<s>
In	O
condensed	O
matter	O
physics	O
,	O
biexcitons	B-General_Concept
are	O
created	O
from	O
two	O
free	O
excitons	O
.	O
</s>
<s>
Three	O
possibilities	O
of	O
observing	O
biexcitons	B-General_Concept
exist	O
:	O
</s>
<s>
(	O
a	O
)	O
excitation	O
from	O
the	O
one-exciton	O
band	O
to	O
the	O
biexciton	B-General_Concept
band	O
(	O
pump-probe	O
experiments	O
)	O
;	O
</s>
<s>
(	O
b	O
)	O
two-photon	O
absorption	O
of	O
light	O
from	O
the	O
ground	O
state	O
to	O
the	O
biexciton	B-General_Concept
state	O
;	O
</s>
<s>
(	O
c	O
)	O
luminescence	O
from	O
a	O
biexciton	B-General_Concept
state	O
made	O
up	O
from	O
two	O
free	O
excitons	O
in	O
a	O
dense	O
exciton	O
system	O
.	O
</s>
<s>
where	O
is	O
the	O
biexciton	B-General_Concept
energy	O
,	O
is	O
the	O
exciton	O
energy	O
,	O
and	O
is	O
the	O
biexciton	B-General_Concept
binding	O
energy	O
.	O
</s>
<s>
When	O
a	O
biexciton	B-General_Concept
is	O
annihilated	O
,	O
it	O
disintegrates	O
into	O
a	O
free	O
exciton	O
and	O
a	O
photon	O
.	O
</s>
<s>
The	O
energy	O
of	O
the	O
photon	O
is	O
smaller	O
than	O
that	O
of	O
the	O
exciton	O
by	O
the	O
biexciton	B-General_Concept
binding	O
energy	O
,	O
</s>
<s>
so	O
the	O
biexciton	B-General_Concept
luminescence	O
peak	O
appears	O
on	O
the	O
low-energy	O
side	O
of	O
the	O
exciton	O
peak	O
.	O
</s>
<s>
The	O
biexciton	B-General_Concept
binding	O
energy	O
in	O
semiconductor	O
quantum	O
dots	O
has	O
been	O
the	O
subject	O
of	O
extensive	O
theoretical	O
study	O
.	O
</s>
<s>
Because	O
a	O
biexciton	B-General_Concept
is	O
a	O
composite	O
of	O
two	O
electrons	O
and	O
two	O
holes	O
,	O
we	O
must	O
solve	O
a	O
four-body	O
problem	O
under	O
spatially	O
restricted	O
conditions	O
.	O
</s>
<s>
The	O
biexciton	B-General_Concept
binding	O
energies	O
for	O
CuCl	O
quantum	O
dots	O
,	O
as	O
measured	O
by	O
the	O
site	O
selective	O
luminescence	O
method	O
,	O
increased	O
with	O
decreasing	O
quantum	O
dot	O
size	O
.	O
</s>
<s>
where	O
is	O
biexciton	B-General_Concept
binding	O
energy	O
,	O
is	O
the	O
radius	O
of	O
the	O
quantum	O
dots	O
,	O
is	O
the	O
binding	O
energy	O
of	O
bulk	O
crystal	O
,	O
and	O
and	O
are	O
fitting	O
parameters	O
.	O
</s>
<s>
where	O
is	O
the	O
binding	O
energy	O
of	O
the	O
biexciton	B-General_Concept
and	O
is	O
the	O
energy	O
of	O
exciton	O
.	O
</s>
<s>
The	O
diffusion	O
Monte	O
Carlo	O
(	O
DMC	O
)	O
method	O
provides	O
a	O
straightforward	O
means	O
of	O
calculating	O
the	O
binding	O
energies	O
of	O
biexcitons	B-General_Concept
within	O
the	O
effective	O
mass	O
approximation	O
.	O
</s>
<s>
For	O
a	O
biexciton	B-General_Concept
composed	O
of	O
four	O
distinguishable	O
particles	O
(	O
e.g.	O
,	O
a	O
spin-up	O
electron	O
,	O
a	O
spin-down	O
electron	O
,	O
a	O
spin-up	O
hole	O
and	O
a	O
spin-down	O
hole	O
)	O
,	O
the	O
ground-state	O
wave	O
function	O
is	O
nodeless	O
and	O
hence	O
the	O
DMC	O
method	O
is	O
exact	O
.	O
</s>
<s>
DMC	O
calculations	O
have	O
been	O
used	O
to	O
calculate	O
the	O
binding	O
energies	O
of	O
biexcitons	B-General_Concept
in	O
which	O
the	O
charge	O
carriers	O
interact	O
via	O
the	O
Coulomb	O
interaction	O
in	O
two	O
and	O
three	O
dimensions	O
,	O
indirect	O
biexcitons	B-General_Concept
in	O
coupled	O
quantum	O
wells	O
,	O
and	O
biexcitons	B-General_Concept
in	O
monolayer	O
transition	O
metal	O
dichalcogenide	O
semiconductors	O
.	O
</s>
<s>
Biexcitons	B-General_Concept
with	O
bound	O
complexes	O
formed	O
by	O
two	O
excitons	O
are	O
predicted	O
to	O
be	O
surprisingly	O
stable	O
for	O
carbon	O
nanotube	O
in	O
a	O
wide	O
diameter	O
range	O
.	O
</s>
<s>
Thus	O
,	O
a	O
biexciton	B-General_Concept
binding	O
energy	O
exceeding	O
the	O
inhomogeneous	O
exciton	O
line	O
width	O
is	O
predicted	O
for	O
a	O
wide	O
range	O
of	O
nanotubes	O
.	O
</s>
<s>
The	O
biexciton	B-General_Concept
binding	O
energy	O
in	O
carbon	O
nanotube	O
is	O
quite	O
accurately	O
approximated	O
by	O
an	O
inverse	O
dependence	O
on	O
,	O
except	O
perhaps	O
for	O
the	O
smallest	O
values	O
of	O
.	O
</s>
<s>
The	O
actual	O
biexciton	B-General_Concept
binding	O
energy	O
is	O
inversely	O
proportional	O
to	O
the	O
physical	O
nanotube	O
radius	O
.	O
</s>
<s>
Experimental	O
evidence	O
of	O
biexcitons	B-General_Concept
in	O
carbon	O
nanotubes	O
was	O
found	O
in	O
2012	O
.	O
</s>
<s>
The	O
enhanced	O
Coulomb	O
interaction	O
in	O
microcrystallites	O
still	O
increase	O
the	O
biexciton	B-General_Concept
binding	O
energy	O
in	O
the	O
large-size	O
regime	O
,	O
where	O
the	O
quantum	O
confinement	O
energy	O
of	O
excitons	O
is	O
not	O
considerable	O
.	O
</s>
