Efficient approach for simulating distorted materials.

The operation principles of nanoscale devices are based upon both electronic and mechanical properties of materials. Because these properties can be coupled, they need to be investigated simultaneously. At this moment, however, the electronic structure calculations with custom-made long-range mechanical distortions are impossible, or expensive at best. Here we present a unified formalism to solve exactly the electronic structures of nanomaterials with versatile distortions. We illustrate the formalism by investigating twisted armchair graphene nanoribbons with the least possible number of atoms. Apart from enabling versatile material distortions, the formalism is capable of reducing computational costs orders of magnitude in various areas of science and engineering.