Low-dimensional Dirac systems offer a versatile platform for quantum-geometric non-linear transport. Hexagonal warping in topological insulator (TI) surface states generates rich momentum-space geometric textures. However, mirror and time-reversal symmetries strictly constrain both the Berry curvature and quantum metric dipoles to zero. Here, we show that proximity-coupling a hexagonally warped TI to a d-wave altermagnet lifts spatial mirror symmetry via the interplay of C_{3v} warping and d-wave spin-splitting. This symmetry breaking enables finite Berry curvature dipole components, which, however, remain heavily suppressed near charge neutrality, establishing the intrinsic quantum metric dipole as the sole driver of the non-linear Hall response. This scattering-independent response vanishes at μ= 0 and exhibits odd parity under chemical potential inversion. Importantly, rotating the altermagnetic orientation angle φcontinuously tunes quantum metric dipole and induces a sign reversal, peaking near φ=0 and vanishing at φ= π/4. Our findings highlight TI-altermagnet interfaces as ideal candidates for gate- and orientation-tunable quantum metric spintronics.
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
′-WTe
2 and 1T
′-ReS
2---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-WTe
2 and TaIrTe
4 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.
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 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.
The photogalvanic effect (PGE), a fundamental nonlinear optical phenomenon in non-centrosymmetric materials, generates direct photocurrent under polarized light. Using quantum kinetic theory within the relaxation-time approximation, we theoretically investigate the PGE as a probe of quantum geometry in anisotropic type-I and type-II semi-Dirac (SD) systems, characterized by distinct electronic structures. We systematically analyse various microscopic contributions to the PGE conductivity, including injection, shift, resonance, higher-order pole, and anomalous terms, and emphasize their connections to different quantum geometric quantities, namely, Berry curvature, quantum metric, and metric connection. By studying the frequency and chemical-potential dependence of the PGE conductivity in SD systems, we find that the optical conductivities in the type-II case are significantly enhanced relative to those in type-I. For the circular PGE (CPGE), Berry-curvature-driven contributions remain qualitatively similar in both phases, whereas the linear PGE (LPGE) displays clear qualitative differences. In particular, the
xxx component of the shift conductivity in the type-II phase reverses sign upon tuning the perturbation parameter
δ, providing a direct signature of the Lifshitz transition. In contrast, other components remain sign-invariant, as in type-I SD systems. These combined CPGE and LPGE signatures provide an unambiguous distinction between the two SD phases. The predicted effects, realizable in TiO
2/VO
2 heterostructures, establish PGE as a sensitive probe of quantum geometry with potential applications in polarization-selective photodetection, optical rectification, and next-generation optoelectronic devices.