Gaps tunable by electrostatic gates in strained graphene

We show that when the pseudomagnetic fields created by long-wavelength deformations are appropriately coupled with a scalar electric potential, a significant energy gap can emerge due to the formation of a Haldane state. Ramifications of this physical effect are examined through the study of various strain geometries commonly seen in experiments, such as strain superlattices and wrinkled suspended graphene. Of particular technological importance, we consider setups where this gap can be tunable through electrostatic gates, allowing for the design of electronic devices not realizable with other materials.