Scaling laws for nonlinear electromagnetic responses of Dirac fermions

TL;DR

This paper develops a theoretical framework describing the giant nonlinear electromagnetic responses of two-dimensional Dirac fermions, such as in graphene and topological insulators, revealing scaling laws based on electromagnetic field strengths and frequency.

Contribution

The authors derive a universal scaling form for nonlinear responses of 2D Dirac fermions to electromagnetic fields, applicable to materials like graphene and topological insulators.

Findings

Derived scaling laws for current and magnetization responses.

Identified characteristic field strengths depending on frequency.

Discussed applications to graphene and topological insulators.

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 $E/E_\omega$ 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.