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

TL;DR

This paper theoretically investigates the electronic band structures of triply-periodic minimal surfaces (P, D, G) and explores how their topological differences influence their electronic properties and symmetries.

Contribution

It provides a detailed analysis of the band structures of P, D, and G surfaces, revealing their interrelations and the impact of topology on electronic states.

Findings

Eigenstates are interconnected at special Brillouin zone points.

Topological differences lead to distinct global band connectivity.

Nodal lines are linked to symmetry properties.

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.