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Physics World Nov 2006
The unique electronic properties of graphene – a one-atom-thick sheet of carbon that was produced
for the first time just two years ago – make it an ideal testing ground for fundamental physics,
describe Antonio Castro Neto, Francisco Guinea and Nuno Miguel Peres

For example, in quantum electrodynamics (QED),
the strength of electromagnetic interactions between
charged particles is described by the fine-structure constant,
α=e^2/hc, where h– is Planck’s constant divided by
2π and c is the speed of light. With a value of 1 divided
by 137.03599911±0.00000046, this is one of the most
precisely measured physical quantities in nature. Unfortunately,
we have no idea why the fine-structure constant
has this value. Since the effective speed of light
for the Dirac fermions in graphene is 300 times less,
graphene’s fine-structure constant should have a much
larger value of about two, though it has not yet been
measured precisely.

Now the above argument is logically the same as mine for gravity.
Above, it is stated that the large-scale collective IR limit effective coupling of electric charge to light is

(index of refraction)(vacuum coupling of electric charge to compensating gauge boson field of light)

in precisely the same way, I claim

(index of refraction)^4(vacuum coupling of gravitational charge to compensating gauge boson field of gravity)

Note that "vacuum coupling" simply means the way the local gauge boson field scatters off virtual off mass shell particles inside the vacuum.

index of refraction = 1 + scattering of the light off the real on mass shell particles outside the vacuum

also note that light is the compensating SPIN 1 gauge boson field from localizing the internal U1 Lie group

Einstein's gravity is the compensating SPIN 1 gauge boson field from localizing the external universal T4 translation Lie group. Here the SPIN 2 graviton is an entangled pair of SPIN 1 gravity "tetrad" quanta.

The fundamental couplings are dimensionless for both light and gravity, hence renormalizable.

"Background independence" = gauge invariance under local T4(x) frame transformations

At a Glance: Graphene
Graphene was first isolated by Andre Geim’s team at the University of Manchester (2004) ...   using the surprisingly simple technique of ripping layers from a graphite surface using adhesive tape. By repeatedly peeling away thinner layers (left), single-atom-thick sheets were obtained (right), as shown in these scanning electron micrographs.

The trademark behaviour that distinguishes a graphene
sheet from an ordinary metal, for example, is
the unusual form of the Hall effect.

In the original Hall effect, discovered in 1879, a current flowing
along the surface of a metal in the presence of a transverse
magnetic field causes a drop in potential at right
angles to both the current and the magnetic field. As
the ratio of the potential drop to the current flowing
(called the Hall resistivity) is directly proportional to
the applied magnetic field, the Hall effect is used to
measure magnetic fields.

A century later, Klaus von Klitzing discovered that
in a 2D electron gas at a temperature close to absolute
zero the Hall resistivity becomes quantized, taking only
discrete values of h/ne^2 (where h is Planck’s constant,
n is a positive integer and e is the electric charge). The
quantization is so precise that this “quantum Hall
effect” (QHE) is used as the standard for the measurement
of resistivity.

During a discussion about the discovery of graphene
at a tea party in Boston in early 2005, the present
authors started to wonder whether the QHE would
be different in graphene. We realized that due to a
quantum-mechanical effect called a Berry’s phase, the
Hall resistivity should be quantized in terms of odd
integers only. Graphene has a Berry’s phase of π, meaning
that if you “rotate” the quantum-mechanical wavefunction
of the Dirac fermions in graphene through a
full 360°, the system does not end up in the state that
it started in; instead the wavefunction changes sign.
A similar prediction to ours was made independently
in 2005 by Valery Gusynin at the Bogolyubov Institute
for Theoretical Physics in Kiev, Ukraine, and Sergei
Sharapov at McMaster University in Canada.
Soon after its prediction, this “anomalous integer
QHE” was observed experimentally by both Geim and
Kim, laying to rest any lingering doubts that graphene
had really been isolated. Interestingly, Geim’s group
observed the QHE in graphene at room temperature,
while it is only observed in ordinary metals at very low
temperatures. This is because the magnetic energy of
the electrons, called the cyclotron energy, in graphene
is 1000 times greater than it is in other materials. The
researchers also found that the anomalous integer
QHE is extremely sensitive to the thickness of the sample.
For instance, a sample with two layers of graphene
displays a different effect again – meaning that the
anomalous integer QHE can be used to distinguish
between single-layer graphene and multilayer samples.
Unlike an ordinary metal,
in which any impurities in the crystal scatter electrons
and so lead to energy loss, the electrical resistance in
graphene is independent of the number of impurities.
This means that electrons can travel for many microns
without colliding with any impurities, making graphene
a promising material for a potential high-speed electronic
switching device called a “ballistic transistor”.

? Graphene is a one-atom-thick sheet of carbon that was isolated for the first time in
2004 – a feat long thought to be impossible
? Graphene’s 2D nature and honeycomb atomic structure cause electrons moving in
the material to behave as if they have no mass
? Electrons in graphene move at an effective speed of light 300 times less than the
speed of light in a vacuum, allowing relativistic effects to be observed without
using particle accelerators
? A key experimental signature of graphene is the way it modifies the quantum Hall
effect seen in metals and semiconductors
? The electrons in graphene can travel large distances without being scattered,
making it a promising material for very fast electronic components

Therefore the effective index of refraction in graphene is 300, which should increase its bending of spacetime by a factor of 300^4 ~ 10^10 - this may be detectable in the lab, though it would still be a tiny effect.

Massless electrons
Graphene’s unique properties arise from the collective behaviour of electrons. That in itself is nothing new: as summarized in Philip Anderson’s famous dictum “more is different”, we know that when a large number of particles interact strongly with each other, unexpected collective motions can emerge. In the case of graphene, however, the interaction between electrons and the honeycomb lattice causes the electrons to behave as if they have absolutely no mass (see box on page 35). Because of this, the electrons in graphene are governed by the Dirac equation – the quantum-mechanical description of electrons moving relativistically – and are therefore called Dirac fermions.

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