https://doi.org/10.1140/epjb/s10051-026-01174-7
Research - Condensed Matter
Spin Hall effect in monolayer black phosphorus
Hunan Provincial Key Laboratory of Intelligent Sensors and Advanced Sensor Materials, School of Physics and Electronics, Hunan University of Science and Technology, 411201, Xiangtan, China
a
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Received:
28
January
2026
Accepted:
21
April
2026
Published online:
8
May
2026
Abstract
Monolayer black phosphorus (BP), characterized by its direct band gap, high carrier mobility, and pronounced in-plane anisotropy, offers a versatile platform for next-generation nanoelectronic devices. Despite the symmetry-enforced vanishing Berry curvature due to the coexistence of inversion and time-reversal symmetries, we demonstrate that monolayer BP hosts a spin-resolved Berry curvature that drives the intrinsic spin Hall effect. Using a four-band 
Hamiltonian, we analytically derive the spin-resolved Berry curvature and the orbital magnetic moment. Both quantities peak at the 
point and exhibit significant anisotropy, decaying more rapidly along the 
direction than the 
direction. Furthermore, the spin Hall conductivity displays a plateau within the band gap that remains robust against temperature fluctuations due to BP’s large energy gap. Finally, we identify a finite circular polarization along the direction as a potential experimental signature for detecting this spin-resolved Berry curvature. Our results establish monolayer BP as a promising candidate for spintronics.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
