Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystals

We study excitonic processes second order in the electric fields in noncentrosymmetric crystals. We derive formulas for shift current and second harmonic generation produced by exciton creation, by using the Floquet formalism combined with the Keldysh Green's function method. It is shown that (i) the steady dc shift current flows by exciton creation without dissociation into free carriers and (ii) second harmonic generation is enhanced at the exciton resonance. The obtained formulas clarify topological aspects of these second order excitonic processes which are described by Berry connections of the relevant valence and conduction bands.

Figure 1

Schematic picture of the Floquet two band model. Bands labeled by ${\psi }_1$ and ${\psi }_2$ denote the valence band with Floquet index $-1$ and the conduction band with Floquet index 0, respectively. Quasienergy for the Floquet band ${\psi }_1$ is smaller than that for ${\psi }_2$. The exciton formation is described by an effective mixing of these two bands in the mean-field approximation of the electron-electron interaction.