AAWSAP DIRD, Quantum Computing and Utilizing Organic Molecules in Automation Technology, December 2010

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is a light element with atomic number 6. Hence, its atomic spin-orbit interaction is weak as
compared to heavier elements. However, such a statement should be taken with care
because, in the solid state, spin-orbit coupling is oftentimes dominated by bulk inversion or
structure inversion asymmetry. Therefore, crystal structures of light elements can (under
certain circumstances) exhibit rather strong spin-orbit coupling.
Prime examples are carbon nanotubes where theory predicted a substantial spin-orbit
coupling (a few hundred µeV) due to the curvature of the tube (73) (74 )(75) which has been
nicely confirmed in recent transport experiments on carbon nanotube quantum dots (76).
Since the surface of graphene is less curved than that of carbon nanotubes, the spin-orbit
coupling in graphene - due to ripples - should still be rather weak (roughly ten times less
than the spin-orbit coupling due to curvature in carbon nanotubes (77)). (ii) Carbon has two
stable isotopes: 12C and 13C. The natural abundance is 99% 12C and 1 % 13C. Since 12C
has nuclear-spin O and 13C has nuclear-spin 1/2, the electron spin of the qubit can only
interact with 1 % of the nuclei via hyperfine interaction. This ratio can even be further
decreased because it is possible to artificially make 12C-enriched graphene.
Spin Relaxation Due to Spin-orbit Interaction
The spin-orbit coupling arises from the band structure and is enhanced by ripples in the
graphene sheet. The orbital motion is influenced by scattering centers and ripple-induced
gauge fields. Spin relaxation due to Elliot-Yafet and Dyakonov-Perel mechanisms and gauge
fields in combination with spin-orbit coupling are discussed. In intrinsic graphene, the
Dyakonov-Perel mechanism and spin flip due to gauge fields dominate and the spin-flip
relaxation time is inversely proportional to the elastic scattering time. The spin-relaxation
anisotropy depends on an intricate competition between these mechanisms.
As Pauli noted, when an electron is in a quantum state it can simultaneously be partially in
the spin up state and partially in the spin down state. During this phenomenon known as
"superposition states" an electron can exist in a free spin cycle oscillating between the up
and down states. A qubit based on the spin of an electron could have nearly limitless
potential because it is neither strictly on or off. Recently, researchers at Princeton University
discovered how to manipulate a single electron without disrupting any surrounding electrons
(78) . By utilizing an interferometer technique where one or two electrons are trapped in
microscopic corrals that are created by applying voltage to miniscule electrodes, "spin qubits"
were formed. This effort is ground-breaking in that previous research utilized techniques
where the electrons were exposed to microwave radiation.
The previous method was ineffective to manipulate individual spin qubits because the
microwave was incapable of isolating to only a single electron. Whereas commonly used
single-spin rotation mechanisms rely on gigahertz frequency magnetic fields, the coherent
rotations between S and T+ demonstrated here occur on a nanosecond time scale set by the
Zeeman energy and are solely driven with local gate-voltage pulses. As a result, it will be
feasible to scale this quantum control method to a large number of spin qubits operating in
close proximity. In addition, it is possible that the spin-flip mechanism employed here, which
relies on coupling to the nuclear-spin bath, could be harnessed under the appropriate
conditions to create a nuclear-spin memory (79).
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