Chemistry Reference
In-Depth Information
world. A remarkable mechanical robustness of single layer graphene was
also revealed. Now, one could prepare, manipulate and study one carbon
atom thick layer for several of its properties. The resulting experimental
and theoretical efforts
[
3
]
have revealed several surprises in simple graphene.
Looking back at the fast developments one begins to wonder at the number
of quantum phenomena that graphene has revealed, arising from a simple
sp
2
bond among only carbon atoms. This is surely a case of an unexpected
and welcome
quantum wealth
.
Behind the quantum wealth is a simple sp
2
bonding among carbon
atoms and a resulting stable 2 dimensional honey comb lattice structure.
Sp
2
hybridization leads to a strong
σ
bond and leaves one electron per 2p
z
orbital
[
4
]
. Neighboring 2p
z
π
∗
bands. The two bands meet at the K and K' points in the Brillouin zone in
the form of a Dirac cone. Further, the Bloch wave functions have special
sublattice structure, a chirality property, which influence various quantum
dynamical properties of graphene.
This stable 2 dimensional system offers a platform for a rich quantum
physics. When we talk about emergent properties in modern times, one is
reminded of multicomponent systems with competing interactions among
many agents or components. Quantum Condensed matter systems seems
to be a play ground for novel and unexpected emergent properties in rather
simple situations, even with one or two components. One can cite the
example of
4
He, which exhibits gas, liquid, superfluid, supersolid, quan-
tized vortices, Josephson phenomena etc. Water molecule H
2
Oprovides
hydrogen bonding, proton tunnelling, clathrate hydrates, amorphous ice,
12 phases of ice, water, turbulence etc. One can give similar account for
iron and so on. Many of these emergent properties are not due to many
competing agents, but due to the peculiar structure of underlying quantum
mechanics.
Inthepresentarticleweintroduceanotionof
quantum complexity
through the example of graphene. After a brief discussion of complex-
ity, we will summarise our own results, which indicates the breadth in
the type of unexpected quantum phenomena that graphene could support.
We review our predictions, (i) spin-1 collective mode in netural graphene,
(ii) relativistic type of phenomena in crossed electric and magnetic fields,
(iii) room temperature superconductivity in doped graphene (iv) composite
Fermi sea in neutral graphene in uniform magnetic field and (v) 2-channel
Kondo effect. In the above, except for the relativistic type of phenomena,
the rest depend on the electron-electron interaction in the 2 dimensional
graphene.
π
orbitals overlap and produce the
and
