Band structures of P-, D-, and G-surfaces

Abstract

We present a theoretical study on the band structures of the electron constrained to move along triply-periodic minimal surfaces. Three well known surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces, are considered. The six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that the eigenstates for these surfaces are interrelated at a set of special points in the Brillouin zones. The global connectivity of the band structures is, however, different due to the topological differences of the surfaces. A numerical investigation of the band structures as well as a detailed analysis on their symmetry properties is presented. It is shown that the presence of nodal lines are closely related to the symmetry properties. The present study will provide a basis for understanding further the connection between the topology and the band structures.

arXiv comment21 pages, 8 figures, 3 tables, submitted to Phys. Rev. B

References in corpus (3)

• Topologically non-trivial quantum layers
• Electronic structure of periodic curved surfaces -- topological band structure
• Electronic structure of an electron on the gyroid surface, a helical labyrinth

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