Electronic structure of helicoidal graphene: massless Dirac particles on a curved surface with a screw symmetry

TL;DR

This paper investigates the behavior of massless Dirac particles on a helicoid surface, revealing their scattering properties and absence of bound states, with implications for helical graphene's electronic structure.

Contribution

It derives the Dirac equation on a helicoid using zweibein and analyzes scattering and bound states, extending understanding of Dirac particles on curved, screw-symmetric surfaces.

Findings

Massless Dirac electrons have no bound states on the helicoid.

Scattering probabilities and phase shifts are computed numerically.

Local density of states shows unique features around the helicoid axis.

Abstract

Massless Dirac particles on the helicoid are theoretically investigated. With its possible application being helical graphene, we explore how the peculiarities of Dirac particles appear on the curved, screw-symmetric surface. The zweibein is used to derive the massless Dirac equation on the helicoid, as well as general curved surfaces. Bound states of massless Dirac electrons are shown to be absent on the helicoid, and then the scattering probabilities and the phase shifts on the surface are obtained from numerically calculated wave functions. We find the local density of states and the phase shifts idiosyncratic especially around the axis of the helicoid. Bound states of massive Dirac electrons on the surface are also shown to be absent as an extension of the above result on massless Dirac electrons.