Chemistry Reference
In-Depth Information
systems such as benzene, naphthane, anthracene, caronene etc, all having
nearly the same value for quantum chemical parameters
.
[
45
]
One
of the consequences of this is that the first excited spin-0 state lies above
the first excited spin-1 state by more than 2 eV. There is a predictable
consequence of this large singlet-triplet splitting: graphene can be viewed
as an end member of a sequence of planar
t
and
U
bonded system.
As we mentioned earlier, Pauling
[
7
]
was the first to recognize domi-
nance of singlet correlation between two neighboring
pπ
electrons in the
ground state. He argued that doubly occupied or empty 2p
z
orbitals (polar
configurations) are less important because of electron-electron repulsion in
the 2p
z
orbital. Pauling thus ignored polar configurations. Once we ignore
polar fluctuations (states with double occupancy) and consider a resonance
among the nearest neighbor valence bond configurations we get the well
known RVB state. However, such a Hilbert space actually describes a Mott
insulating state rather than a metal. Experimentally, undoped graphene is
a broad band conductor, albeit with a linearly vanishing density of states
at the Fermi energy.
To recover metallicity in Pauling's RVB theory, we combined the broad
band feature of
pπ
electrons with Pauling's real space singlet (covalent)
bonding tendency and suggested
[
39
]
a low energy phenomenological model
for graphene:
pπ
t
ij
c
iσ
c
jσ
+
b
ij
b
ij
H
GB
=
−
h.c. − J
(20)
ij
ij
creates a spin singlet on the
b
ij
c
i↑
c
j↓
− c
i↓
c
j↑
=
√
2
where
i − j
bond.
J
0) is a measure of singlet or valence bond correlations emphasized by
Pauling, i. e., a nearest neighbour attraction in the spin singlet channel.
In the present paper we call it as a 'bond singlet pairing' (BSP) pseudo
potential. The parameter
(
>
was chosen as the singlet triplet splitting in a
2 site Hubbard model with the same
J
U
2
+16
t
2
)
1
/
2
− U
t
and
U
,
J
=((
)
/
2.
As
becomes larger than the bandwidth this psuedo-potential will become
the famous superexchange characteristic of a Mott insulator. As shown in
[
39
]
, this model predicts that undoped graphene is a “normal” metal. The
linearly vanishing density of states at the chemical potential engenders a
critical strength
U
J
c
for the BSP to obtain a finite mean field superconduct-
ing
T
c
.
J
for graphene was less than the critical value,
and undoped graphene is not a superconductor despite Pauling's singlet
correlations. Doped graphene has a finite density of state at the chemical
potential and a superconducting ground state is possible. Black-Schaffer
The parameter
