▎ 摘　　要

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. Zweibein is used to derive the massless Dirac equation on the helicoid and on general curved surfaces. We show that bound states of massless Dirac electrons on the helicoid are absent, and thus the system is fully characterized by the scattering probabilities and the phase shifts. We obtain these quantities from numerically calculated wave functions. We find the local density of states and the phase shifts behave characteristically 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. A comparison with the nonrelativistic case is also made.