2D materials are elastic substances that can sustain high strain. While the response of these materials to spatially uniform strain is well studied, the effects of spatially non-uniform strain are understood much less. In this review, we examine the response of two different 2D materials, transition metal dichalcogenides and graphene, under non-uniform strain. First, we analyze pseudo-magnetic fields formed in graphene subjected to highly localized non-uniform strain. Second, we discuss the effect of non-uniform strain on excitons in non-uniformly strained TMDC. We show that while transport or “funneling” of excitons is relatively inefficient, a different process, a strain-related conversion of excitons to trions is dominant. Finally, we discuss the effects of uniform and non-uniform strain in a graphene-based phononic crystal. We find that uniform strain can be used to broadly tune the frequency of the phononic bandgap by more than 350 % and non-uniform strain smears that bandgap.
