Effect of renormalization and non-Hermiticity on nonlinear response in strongly-correlated electron systems

Nonlinear responses in condensed matter are intensively studied because they provide rich information about the materials [1] and hold the possibility of being applied in diodes or high-frequency optical devices [2]. 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 talk, we first give an analytical derivation of nonlinear responses using Green's function methods at finite temperature, which is useful to include the correlation effects. Then, we demonstrate two results [3]: First, the relaxation time approximation, which is commonly used to calculate the nonlinear responses, leads to severe limitations and gives incorrect results especially about nonlinear optical responses. Second, correlation effects, such as the renormalization of the band structure and different lifetimes in orbitals or sublattices, can significantly enhance nonlinear responses and even change the sign of the nonlinear conductivity. These effects can be often seen in $d$ or $f$-electron materials. Moreover, we calculated nonlinear conductivity in concrete model about Ce$_3$Bi$_4$Pd$_3$, which is a candidate material for Weyl-Kondo semimetal [4] and has the giant nonlinear responses [5], and show the giant nonlinear conductivity in Ce$_3$Bi$_4$Pd$_3$ can be explained by the strong renormalization effect [6].

[1] J. Orenstein, {\it et al}, Annual Review of Condensed Matter Physics, {\bf 12}, 247-272(2021).
[2] H. Isobe, S. Xu, and L. Fu, Science Advances, {\bf 6}, 13eaay2497(2020).
[3] Y. Michishita, and R. Peters, Physical Review B, {\bf 103}, 195133(2021).
[4] S. Dzsaber, {\it et al}, Physical Review Letters, {\bf 118}, 246601(2017).
[5] S. Dzsaber, {\it et al}, Proceedings od the National Academy of Sciences, {\bf 118}, e2013386118(2021).
[6] A. Kofuji, Y. Michishita, and R. Peters, arXiv:2103.03522(2021).