Imaging the topological sign of a Dirac mass with spin-polarized tunneling

Abstract

A Dirac mass is characterized not only by its magnitude but also by its sign, which influences the Berry curvature, Hall response, and the propagation direction of chiral boundary modes. However, local spectroscopy of magnetic topological surfaces has so far accessed only the gap magnitude $|M|$. Here we show how the topological sign of $M$ can be determined locally. We first establish the sign information that spin-resolved tunneling can access and the reference required to obtain an absolute Hall sign. Although spin--orbital entanglement generally obscures the relation between measured spin and Dirac pseudospin, crystalline rotation symmetry alleviates this ambiguity at the band edge. On a $C_3$ axis, an axial tip couples to a fully spin-polarized state whose tunneling asymmetry directly reveals the sign of the occupied-band Berry curvature, independent of orbital composition. We further show that the zeroth Landau level provides an independent mass-sign measurement with an unpolarized tip, while opposite domains and their chiral domain-wall modes provide self-consistency checks. These results pave the way for imaging the locations where the topological character changes within a material, rather than merely identifying where a spectral gap appears.