair-like Bose-particles and the exciton condensate, called the excitonic
insulator, is analogous to the BCS superconductor state. In contrast to the BCS superconductor
state, because the pairing in the excitonic insulator is due to electron-hole interaction,
the pairs are neutral and the state is insulating. For the exciton condensation in a dense
electron-hole system, nesting of the electron and hole Fermi-surfaces is required.

The nature of the exciton condensation is different in these two limits. In the case of
BEC of excitons in the low density limit, excitons exist well above the critical temperature,
the number of excitons is fixed and does not change at the critical temperature, and the critical
temperature for the exciton condensation is determined by the statistical distribution in momentum
space of weakly interacting bosons (i.e. excitons). In contrast, in the case of BCS-like condensation
of excitons in the high density limit, excitons are formed at the critical temperature and the
critical temperature for exciton condensation is determined by the pairing, similar to the case of
Cooper pairs. The transition between the dilute and the dense limit is smooth and the condensation
has a mixed nature for intermediate densities.