Extrinsic Spin-Orbit Coupling and Spin Relaxation in Phosphorene

Abstract

An effective Hamiltonian is derived to describe the conduction band of monolayer black phosphorus (phosphorene) in the presence of spin-orbit coupling and external electric field. Envelope function approximation along with symmetry arguments and Lowdin partitioning are utilized to derive extrinsic spin-orbit coupling. The resulting spin splitting appears in fourth order perturbation terms and is shown to be linear in both the magnitude of the external electric field and the strength of the atomic spin-orbit coupling, similar to the Bychkov-Rashba expression but with an in-plane anisotropy. The anisotropy depends on the coupling between conduction band and other bands both close and distant in energy. The spin relaxation of conduction electrons is then calculated within the Dyakonov-Perel mechanism where momentum scattering randomizes the polarization of a spin ensemble. We show how the anisotropic Fermi contour and the anisotropic extrinsic spin splitting contribute to the anisotropy of spin-relaxation time. Scattering centers in the substrate are considered to be charged impurities with screened Coulomb potential.

arXiv comment8 pages, 3 figures

References in corpus (20)

• Electric Field Effect in Atomically Thin Carbon Films
• Black phosphorus field-effect transistors
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Phosphorene: A New 2D Material with High Carrier Mobility
• High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus
• Rediscovering Black Phosphorus: A Unique Anisotropic 2D Material for Optoelectronics and Electronics
• Electronic spin transport and spin precession in single graphene layers at room temperature
• New Perspectives for Rashba Spin-Orbit Coupling
• Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors
• Isolation and characterization of few-layer black phosphorus
• Electric field effect in ultrathin black phosphorus
• Direct Observation of Layer-Dependent Electronic Structure in Phosphorene
• Semiconductor Spintronics
• Giant Spin Relaxation Anisotropy in Zinc-Blende Heterostructures
• Spin Relaxation Anisotropy in Two-Dimensional Semiconductor Systems
• Electrons and holes in phosphorene
• Gate-tunable black phosphorus spin valve with nanosecond spin lifetimes
• Transport and Optical Properties of Single- and Bilayer Black Phosphorus with Defects
• Mobility anisotropy in monolayer black phosphorus due to charged impurities
• Spin-orbit coupling and spin relaxation in phosphorene: Intrinsic versus extrinsic effects

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