Electronic structure of an electron on the gyroid surface, a helical labyrinth

TL;DR

This paper analyzes the electronic band structure of an electron confined to the gyroid surface, revealing how its helical symmetry influences band sticking and density of states, with implications for understanding electrons on complex minimal surfaces.

Contribution

It applies a formulation for electrons on curved surfaces to the gyroid, highlighting the effects of helical symmetry on band structure and density of states.

Findings

Bands stick together at Brillouin zone boundaries due to helical structure

Breaking symmetries lifts band sticking effects

Symmetries cause peaks in the density of states

Abstract

Previously reported formulation for electrons on curved periodic surfaces is used to analyze the band structure of an electron bound on the gyroid surface (the only triply-periodic minimal surface that has screw axes). We find that an effect of the helical structure appears as the bands multiply sticking together on the Brillouin zone boundaries. We elaborate how the band sticking is lifted when the helical and inversion symmetries of the structure are degraded. We find from this that the symmetries give rise to prominent peaks in the density of states.