Topical Review: Electronic and optical properties ofKekul´e and other short wavelength spatialmodulated textures of graphene.

Abstract

A review of the electronic and optical properties of Kekul'e and other short wavelength modulations textures on graphene is presented. Starting from the experimental realization of such textures, the review discuss the electronic and optical properties in terms of several theoretical models like the tight-binding Hamiltonian and effective low energy models based on the Dirac equation. Other surveyed subjects are, strain effects, valley engineering, Keul'e bilayers, zitterbewegung, Kekul'e interfaces, valley birefringence and the skew valley scattering. Specific signatures in the optical and electronic conductivities of Kekule textures are next discussed using several approaches like linear response theory, the random phase approximation and Floquet theory. Plasmons are also presented by considering the dielectric function. Finally, a discussion is presented on how Kekulé textures are related with highly correlated phases, including its importance in magic angle twisted bilayer graphene (MATBG) superconductivity and related quantum phases.