Two-dimensional weak topological insulator with gapless edge states in RhBi2 monolayer

Topological insulators (TIs) as the focus of recent interests have reshaped our understanding of physics and materials, however, the two-dimensional (2D) weak TIs (WTIs) with gapless edge states have not been reported so far. Here we put forward that, in contrast to previously reported TIs, WTIs can emerge in two dimensions with band inversions at generic $k$ points, rather than the high-symmetry momenta. In particular, as a probable candidate for the experimental realization of 2D WTIs, we propose the stable ${\mathrm{RhBi}}_{2}$ monolayer with supporting evidence based on first-principles calculations. The weak topological nature is explicitly confirmed via the nonzero topological invariant $({\ensuremath{\nu}}_{0};{\ensuremath{\nu}}_{1}{\ensuremath{\nu}}_{2})=(0;01)$ and two pairs of gapless edge states along the (01) direction. Moreover, the robustness of the 2D WTIs is further confirmed by strain engineering. Our results uncover a novel nontrivial state that will provide a wonderful platform to investigate the topological phases in two dimensions.