Quantum walk transport properties on graphene structures

Abstract

We present numerical studies of quantum walks on \C60 and related graphene structures, to investigate their transport properties. Also known as a \emph{honeycomb lattice}, the lattice formed by carbon atoms in the graphene phase can be rolled up to form nanotubes of various dimensions. Graphene nanotubes have many important applications, some of which rely on their unusual electrical conductivity and related properties. Quantum walks on graphs provide an abstract setting in which to study such transport properties independent of the other chemical and physical properties of a physical substance. They can thus be used to further the understanding of mechanisms behind such properties. We find that nanotube structures are significantly more efficient in transporting a quantum walk than cycles of equivalent size, provided the symmetry of the structure is respected in how they are used. We find faster transport on zig-zag nanotubes compared to armchair nanotubes, which is unexpected given that for the actual materials the armchair nanotube is metallic, while the zig-zag is semiconducting.

arXiv comment12 pages, 21 figures, accepted by Physical Review A, clarification relating to shift operator added after publication

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Cited by in corpus (10)

• The Dirac equation as a quantum walk over the honeycomb and triangular lattices
• Continuous-time quantum walk on spatially correlated noisy lattices
• From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
• Quantum walk transport on carbon nanotube structures
• Continuous-time quantum walks on planar lattices and the role of the magnetic field
• Percolated quantum walks with a general shift operator: From trapping to transport
• A counterintuitive role of geometry in transport by quantum walks
• How to Compute Using Quantum Walks
• Staggered Quantum Walk on Hexagonal Lattices
• Quantum walk on a chimera graph