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

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Electrostatic Quantum Dots in Graphene
The graphene form of carbon, a hexagonal sheet array single atom thick, is a candidate
substrate for quantum dots. However, two fundamental challenges need to be overcome
before graphene can be used to form and operate spin qubits. First, it is difficult to create a
tunable quantum dot in graphene because of the absence of an energy gap in the band
spectrum. Electrons in such low energy gap materials exhibit Klein tunneling, and
complicating efforts to confine particles (33) (34) (35). Second, due to the valley degeneracy
that exists in graphene, (36)(37)(38) it is non-trivial to form two-qubit gates using
Heisenberg exchange coupling for spins in tunnel-coupled dots. Attempts have been made to
solve the first problem, such as to use suitable transverse states in graphene ribbons to
confine electrons (39), to combine single and bilayer regions of graphene (40), or to achieve
confinement by using inhomogeneous magnetic fields. ( 41) The second problem has only
been realized recently, and scientists have created a method to confine the electrons in a
unique valley through suitable transverse states in a ribbon of graphene which appears to
overcome these limitations. (42) The approach as used in GaAs quantum dots ( 43) is not
possible due to Klein tunneling.
Figure 1. Hexagonal structure of graphene.
Several ways are possible to induce a gap in bulk graphene. In general, quantum
confinement can lead to the opening of a gap in ribbons (44) (45) (46). Within the tight­
binding approximation of graphene, armchair boundary conditions can lead to an insulator
and gate-tunable quantum dots (Figure 2).
Another promising direction is to start with bulk grapheme and induce a gap via the
interaction with a substrate. (47)(48)(49) Three quantum dot architectures that allow for
bound states tunable by electrostatic fields are: (i) graphene nanoribbons with armchair­
terminated boundaries, (ii) discs in single-layer graphene, and (iii) discs in bilayer graphene.
Special emphasis is given on the ability to controllably break the valley degeneracy, a
prerequisite for two-qubit spintronic gates (50) (51) in graphene.
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