Nonlinear Optical Response of Spin Density Wave Insulators

TL;DR

This paper investigates the third order nonlinear optical response in spin density wave insulators modeled by the Hubbard model, revealing dimensional dependence and clarifying the role of stress tensor contributions in two-photon absorption.

Contribution

It provides analytical results for nonlinear optical responses in SDW insulators in 1D and 2D, highlighting the stronger response in 2D and the gauge invariance effect on TPA.

Findings

Nonlinear optical response is stronger in 2D than in 1D and 3D.

Stress tensor contribution to TPA peak is nullified when gauge invariance is properly considered.

Analytical expressions for third order response are derived in 1D and 2D.

Abstract

We calculate the third order nonlinear optical response in the Hubbard model within the spin density wave (SDW) mean field ansatz in which the gap is due to onsite Coulomb repulsion. We obtain closed-form analytical results in one dimension (1D) and two dimension (2D), which show that nonlinear optical response in SDW insulators in 2D is stronger than both 3D and 1D. We also calculate the two photon absorption (TPA) arising from the stress tensor term. We show that in the SDW, the contribution from stress tensor term to the low-energy peak corresponding to two photon absorption becomes identically zero if we consider the gauge invariant current properly.