  Two-dimensional transition metal dichalcogenides (TMDs) of Mo and W in their
1T' crystalline phase host the quantum spin Hall (QSH) insulator phase. We
address the electronic properties of the QSH edge states by means of
first-principles calculations performed on realistic models of edge
terminations of different stoichiometries. The QSH edge states show a tendency
to have complex band dispersions and coexist with topologically trivial edge
states. We nevertheless identify two stable edge terminations that allow
isolating a pair of helical edge states within the band gap of TMDs, with
monolayer 1T'-WSe2 being the most promising material. We also characterize the
finite-size effects in the electronic structure of 1T'-WSe2 nanoribbons. Our
results provide a guidance to the experimental studies and possible practical
applications of QSH edge states in monolayer 1T'-TMDs.
