Landau quantisation of photonic spin Hall effect in monolayer black phosphorus

Guangyi Jia,Xiaoying Zhou,Geng Li,Yan Zhou,Xianglong Miao

doi:10.1515/nanoph-2019-0424

Guangyi Jia, Xiaoying Zhou + Show 3 more

Open Access

https://doi.org/10.1515/nanoph-2019-0424

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Abstract

Abstract The photonic spin Hall effect (PSHE) is a promising candidate for controlling the spin states of photons and exploiting next-generation photonic devices based on spinoptics. Herein, the influences of a perpendicular magnetic field on the PSHE appearing on the surface of monolayer black phosphorus (BP) are investigated. Results reveal that both the in-plane and transverse spin-dependent shifts are quantised and show an oscillating pattern due to the splitting of Landau levels (LLs) induced by the external magnetic field B. And the oscillation period of spin Hall shifts gradually increases with strengthening B because of the increase of LL spacings. By contrast, for a fixed magnetic field, as the LL spacings become smaller and smaller with increasing the LL index, the oscillation period of spin Hall shifts gradually decreases as the photonic energy increases. Moreover, it is possibly due to the synergistic role of intrinsic anisotropy, high crystallinity, and quantisation-incurred localised decreases in beating-like complex conductivities of the BP film, giant spin Hall shifts, hundreds of times of the incident wavelength, are obtained in both transverse and in-plane directions. These unambiguously confirm the strong impact of the external magnetic field on the PSHE and shed important insights into understanding the rich magneto-optical transport properties in anisotropic two-dimensional atomic crystals.

Highlights

The photonic spin Hall effect (PSHE) is a photonic counterpart of the spin Hall effect in electronic systems, in which the electron spin and electric potential gradient are replaced by the optical helicity of incident photons and the refractive index gradient, respectively [1,2,3,4]
Spurred by advances in the PSHE and novel 2D materials, in this work, we theoretically investigate the PSHE in a monolayer of black phosphorus (BP) which is exposed to an external magnetic field and is illuminated by an excitation source in the direct bandgap energies of monolayer BP
The Landau quantisation of PSHE appearing on the surface of monolayer BP has been studied in detail

Summary

Introduction

The photonic spin Hall effect (PSHE) is a photonic counterpart of the spin Hall effect in electronic systems, in which the electron spin and electric potential gradient are replaced by the optical helicity of incident photons and the refractive index gradient, respectively [1,2,3,4]. The latest research on graphene shows that 2D electron gases being exposed to a magnetic field may result in an exceptionally high infrared magnetooptical transitions between the Landau levels (LLs) [16] It is accompanied by a colossal amendment of magnetooptical conductivity which is a key parameter to tailor the PSHE occurring at a planar dielectric interface [16, 17]. Even though the effects of the magnetic field on the PSHE along with quantised spin Hall shifts have been recently reported in graphene [17,18,19,20], they are either confined to the terahertz region (even made excessive approximations in theoretical model) [17,18,19] or only considering the graphene-like planar microcavity [20]. Giant spin Hall shifts as well as the possible enhancement mechanism are presented

Model and theory

Results and discussion

Conclusions