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We derive a low-energy theory for edge states in transition metaldichalcogenide monolayers for a two-band $\bm{kp}$-Hamiltonian in case ofuncoupled valleys. In the absence of spin-orbit interaction at the edge, thesestates possess a linear dispersion described by a single phenomenologicalparameter characterizing the edge structure. Depending on the sign of theparameter, the edge state spectrum can either cross the band gap or lie outsideof it. In the first case, the presence of edge states leads to resonantenhancement of the second harmonic generation at frequencies about the half ofthe band gap, in agreement with recent experiments. The value of thephenomenological boundary parameter is extracted from the resonance frequencyposition.

Resonant Enhancement of Second Harmonic Generation by Edge States in Transition Metal Dichalcogenide Monolayers