Chemistry Reference
In-Depth Information
Quantum Complexity in Graphene
2
Carbon Atom 1s 2s 2p
22
Graphene
sp
2
sp
3
sp
3
+
World
Diamond
world
sp
2
World of
carbon nanotube,
Fullerene
graphene−nanotube composite
amorphous carbon etc.
σ
− bond
π −
bond
*
Honeycomb Lattice
2 dimensional
Doped Graphene
Room Temperature Superconductivity ?
*
π and
π
bands
Pauling's
Flat Bands at Edges
Magnetism ?
Resonating Valence Bond State
Room Temperature
Ferromagnetism ?
Dirac Cones at K and K'
Chirality of
spin−1 Collective
Mode ?
*
Bloch wave functions
fQH States
2−Channel
Effect
Zitterbewegung
Kondo
*
anomalous
Klein tunnelling
Room Temperature
Anti localization
Parity Anamoly
Landau Level
Quantum Hall States
spacing
Defects as
Gauge Fields
Spin Hall Effect ?
*
Half filled
Crossed magnetic & electric field
Lorenz Boost,
n = 0 Landau level
Time dilation
Composite Fermi sea ?
Lorenz contraction
*
Vacuum collapse ?
Fig. 1. Some of the important quantum aspects of graphene. Boxes marked with an
asterisk indicate theoretical suggestions of ours with collaborators, discussed in this
article.
Further, the Bloch states acquires a chirality, in the sense of a momentum
dependent phase relation between the amplitudes of the wave functions in
the two sublattices. This leads to a special
spinor
like character to the
non relativistic electrons wave function. These are at the heart of several
phenomena, including Zitterbewegung, Klein tunnelling, antilocalization,
parity anomaly and so on. Further, the small spin orbit coupling can make
use of the above structure and lead to
spin Hall effect
as predicted by Kane
and Mele
[
12
]
.
Honeycomb lattice offers some special type of topological defects, such
as Stone-Walls defect, containing a pentagon and heptagon ring. It has
been shown that an isolated pentagon or heptagon defect act like Z
2
gauge
fields, as far as electron dynamics is concerned. It has been suggested that
even lattice strain acts like an effective magnetic field.
Since graphene is a two dimensional electronic system, it provides op-
portunity to study quantum Hall phenomena. As far as integer quantum
