Chemistry Reference
In-Depth Information
of hole development in g(r) and the corresponding energy gain to be about
1
4
=
2
×
2
of energy gain within a given composite fermi sea. Since a
given electron can reduce coulomb energy by correlating with three other
composite fermi sea, the net energy we gain from the 3
×
4
. Putting these
numbers we get our estimate of our state as:
46
e
2
8
e
2
0
B
(1 +
3
U
CF
≈−
4
)0
.
0
B
≈−
0
.
(30)
This energy is lower than that of the fully spin polarized filled Landau
level states (Eq. (3)). It is the valley degeneracy which helps us to get a
lower energy for the composite fermi sea!
We test our simple argument against a known case, namely stability of
the standard n = 1 fully polarized quantum Hall state (no valley degener-
acy) with a spin singlet compsite fermi sea. Experimentally it is known (at
least for lower odd integer Hall states) that fully polarized quantum Hall
state always wins. Interestingly, in our estimate, absence of valley degen-
eracy reduces the factor
4
1
4
to
and keeps the spin polarized filled n = 1
state marginally stable.
After the composite fermi sea is formed, the Zeeman energy creates spin
polarization in an otherwise spin singlet composite fermi sea.
The spin
gµ
B
B
U
CF
polarization of the composite fermi sea is easily estimated to be
.
We estimate that for graphene for a field of 30 T, spin polarization is less
than a few percent.
Very good signatures of composite fermion and fermi sea effects, in
standard quantum Hall systems have been experimentally studied
[
83
]
.It
will be very interesting to perform such studies and look for composite fermi
sea in neutral graphene in strong magnetic fields.
Composite fermions are neutral and they carry certain dipole moment
[
84
]
, as a function of their momenta. The response of the composite fermion
fermi surface to external perturbations such as a local defect will be inter-
esting. We will have a Friedel oscillation in dipole density.
Further graphene may offer alternate methods to study composite
fermions, because of new access through ARPES, STM etc, which are not
possible in standard quantum Hall devices.
Sofarwehavebeentalkingaboutlow temperature normal state.
Residual interactions will introduce low temperature pairing instabilities
in graphene either in the particle-particle or particle-hole channels. The
small spin polarization will interfere with the standard instabilities.
≈
