The Goos–Hänchen-like (GH) shift of electron wavepackets at potential interfaces provides a powerful method for probing the properties of quantum materials. In this work, we theoretically investigate the spin- and valley-resolved GH shift in a monolayer of jacutingaite (Pt2HgSe3), a quantum spin Hall insulator, subjected to both a perpendicular electric field and off-resonant circularly polarized light. Using a low-energy effective Hamiltonian and a scattering formalism, we calculate the lateral displacement of transmitted electron beams across a finite barrier. Our results demonstrate that external fields can induce a nearly perfect spin- and valley-filtering effect and a fundamental electric-optical duality. Unlike simpler Dirac systems, such as graphene, where the GH shift typically exhibits a single resonant structure, the multi-gap Kane–Mele physics of jacutingaite gives rise to a unique multi-resonance hierarchy. Our central finding is revealed in energy–angle phase-space maps of the total GH shift, which exhibit prominent resonance ridges of giant displacement. We demonstrate that the pattern and structure of these contours serve as a distinct macroscopic fingerprint for the material’s underlying topological phases. This establishes the measurement of the GH shift as a sensitive tool for topological metrology, offering a clear experimental pathway for identifying microscopic topological phase transitions through macroscopic transport signatures.
Zafar et al. (Fri,) studied this question.