We systematically investigate nonlinear Ohmic responses in second-harmonic generation and bilinear magnetoelectric effects within the Matsubara Green's function formalism. The optical nonlinear Ohmic conductivity is shown to consist of a nonlinear Drude-like part and an intrinsic term determined by the fully symmetrized normalized quantum metric dipole. Notably, we predict a previously unrecognized intrinsic Ohmic conductivity arising from band geometry in the bilinear magnetoelectric response, which exhibits transverse behavior similar to its optical counterpart. Using a two-dimensional Dirac model, we demonstrate that this geometrically induced nonlinear Ohmic response is observable in materials with high Fermi velocity and narrow band gaps. Our work provides a systematic quantum field-theoretic framework for describing nonlinear Ohmic transport in condensed matter systems.
We systematically investigate nonlinear Ohmic responses in second-harmonic generation and bilinear magnetoelectric effects within the Matsubara Green's function formalism. The optical nonlinear Ohmic conductivity is shown to consist of a nonlinear Drude-like part and an intrinsic term determined by the fully symmetrized normalized quantum metric dipole. Notably, we predict a previously unrecognized intrinsic Ohmic conductivity arising from band geometry in the bilinear magnetoelectric response, which exhibits transverse behavior similar to its optical counterpart. Using a two-dimensional Dirac model, we demonstrate that this geometrically induced nonlinear Ohmic response is observable in materials with high Fermi velocity and narrow band gaps. Our work provides a systematic quantum field-theoretic framework for describing nonlinear Ohmic transport in condensed matter systems.
Nonlinear Hall effects provide a powerful probe of quantum geometry in solids and enable rectification phenomena beyond the constraints of linear response. In this Letter, we predict a \emph{layer nonlinear Hall effect} (LNHE) in stacked bilayer systems composed of nonmagnetic or antiferromagnetic materials with a vanishing linear Hall conductivity. In such systems, the second- or third-order nonlinear Hall responses are intrinsically layer odd: the contributions from the two constituent layers have equal magnitude but opposite sign, resulting in exact cancellation under layer-exchange symmetry. An out-of-plane electric field Ez can break this symmetry, thereby unveiling the hidden response and converting it into a switchable macroscopic nonlinear Hall signal. Using a minimal k⋅p model, we demonstrate that the LNHE can originate from the Berry curvature dipole mechanism. A systematic symmetry analysis of all 80 layer groups further yields a complete classification of the symmetry constraints and stacking configurations that allow for this type of LNHE. Beyond this mechanism, additional symmetry analysis reveals that LNHE may also arise from quantum metric dipole or inversed mass dipole. Remarkably, even in cases where second-order nonlinear Hall responses are symmetry forbidden, a third-order LNHE can still survive in certain stacked bilayer configurations. First-principles calculations on representative bilayers---nonmagnetic 1T′-WTe2 and 1T′-ReS2---explicitly demonstrate electrically reversible second-order LNHE, in full agreement with our symmetry-based predictions. Overall, our results establish LNHE as a universal phenomenon in a wide range of layered quantum materials and provide a robust route toward electrically tunable nonlinear transport.
Nonreciprocal control of thermoelectric responses offers a promising strategy for next-generation thermal-management and energy-conversion. While nonlinear electrical transport has recently emerged as an intrinsic property of low-symmetry quantum materials, their thermoelectric counterparts have not been demonstrated. Here, exploiting harmonic detection with gradient-reversal techniques, we report intrinsic nonlinear thermoelectric responses up to room temperature in the low-symmetry type-II Weyl semimetals Td-WTe2 and TaIrTe4 in the absence of magnetic fields or magnetic materials. We resolve all symmetry-allowed components of the second-order thermoelectric tensor, including the nonlinear Seebeck, nonlinear Nernst, and nonlinear mixed-directional thermoelectric effects and demonstrate that both Berry-curvature-related and scattering-induced contributions govern the different nonlinear thermoelectric responses. Our results show that nonlinear thermoelectricity arises intrinsically from reduced crystal symmetry and that engineering effects related to scattering in these materials provides a versatile platform for exploring higher-order heat-to-charge current conversion beyond the linear response.
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].
We propose a mechanism for the inverse Faraday and the inverse Cotton--Mouton effects arising from quantum geometry, characterized by the quantum metric quadrupole and the weighted quantum metric. Within a semiclassical framework based on the Boltzmann transport theory, we establish a general formalism describing light-induced magnetization in electronic systems as a second-order response to the electric field of light. Using continuum and tight-binding models, we discuss the symmetry constraints on these effects and estimate the magnitudes of the resulting magnetizations. Our results highlight a direct manifestation of quantum-geometric quantities in nonlinear magneto-optical responses and suggest a viable pathway for experimental detection.
Predicting phenomena that mix few-photon quantum optics with strong field nonlinear optics is hindered by the use of separate theoretical formalisms for each regime. We close this gap with a unified effective field theory valid for frequencies lower than the material-dependent cutoff set by the band gap, plasma frequency, or similar scale. The action couples the electromagnetic gauge field to vector polarisation modes. An isotropic potential generates the optical susceptibilities, while a higher-dimension axion-like term captures magnetoelectric effects; quantisation on the Schwinger-Keldysh contour with doubled BRST ghosts preserves gauge symmetry in dissipative media. One-loop renormalisation-group equations reproduce the measured dispersion of the third-order susceptibility from terahertz to near-visible frequencies after matching a single datum per material. Real-time dynamics solved with a matrix-product-operator engine yield good agreement with published results for GaAs polariton cavities, epsilon-near-zero indium-tin-oxide films and superconducting quarton circuits. The current formulation is limited to these 1-D geometries and sub-cut-off frequencies; higher-dimensional or above-cut-off phenomena will require additional degrees of freedom or numerical methods.
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.