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.
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.
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.
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.
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.
The nonlinear response of noninteracting (Bloch) electrons is examined within a nonequilibrium formalism on the infinite-dimensional hypercubic lattice. We examine the effects of a spatially uniform, but time-varying electric field (ignoring magnetic-field effects). The electronic Green's functions, Wigner density of states, and time-varying current are all determined and analyzed. We study both constant and pulsed electric fields, focusing on the transient response region and on local properties. These noninteracting Green's functions are an important input into nonequilibrium dynamical mean field theory for the nonlinear response of strongly correlated electrons.
Recent progress in experimental techniques has made it possible to extract detailed information on dynamics of carriers in a correlated electron material from its optical conductivity, [Formula: see text]. This review consists of three parts, addressing the following three aspects of optical response: (1) the role of momentum relaxation; (2) [Formula: see text] scaling of the optical conductivity of a Fermi-liquid metal, and (3) the optical conductivity of non-Fermi-liquid metals. In the first part (section 2), we analyze the interplay between the contributions to the conductivity from normal and umklapp electron-electron scattering. As a concrete example, we consider a two-band metal and show that although its optical conductivity is finite it does not obey the Drude formula. In the second part (sections 3 and 4), we re-visit the Gurzhi formula for the optical scattering rate, [Formula: see text], and show that a factor of [Formula: see text] is the manifestation of the 'first-Matsubara-frequency rule' for boson response, which states that [Formula: see text] must vanish upon analytic continuation to the first boson Matsubara frequency. However, recent experiments show that the coefficient b in the Gurzhi-like form, [Formula: see text], differs significantly from b = 4 in most of the cases. We suggest that the deviations from Gurzhi scaling may be due to the presence of elastic but energy-dependent scattering, which decreases the value of b below 4, with b = 1 corresponding to purely elastic scattering. In the third part (section 5), we consider the optical conductivity of metals near quantum phase transitions to nematic and spin-density-wave states. In the last case, we focus on 'composite' scattering processes, which give rise to a non-Fermi-liquid behavior of the optical conductivity at T = 0: [Formula: see text] at low frequencies and [Formula: see text] at higher frequencies. We also discuss [Formula: see text] scaling of the conductivity and show that [Formula: see text] in the same model scales in a non-Fermi-liquid way, as [Formula: see text].
Abstract Motivated by the recent developments in terahertz spectroscopy using pump-probe setups to study correlated electronic materials, we review the field theoretical formalism to compute finite frequency nonlinear electro-optical responses in centrosymmetric systems starting from basic time dependent perturbation theory. We express the nonlinear current kernel as a sum of several causal response functions. These causal functions cannot be evaluated using perturbative field theory methods, since they are not contour ordered. Consequently, we associate each response function with a corresponding imaginary time ordered current correlation function, since the latter can be factorized using Wick’s theorem. The mapping between the response functions and the correlation functions, suitably analytically continued to real frequencies, is proven exactly. We derive constraints satisfied by the nonlinear current kernel and we prove a generalized f-sum rule for the nonlinear conductivity, all of which are consequences of particle number conservation. The constraints guarantee that the nonlinear static responses are free from spurious divergences. We apply the theory to compute the gauge invariant nonlinear conductivity of a system of noninteracting electrons in the presence of weak disorder. As special cases of this generalized nonlinear response, we discuss its third harmonic and its instantaneous terahertz Kerr signals. The formalism can be used to compute the nonlinear conductivity in symmetry broken phases of electronic systems such as superconductors, density waves and nematic states.