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Random walks and the electronic structure of grapheneNino Bašić,
Patrick W. Fowler,
Barry T. Pickup,
Primož Potočnik, 2026, original scientific article
Abstract: Results from the mathematical literature on random walks reveal a closed-form analytical expression for the ▫$\pi$▫-energy and bond number of graphene in the simplest tight-binding model and its Hartree-Fock Hubbard extension. Closed-form expressions follow for all ▫$\pi$▫ spectral moments of graphene. Bond numbers of carbon and boron nitride (BN) zigzag nanotubes are found as finite sums, with graphene and hexagonal boron nitride sheets as asymptotes.
Keywords: graph theory, random walks, graphene, bond number, tight-binding model, spectral moments, Hubbard model, zigzag nanotubes, hexagonal boron nitride, gamma function
Published in RUP: 10.03.2026; Views: 465; Downloads: 6
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