  The Kane-Mele model has been modified to achieve versatile topological
phases. Previous work [Phys. Rev. Lett. 120, 156402 (2018)] introduced a
staggered intrinsic spin-orbit coupling effect to generate pseudohelical edge
states, with Rashba spin-orbit coupling facilitating spin flips in alternating
sublattices. Our study demonstrates that, in the absence of Rashba spin-orbit
coupling, the modified Kane-Mele model with staggered intrinsic spin-orbit
coupling evolves into a $Z_{2}$ class topological metal, specifically a
two-dimensional Weyl nodal-line semimetal. In a nanoribbon geometry, we predict
the emergence of antihelical edge states, which support spin-polarized currents
flowing in the same direction along parallel boundaries. Unlike pseudohelical
edge states, antihelical edge states can be viewed as a superposition of two
antichiral edge states related by time-reversal symmetry. However, the spin
Hall conductance from antihelical edge states is not quantized due to the
presence of gapless bulk states. Additionally, we examine the robustness of
helical, pseudohelical, and antihelical edge states in the presence of
nonmagnetic disorders, highlighting the particular fragility of antihelical
edge states. Our findings enhance the understanding of the modified Kane-Mele
model, providing new insights into its topological properties.
