Effects of renormalization and non-Hermiticity on nonlinear responses in strongly-correlated electron systems

TL;DR

This paper analytically investigates how strong electron correlations and non-Hermiticity influence nonlinear optical responses in condensed matter, revealing that correlations can significantly enhance and alter the sign of nonlinear conductivities.

Contribution

It provides an analytical framework for nonlinear responses in strongly correlated systems and discusses the limitations of conventional dissipation models.

Findings

Correlation effects can enhance nonlinear responses.

Renormalization of band structure impacts nonlinear conductivity.

Correlation can change the sign of nonlinear response.

Abstract

Nonlinear responses in condensed matter are intensively studied because they provide rich information about materials and hold the possibility of being applied in diodes or high-frequency optical devices. While nonlinear responses in noninteracting models have been explored widely, the effect of strong correlations on the nonlinear response is still poorly understood, even though it has been suggested that correlations can enhance the nonlinear response. In this work, we first give an analytical derivation of nonlinear responses using the Green's function methods at finite temperature. Then, we discuss the difficulties of considering dissipation using conventional methods, such as the reduced density matrix method. We reveal that the relaxation time approximation leads to severe limitations when considering optical responses. Finally, we demonstrate that correlation effects, such as the renormalization of the band structure and different lifetime in orbitals or sublattices, can significantly enhance nonlinear responses and can even change the sign of the nonlinear conductivity.