Quantum Spin Hall Effect and Topological Insulators

Topological insulators (TIs), which exist in two and three dimensions, represent a new electronic phase stemming from the topological character of the bulk wave functions of certain materials and compounds. To overcome the limitations imposed by the low spin-orbit interaction in graphene, the quantum spin Hall (QSH) phase was early on proposed by Bernevig and Zhang in intricate strain architecture promoted by strong spin-orbit coupling. Three-dimensional TIs have several attributes in common with graphene, such as their low-energy electronic properties dominated by massless Dirac Fermion excitations, where the energy dispersion relations are described by a Dirac cone. Several possibilities for generating photo-induced bandgaps in graphene and the formation of states akin to those of TIs have been proposed theoretically, opening another field of research in which light illumination becomes an intriguing enabling tool to switch on and off the formation of the topological state.