Electronic structure of periodic curved surfaces -- continuous surface versus graphitic sponge

Details Electronic structure of periodic curved surfaces -- continuous surface versus graphitic sponge Electronic structure of periodic curved surfaces -- continuous surface versus graphitic sponge

2003-06-30

arxiv.org/abs/cond-mat/0306729v2

Physics

Condensed Matter

Materials Science

4 pages

Scientific paper

10.1016/j.physe.2003.12.102

We investigate the band structure of electrons bound on periodic curved surfaces. We have formulated Schr\"{o}dinger's equation with the Weierstrass representation when the surface is minimal, which is numerically solved. Bands and the Bloch wavefunctions are basically determined by the way in which the ``pipes'' are connected into a network, where the Bonnet(conformal)-transformed surfaces have related electronic strucutres. We then examine, as a realisation of periodic surfaces, the tight-binding model for atomic networks (``sponges''), where the low-energy spectrum coincides with those for continuous curved surfaces.

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