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2 valley), on
the other hand, is more ecient in building coulomb hole between electrons
belonging to different valleys and also different spins (because of the half
filled band character and less Pauli blocking), through two body scattering.
The process of building correlation hole and avoiding coulomb repulsion will
introduce short range SU(4) singlet correlation in the composite fermi sea.
To this extent
our proposal is somewhat similar to generic stability of spin
liquid or antiferromagnetic state, compared to ferromagnetic state in half
filled band of strongly correlated electrons
.
Further, for graphene, correlation and exchange energies are both com-
parable in magnitude and
b) Our composite fermi sea, a global SU(4) singlet (2 spin
130
√
BK
e
2
∼
0
B
≈
(B measured in Tesla); Zee-
man energy is negligible for B
30 T. In order to get a good ground state
both correlation and exchange energies need to be considered.
We focuss on the n = 0 Landau level of our neutral graphene and assume
that the lattice parameter of graphene 'a' is small compared to the magnetic
length
∼
B
; i.e.
a
B
<<
1. Appropriately normalized lattice coordinates of an
electron are complex numbers
z
στ
,where
σ
=
↑, ↓
and
τ
=
±
are the spin
and valley indeces.
We will make a brief remark about Jain's composite fermion
[
60; 61;
62
]
approach. In 2D quantum Hall problems, external magnetic fields gen-
erate quantized vortices. Stable many body states are formed, when there
is a commensurate relation between total number of vortices and total
number of electrons. In most of the stable quantum Hall states an elec-
tron gets 'bound' (associated) to a finite number of vortices (flux quanta)
to become a quasi particle, in terms of which the complex many body
problem becomes essentially non-interacting. When number of bound vor-
tices are even, statistics of the composite object remains a fermion. They
are the composite fermions. As these composites have already absorbed
the effect of external magnetic field they see an effective magnetic field
B
∗
<B
, the externally applied field. At the end of some hierarchies (eg.
p
2
p
+1
=
2
p →∞,
), the effective magnetic field seen by a composite fermion
vanishes, leading to a compressible composite fermi liquid state. Composite
fermion formation is a profound modification of the bare constituent elec-
tron. It also turns out to be an ecient way to build correlation/exchange
holes and avoid coulomb repulsion.
Now we will estimate and compare energies of spin polarized (upspin)
completely filled n = 0 Landau levels of 2 valleys Ψ
↑
G
, with our proposed
composite fermi sea state, Ψ
F
G
. The explicit form of the spin polarized
