Light-mediated Phase Transitions Advance Quantum Hall Response in Topological Systems

The interplay between magnetism and topology represents a frontier in modern physics, and recent work by Karyn Le Hur from CPHT, CNRS, Institut Polytechnique de Paris, and Andrea Baldanza from Dipartimento di Fisica, Università di Roma La Sapienza, et al., advances understanding of this connection through a novel geometrical approach. The researchers investigate the spin response of a magnetic monopole, revealing its relationship to the quantum Hall effect within topological lattice models, and demonstrate how this behaviour arises from fundamental local invariants. This work establishes a clear link between the monopole’s magnetic susceptibility and topological phases, showing that it remains quantized until a phase transition occurs, and importantly, connects these theoretical findings to real-world materials like the honeycomb Haldane model. By developing a formalism that incorporates circularly polarized light and addresses the spin Hall effect, the team provides new insights into the behaviour of topological systems and their potential applications in advanced materials science.

Topological Materials and Protected Edge States

Research into topological materials focuses on understanding materials with unique electronic properties stemming from their topology, leading to robust edge states and unusual phenomena like quantized conductance. Scientists are investigating how the Berry phase, a geometric property of electron wavefunctions, contributes to these effects and how light can manipulate topological properties, inducing phase transitions and controlling edge states. This work extends to exploring complex topological phases, including fractional topology, and understanding how disorder affects the robustness of edge states. A key area of investigation involves utilizing circularly polarized light to detect topological phase transitions and quantify topological invariants.

By analyzing photo-induced currents and the response of Dirac points, critical points in a material’s electronic structure, scientists can directly link light absorption to underlying topological properties. This technique has been successfully applied to coupled-plane systems, such as graphene combined with the Haldane model, revealing the induction of Z2 topological states and demonstrating alternating topological invariants. Further research establishes a connection between geometrical properties, magnetic moments, and measurable electrical currents, particularly the Hall current. Theoretical models involving magnetic monopoles demonstrate how an applied field influences these monopoles and mediates transitions between quantum states.

Measurements of magnetic susceptibility reveal quantization within the topological phase, serving as a measure of a topological invariant, and demonstrate a direct link between the spin response and the magnetic structure at the poles. This work extends to exploring the relationship between topological lattice models, such as the Haldane model, and the quantum Hall effect. Researchers are formulating correspondences between local topological invariants and physical observables, like responses to circularly polarized light, and investigating how these invariants remain consistent within the topological phase. Ongoing research aims to fully explore practical applications, including utilizing circuit quantum electrodynamics lattices and locally resolved photoluminescence studies.

Topological Transitions Detected with Circularly Polarized Light

Scientists have pioneered a technique for detecting topological phase transitions using circularly polarized light and detailed analysis of photo-induced currents. This method reveals connections between geometrical approaches, magnetic monopoles, and topological lattice models. Researchers quantify topological invariants by examining the response of Dirac points to circularly polarized light, establishing a direct link between light absorption and the underlying topological properties of materials. The study employs precise measurement of photo-induced currents to probe the behavior of electrons at Dirac points, and demonstrates that peak heights in the induced currents remain consistent within the topological phase, providing a robust indicator of the material’s state. This approach extends to coupled-plane systems, revealing the induction of Z2 topological states through proximity effects and demonstrating alternating topological invariants in multi-layered materials.

Topological Phase Transitions and Hall Current Link

Scientists have developed a novel approach to understanding topological quantum phase transitions, establishing a direct link between geometrical properties, magnetic moments, and measurable electrical currents. Theoretical models involving magnetic monopoles demonstrate how an applied field influences these monopoles and mediates transitions between quantum states. Measurements of magnetic susceptibility reveal quantization within the topological phase, serving as a measure of a topological invariant. Crucially, research establishes a correspondence between geometrical response and the behavior of topological charge at the transition, demonstrating that the charge effectively “leaks out” as the transition occurs.

Experiments reveal a direct link between the spin response and the magnetic structure at the poles, clearly indicating the quantum phase transition. Measurements of the transverse pumped current demonstrate that the transported charge is directly proportional to the topological invariant within the topological phase. Researchers have developed a formula to quantify the mean transverse pumped charge, demonstrating that it is directly related to the topological invariant when no external magnetic field is applied. Analysis extending to include applied magnetic fields introduces a parameter representing the effective spin response, confirming its proportionality to both the magnetic field and the topological invariant within the topological phase.

Monopoles, Topology and the Quantum Hall Effect

This work develops a geometrical approach linking magnetic monopoles to topological lattice models, particularly the Haldane model, and explores the associated quantum phase transitions. Researchers establish a connection between local topological invariants and physical observables, such as the quantum Hall response and responses to circularly polarized light, demonstrating how these invariants remain consistent within the topological phase. An effective magnetic moment for the quantum monopole is introduced, allowing for analysis of susceptibility responses to external magnetic fields and application to the topological phase transition in the Haldane honeycomb model. Numerical analysis confirms the efficiency of this geometrical approach in momentum space, revealing a simple method for understanding complex topological phenomena.

Investigations into coupled-plane systems demonstrate an alternating relationship between the quantum anomalous Hall effect and the quantum spin Hall effect. Researchers have formulated a correspondence between a one-half topological invariant at an interface and the Ramanujan infinite alternating series when considering the system in the thermodynamic limit. Ongoing research aims to fully explore practical applications, including utilizing circuit quantum electrodynamics lattices and locally resolved photoluminescence studies.