Extraordinary Bending Effects in MoS2, Phosphorene, and Graphene Nanoribbons*

The two-dimensional (2D) materials show great potential for flexible electronics and energy applications. They have remarkable mechanical, electronic, thermal and optical properties, which are often coupled to each other. In this talk, we shall present our first principles study on the bending effects in the electronic structure of MoS$_2$, phosphorene, and graphene nanoribbons. We predict that mechanical bending, as a unique attribute of thin 2D materials, can be used to control conductivity and Fermi-level shift. We find that bending can control the charge localization of top valence bands in both MoS$_2$ and phosphorene nanoribbons. The donor-like in-gap edge-states of armchair MoS$_2$ ribbon and their associated Fermi-level pinning can be removed by bending. A bending-controllable new in-gap state and accompanying direct-indirect gap transition are predicted in armchair phosphorene nanoribbon. We demonstrate that such emergent bending effects are realizable in experiment and can be attributed to the highly non-uniform and enormously large local in-plane strains induced by bending. The bending stiffness as wells as the effective thickness of 2D materials are also derived from first principles.