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Physical review. B./Physical review. B

Two-particle correlation effects on nonlinear optical responses in the one-dimensional interacting Rice-Mele model

Akira Kofuji, Robert Peters

Published Apr 2, 2024• 5 citations
Publisher

Abstract

Nonlinear responses in crystalline solids are attracting a great deal of attention because of exciting phenomena, such as the bulk photovoltaic effect in noncentrosymmetric crystals and the third-harmonic generation related to Higgs modes in superconductors, and their potential applicability to electronic devices. Recently, nonlinear responses have also been studied in strongly correlated electron systems. Experimental evidence has revealed that correlations play a significant role in nonlinear responses. However, most theoretical calculations only consider excitonic effects or involve numerically demanding approaches, making interpreting the results challenging. In this paper, we adopt another approach, which is based on real-time evolution using the correlation expansion method. We focus in particular on the one-dimensional interacting Rice-Mele model. We analyze the impact of the density-density interaction on the linear and nonlinear conductivities, and we demonstrate that two-particle correlations beyond the mean-field level enhance second-order nonlinear responses, especially the second-harmonic generation, while the linear response is not strongly affected. Furthermore, by decomposing the current into a one-particle contribution and six two-particle contributions, we show that the ``biexciton transition'' term and its nonlinear oscillations are the most dominant two-particle contribution to the nonlinear response. In addition, we also show that the intercell charge-charge correlation is strongly enhanced when the system is driven with the frequency corresponding to the excitonic peak, and it can even exceed the intracell correlation. This implies the possibility of manipulating two-particle correlations with external fields.

DOI
10.1103/physrevb.109.155111

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Nonlinear responses in crystalline solids are attracting a great deal of attention because of exciting phenomena, such as the bulk photovoltaic effect in noncentrosymmetric crystals and the third-harmonic generation related to Higgs modes in superconductors, and their potential applicability to electronic devices. Recently, nonlinear responses have also been studied in strongly correlated electron systems. Experimental evidence has revealed that correlations play a significant role in nonlinear responses. However, most theoretical calculations only consider excitonic effects or involve numerically demanding approaches, making interpreting the results challenging. In this paper, we adopt another approach, which is based on real-time evolution using the correlation expansion method. We focus in particular on the one-dimensional interacting Rice-Mele model. We analyze the impact of the density-density interaction on the linear and nonlinear conductivities, and we demonstrate that two-particle correlations beyond the mean-field level enhance second-order nonlinear responses, especially the second-harmonic generation, while the linear response is not strongly affected. Furthermore, by decomposing the current into a one-particle contribution and six two-particle contributions, we show that the ``biexciton transition'' term and its nonlinear oscillations are the most dominant two-particle contribution to the nonlinear response. In addition, we also show that the intercell charge-charge correlation is strongly enhanced when the system is driven with the frequency corresponding to the excitonic peak, and it can even exceed the intracell correlation. This implies the possibility of manipulating two-particle correlations with external fields.
Nonlinear responses in crystalline solids are attracting a great deal of attention because of exciting phenomena, such as the bulk photovoltaic effect in noncentrosymmetric crystals and the third harmonic generation related to Higgs modes in superconductors, and their potential applicability to electronic devices. Recently, nonlinear responses have also been studied in strongly correlated electron systems. Experimental evidence has revealed that correlations play a significant role in nonlinear responses. However, most theoretical calculations only consider excitonic effects or involve numerically demanding approaches, making interpreting the results challenging. In this paper, we adopt another approach, which is based on real-time evolution using the correlation expansion method. Particularly, we focus on the 1d interacting Rice-Mele model. We analyze the impact of the density-density interaction on the linear and nonlinear conductivities and demonstrate that two-particle correlations beyond the mean-field level enhance second-order nonlinear responses, especially the second harmonic generation, while the linear response is not strongly affected. Furthermore, by decomposing the current into a one-particle contribution and six two-particle contributions, we show that the ``biexciton transition" term and its nonlinear oscillations is the most dominant two-particle contribution to the nonlinear response. In addition, we also show that the intercell charge-charge correlation is strongly enhanced when the system is driven with the frequency corresponding to the excitonic peak and can even exceed the intracell correlation. This implies the possibility of manipulating two-particle correlations with external fields.
For both, fundamental physics and novel applications, nonlinear effects are crucial.Powerful laser fields require to treat mobile electrons beyond linear response theory.Phenomena familiar from nonlinear optics are manifest in ultracold Rydberg systems, which have a high potential for advancing the understanding of many-body physics via quantum simulations and promote progress in quantum computation and -information.Various devices and plasmonics systems are based on thin, nearly two dimensional (2D) layers, such as quantum wells, graphene-like structures or transition metal dichalcogenides.We here derive an expression for nonlinear response functions in arbitrary order, and evaluate it explicitly in 2D for the quadratic and the cubic density response of non-interacting fermions.As correlations are of enhanced importance in low dimensions, we next incorporate screened interactions.This results in the generation of 2nd and 3rd harmonics of the collective modes (zero sound and plasmons), damped by multiple particle-hole continua.
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.
The pump-and-probe response of a ZnSe quantum well is investigated. In this particular sample the binding energy far exceeds both the exciton damping and the inhomogeneous broadening. A comparison between experimental data and model calculations shows that with co-circularly polarized beams the nonlinear mean-field contributions dominate those induced by four-particle correlations. In contrast, only the four-particle correlations contribute to the signal in counter-circular configuration. For this configuration, the exciton–biexciton interaction dominates the response for resonant excitation of the exciton. The occurrence of exciton–biexciton transitions leads to a renormalization of the period of coherent oscillations at negative pulse delay.
Summary form only given. The ultrafast nonlinear optical response of semiconductor-microcavities (SMCs) in the nonperturbative regime is attracting growing interest for exploring fundamental light-matter interactions in many-particle quantum systems, as well as for the future implementations of ultrafast photonic devices. In spite of many investigations, the coherent dynamics of excitonic nonlinear-response in the nonperturbative regime has not been fully understood. Open questions are how strong exciton-cavity coupling affects exciton-exciton (X-X) interactions, and how in turn the X-X correlation influences the nonlinear response of SmCs. We investigate these open questions and show that the nonperturbative regime provides an unprecedented tool for investigating four-particle correlations.We start from the equations for the third order exciton polarization and cavity field describing quantum optical effects and coherent nonlinear optics in SMCs, perform the semiclassical factorization and include multiple scattering processes.
Nonlinear responses in condensed matter are intensively studied because they provide rich information about the 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 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 lifetimes in orbitals or sublattices, can significantly enhance nonlinear responses and even change the sign of the nonlinear conductivity.