Chemistry Reference
In-Depth Information
NMR, quantum optics, cold atoms etc., a variety of experimental and the-
oretical studies exist now: from detailed wave packet dynamics in chemical
reactions, to non equilibrium Kondo phenomena in mesoscopic systems to
a rich quantum kinetic behaviour in supersolid
4
He etc.
1.2.
Novel phenomena in graphene
One of the first persons to appreciate a novel quantum phenomenon in
graphene/graphite was Pauling, back in 1936. He recognized
[
7
]
presence
of unsaturated
bonds and emphasized resonance of covalent bonds and
tried to understand graphite/graphene, before band theory was developed.
As we will see later, while Pauling's theory was not entirely correct, there
is a key feature, which captures among other things a predicted spin-1 col-
lective mode
[
8
]
and possibility of room temperature superconductivity in
optimally doped graphene
[
9
]
. An important property of graphite, namely
Landau diamagnetism was discovered by K S Krishnan and Ganguly
[
10
]
in
the late 30's. K S Krishnan also discovered the extreme anisotropic conduc-
tivity of graphite [11], thereby paving way for study of quasi 2 dimensional
and quasi 1 dimensional metals.
Once graphene was separated from graphite by a simple method by
Noveselov et al., intense experimental and theoretical activities started in
the field of graphene. We will briefly mention the variety of novel phe-
nomena that graphene exhibits and trace its origin to a special quantum
mechanical property of carbon atom. Quantum complexity in graphene is il-
lustrated in Fig. 1. Carbon atom has an electronic configuration 1s
2
2s
2
2p
2
.
There are four valence electrons in the 2s and 2p orbitals. A remarkable
property of carbon is its ability to form stable sp
2
and
π
sp
3
bonds and the
near equality of bond energies. On the pure sp
2
end it gives rise to graphene
and on the
sp
3
end it gives diamond. In between, a continuous mixing of
sp
2
and sp
3
gives rise to myriad forms (allotropes) of pure carbon - carbon
nano tubes, bucky balls, nanotube-graphene hybrids, amorphous carbon,
carbon black and so on. In the present article we will focus on graphene.
sp
2
bonding leads to a strong
bond, which stabilizes a honey comb
lattice structure. In turn, a lone electron in the remaining 2
σ
p
z
orbital gets
involved in p
bonding and we get a simple tight binding system on the
honey comb lattice. Honey comb lattice and two atoms per unit cell leads
to the formation of
π
π
∗
bands that touch each other at the K and
K' points in the Brillouin zone in the form of Dirac cones (Fig. 2). The
two valleys lead to a valley pseudo spin, a flavor index for the Dirac spinor.
π
and
