Nonlinear Response in Quantum Geometry Dominated Two-Dimensional Systems

Abstract

Quantum geometry—encompassing Berry curvature, the quantum metric tensor (QMT), and related quantities—has emerged as a fundamental framework for understanding intrinsic response mechanisms in condensed matter systems. This work systematically investigates nonlinear responses governed by quantum geometry in two-dimensional (2D) materials, with a focus on twisted van der Waals structures and topological semimetals. We elucidate the underlying symmetry constraints and propose experimental control strategies, thereby establishing a theoretical foundation for next-generation quantum devices.

We first extend our analysis to the 2D regime of Weyl and Dirac semimetals, introducing a universal quantum geometric mechanism for bilinear magneto-transport j ∼ EB. Utilizing an advanced semiclassical approach, we disentangle the interplay between orbital and spin degrees of freedom, and classify bilinear responses according to their relaxation-time scaling: τ⁰ (intrinsic), τ¹ (T-breaking), and τ² (Drude-like). The intrinsic τ⁰ response is attributed to quantum geometric quantities such as anomalous orbital polarizability(AOP) and anomalous spin polarizability(ASP), while the planar Hall effect requiring band tilting to break spatial symmetries. In contrast, the τ¹ response arises exclusively in magnetic systems, reflecting the coupling between band topology and magnetic order. By comparing Dirac models with linear, quadratic, and cubic dispersions, we show that the chemical potential dependence (e.g., χ ∼ μ^-1 or μ^-2) of bilinear currents serves as a fingerprint for distinguishing topological degeneracies, offering a powerful tool for characterizing low-dimensional topological phases.

Furthermore, using twisted multilayer graphene as a model system, we reveal the pivotal role of QMT in enabling the nonlinear valley Hall effect (NVHE). Continuum modeling demonstrates that moiré flat bands, subjected to strain or interlayer sliding (which reduces symmetry), exhibit pronounced enhancement of the quantum metric near momentum-space band anti-crossings, giving rise to strong second-order nonlinear valley currents. Our theoretical calculations show that asymmetric QMT dipole distributions near these anti-crossings lead to peak NVHE responses around the magic angle, which can surpass conventional linear valley Hall effects. This effect is directly linked to topological band inversions and allows for electrical control of valley polarization via non-local resistance measurements, establishing NVHE as a sensitive probe of topological transitions.

Our findings position the QMT, ASP, AOP as the central order parameter controlling 2D nonlinear responses, which can be precisely tuned through symmetry engineering—via strain, twist, or external fields. This work not only clarifies the dominance of quantum geometry in nonlinear transport, but also proposes experimental protocols based on non-local measurements and scaling analyses. These insights lay the groundwork for the development of high-sensitivity sensors, energy-efficient valleytronic devices, and topological quantum components.

Date of Award	20 Aug 2025
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Xiao LI (Supervisor)