Electronic and optical properties of strained graphene and other strained 2D materials: a review.

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Low-energy theory for strained graphene: an approach up to second-order in the strain tensor.

An analytical study of low-energy electronic excited states in uniformly strained graphene is carried out up to second-order in the strain tensor. We report a new effective Dirac Hamiltonian with an anisotropic Fermi velocity tensor, which reveals the graphene trigonal symmetry being absent in first-order low-energy theories. In particular, we demonstrate the dependence of the Dirac-cone elliptical deformation on the stretching direction with respect to graphene lattice orientation. We further analytically calculate the optical conductivity tensor of strained graphene and its transmittance for a linearly polarized light with normal incidence. Finally, the obtained analytical expression of the Dirac point shift allows a better determination and understanding of pseudomagnetic fields induced by nonuniform strains.