Scaling laws for nonlinear electromagnetic responses of Dirac fermions

We theoretically propose that the Dirac fermion in two-dimensions shows the giant nonlinear responses to electromagnetic fields in terahertz region. A scaling form is obtained for the current and magnetization as functions of the normalized electromagnetic fields $E/E_\omega$ and $B/B_\omega$, where the characteristic electric (magnetic) field $E_\omega$ ($B_\omega$) depends on the frequency $\omega$ as $\hbar\omega^2/ev_F$ ($\hbar\omega^2/ev_F^2$), and is typically of the order of 80 V/cm ( 8 mT) in the terahertz region. Applications of the present theory to graphene and surface state of a topological insulator are discussed.