Spin Hall conductivity in Bi_1-xSb_x alloy as an experimental test of the bulk-boundary correspondence

Bulk-boundary correspondence is a foundational principle underlying the electronic band structure and physical behavior of topological materials. While it has been rigorously tested in topological systems where the physical properties involve charge currents, whether bulk-boundary correspondence should also hold for non-conserved physical quantities, such as spin currents, remains unclear. In this work, we study charge-to-spin conversion in a canonical topological insulator, Bi_1-xSb_x, to address this fundamentally unresolved question. The spin Hall conductivity (SHC) in epitaxial Bi_1-xSb_x thin films of high structural quality grown by molecular beam epitaxy is probed via spin-torque ferromagnetic resonance measurements. Both trivial and topological band structures from various compositions of Bi_1-xSb_x are verified using angle-resolved photoemission spectroscopy. The deduced effective SHC shows excellent agreement with the values predicted by tight-binding calculations for the intrinsic SHC of the bulk bands, which points to the generic robustness of bulk-boundary correspondence even for topological systems involving non-conserved spin currents.