Magnetic field Characterization of edge currents in quantum spin Hall insulators

Quantum spin Hall (QSH) insulators are materials with nontrivial topological properties, characterized by helical edge currents. In 2D strips, the application of a bias voltage along the edge generates a magnetization that can be measured using quantum sensors and magnetometry techniques. In this work, we calculate the magnetic field in the vicinity of the edge and explore the potential role of nitrogen-vacancy (NV) centers in diamond as local probes for the characterization of QSH edge states in topological insulators. We characterize the magnetic field near the edges produced by both electron currents and spin accumulation at the edge. We focus on identifying the position from the edge at which the effects of spin accumulation become detectable. We observe that a larger gap between the conduction and valence bands, along with a lower Fermi velocity, results in a stronger magnetic field, with the detectable spin accumulation being more concentrated near the edge. Conversely, a smaller gap results in a slight reduction in the magnetic field magnitude, but the field associated with spin accumulation becomes detectable further from the edge. This work provides insights that could be useful for the characterization of topological materials and the development of novel electro-optical devices.