Scaling laws for nonlinear electromagnetic responses of Dirac fermions

Abstract

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 $E/E_ω$ and $B/B_ω$, where the characteristic electric (magnetic) field $E_ω$ ($B_ω$) depends on the frequency $ω$ as $\hbarω^2/ev_F$ ($\hbarω^2/ev_F^2$), 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.

9 pages, 3 figures