抄録
We introduce the topological aspects of Dirac electrons in graphene, and relation between topology and Hall effect is briefly overviewed for the models introduced by Haldane and by Kane-Mele. We then describe recent proposals for how to control the topological Hall effect by lasers applied to graphene. Namely, nonlinear optical properties of Dirac electrons are discussed where one can generate a dynamical mass at the Dirac point, which is predicted to induce a “photovoltaic Hall effect”. This effect can be measured by electric transport or nonlinear optical methods.