Probing Quantum Geometric Phenomena in Antiferromagnetic Topological Insulators

Abstract

Recent advances in condensed matter physics have revealed that the geometry of electronic wavefunctions—known as quantum geometry—plays a decisive role in shaping diverse electronic, optical and transport phenomena. This dissertation explores how the quantum geometric tensor, composed of its imaginary part (the Berry curvature) and real part (the quantum metric), governs a new generation of Hall effects and nonlinear responses in magnetic topological materials. Using the intrinsic antiferromagnetic topological insulator MnBi2Te4 and its engineered van der Waals heterostructures, we systematically investigate how symmetry, topology, and magnetism intertwine to produce emergent Hall phenomena and functional nonlinear devices. We begin by introducing the theoretical foundation of quantum geometry in Bloch electron systems. The Berry curvature describes the rotational “twisting” of electron wavefunctions in momentum space, underpinning classic phenomena such as the anomalous and quantum Hall effects. In addition to this, the quantum metric describes the local distance between nearby quantum states, reflecting the “shape” of the Hilbert space. Whereas Berry curvature effects have long been associated with Hall responses, the role of the quantum metric has remained largely elusive. In this paper, we explore the effects of Berry curvature and quantum metric, presenting their manifestations including the layer Hall effect, the nonlinear Hall effect, and the quantum anomalous Hall effect in the MnBi2Te4 system. Building on this theoretical framework, the dissertation reports the experimental realization of the anomalous Hall signal in both even- and odd-layer MnBi2Te4 thin flakes. In even-layer samples, we demonstrate the layer Hall effect, where the Berry curvature is locked to opposite layers of the antiferromagnet, allowing electrical manipulation of the topological axion fields (E·B). This axion-controlled magnetoelectric coupling permits switching between degenerate AFM states, representing a novel form of electric control over topological magnetism. In odd-layer MnBi2Te4, we realize the quantum anomalous Hall effect, characterized by a quantized Hall conductance without external magnetic fields, thus completing the full topological phase diagram of this material family. We further investigate its topology transition using an electric field to break the layer degeneracy and detect a topology singularity. We further extend these findings to a broader class of Hall phenomena in MnBi2Te4, which is the experimental realization of the quantum metric dipole nonlinear Hall effect in BP/MnBi2Te4 heterostructures. We successfully measure a second-harmonic transverse voltage that depends on its antiferromagnetic states. By systematically excluding alternative mechanisms—including Berry curvature dipole, skew scattering, and Joule heating—we identify the observed effect as intrinsic to the quantum metric dipole of the antiferromagnetic MnBi2Te4. The result represents the first clear electrical detection of a quantum metric response, opening a new avenue for “quantum geometry engineering” in van der Waals materials. To disentangle overlapping transverse responses in complex materials, we develop a unified experimental protocol to distinguish Hall and non-Hall transverse signals in both linear and nonlinear regimes. By interchanging the current and voltage directions and analyzing the symmetry or antisymmetry of the conductivity tensor (σyx and σyxx), we can uniquely identify the geometric origin of the observed signals. Applying this framework to MnBi2Te4, black phosphorus, and WTe2, we confirm that Hall-type responses arise from Berry curvature or quantum metric dipoles, while non-Hall responses emerge from anisotropic Drude mechanisms. This methodological advance provides a general toolkit for probing quantum geometry in emergent quantum materials, especially in the nonlinear regime. In summary, this thesis bridges the conceptual gap between topology, symmetry, and electronic geometry by revealing how quantum geometry manifests in both linear and nonlinear transport. Through precision experiments, theoretical modeling, and device engineering, it identifies MnBi2Te4 as a model system for exploring geometrydriven electronic responses. The work establishes new directions for topological antiferromagnetic spintronics, quantum geometry–based rectifiers, and future quantum materials where electrical, magnetic, and geometrical degrees of freedom are deeply intertwined. The discovery of the layer Hall effect, quantum metric dipole nonlinear Hall effect and quantum anomalous Hall effect not only deepens our understanding of quantum matter but also heralds a generation of self-powered, geometry-controlled electronic devices.