Chemistry Reference
In-Depth Information
y
(a)
x
(c)
(b)
b
1
Κ
Κ
Γ
Μ
Γ
k
c
a
1
Κ
a
2
b
2
k
y
k
x
Fig. 2. (a) Honeycomb lattice of carbon atoms in real space;
a
1
,
2
=
2
(
√
3
, ±
1) (b)
K-space and the Brillouin Zone;
b
1
,
2
=
2
a
(
√
3
, ±
1) (c) Dirac cone spectrum at a
K
point.
Hall effect is concerned there is an extra Berry phase in the problem, leading
to a general half integer shift in the quantized Hall conductance. Because
of the extra degeneracy (flavor index) the nature of fractional and integer
quantum Hall effect becomes richer. Recently fQHE and filling
1
3
and a
many body quantum Hall state in neutral graphene have been experimen-
tally observed. Further, the band parameters are such that one gets room
temperature quantized Hall effect. There is also a possibility of composite
fermi sea that we will see later. If the composite fermi sea starts supporting
paired quantum Hall state, we will have the possibility of producing Non
Abelian quasi particle, which are very desirable to implement topological
quantum computation.
Electromagnetic absorption property by graphene is remarkable. The-
ory and experiment shows that the absorption coecient is
is
the fine structure constant. In other words there is no dependence on ma-
terial properties such as electron density or lattice parameters, Soft flexural
modes trap electrons and holes, leading to charge puddles. There is mag-
netism at graphene edge
[
13
]
, spin-1 collective mode at the bulk. Graphene,
after appropriate doping is predicted to become a room temperature super-
conductor. High temperature ferromagnetism has been also reported.
In what follows we will summarise our own predictions for graphene
exhibiting the possible richness of graphene. They are manifestations
of a simple underlying chemical property namely sp
2
bonding and elec-
tron electron interaction, leading to complex consequences as shown in
Fig. 1.
πα
,where
α
