  In a typical situation, gapless surface states of a three-dimensional (3D)
weak topological insulator (WTI) appear only on sides, leaving the top and
bottom surfaces gapped. To describe massless Dirac electrons emergent on such
side surfaces of a WTI, a two-dimensional (2D) model consisting of a series of
one-dimensional helical channels is usually employed. Yet, explicit derivation
of such a model from a 3D bulk Hamiltonian has been lacking. Here, we
explicitly derive an effective 2D model for the WTI surface states starting
from a Wilson-Dirac Hamiltonian for the bulk WTI and establish a firm basis to
the hitherto hypothesized 2D model. We show that the resulting 2D model
accurately reproduces the excitation spectrum of surface Dirac electrons
determined by the 3D model. We also show that the 2D model is applicable to a
side surface with atomic steps.
