Mesoscopic spin Hall effect along a potential step in graphene

Abstract

We consider a straight one-dimensional potential step created across a graphene flake. Charge and spin transport through such a potential step are studied in the presence of both intrinsic and extrinsic (Rashba) spin-orbit coupling (SOC). At normal incidence electrons are completely reflected when the Rashba interaction (with strength ${\lambda }_R$) is dominant whereas they are perfectly transmitted if the two types of SOC are exactly balanced. At normal incidence, the transmission probability of the step is thus controlled continuously from 0 to 1 by tuning the ratio of the two types of SOC. Besides the transport of charge in the direction normal to the barrier, we show the existence of a spin transport along the barrier. The magnitude of the spin Hall current is determined by a subtle interplay between the height of the potential step and the position of Fermi energy. It is demonstrated that contributions from inter-band matrix elements and evanescent modes are dominant in spin transport. Moreover, in the case of vanishing extrinsic SOC (${\lambda }_R=0$), each channel carries a conserved spin current, in contrast to the general case of a finite ${\lambda }_R$, in which only integrated spin current is a conserved quantity. Finally, we provide a quasi-classical picture of the charge and spin transport by imaging flow lines over the entire sample and Veselago lensing (negative refraction) in the case of a $p-n$ junction.

14 pages, 11 figures

References in corpus (26)

• Topological Insulators
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Chiral tunneling and the Klein paradox in graphene
• Dissipationless Quantum Spin Current at Room Temperature
• Gate-induced insulating state in bilayer graphene devices
• The quantum spin Hall effect and topological insulators
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Spin-orbit gap of graphene: First-principles calculations
• Nonlocal edge state transport in the quantum spin Hall state
• The Quantum Spin Hall Effect: Theory and Experiment
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Evidence of Klein tunneling in graphene p-n junctions
• Transport measurements across a tunable potential barrier in graphene
• Electronic transport and quantum Hall effect in bipolar graphene p-n-p junction
• Evidence of the role of contacts on the observed electron-hole asymmetry in graphene
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Conductance of p-n-p graphene structures with 'air-bridge' top gates
• Caustics due to Negative Refractive Index in Circular Graphene p-n Junctions
• Contact resistance and shot noise in graphene transistors
• Intrinsic Spin Hall Edges
• Equilibrium spin currents in the Rashba medium
• Dynamics of the (spin-) Hall effect in topological insulators and graphene
• Spin-Hall effect in triplet chiral superconductors and graphene

Cited by in corpus (11)

• Introduction to Dirac materials and topological insulators
• Charge transport in pn and npn junctions of silicene
• Topological carbon materials: a new perspective
• In-plane Topological p-n Junction in the Three-Dimensional Topological Insulator Bi${}_{2-x}$Sb${}_x$Te${}_{3-y}$Se${}_y$
• Spin-dependent thermoelectric transport in HgTe/CdTe quantum wells
• Graphene p-n junctions with nonuniform Rashba spin-orbit coupling
• Theory of tunneling spectroscopy for chiral topological superconductors
• Thermoelectric and thermospin transport in a ballistic junction of graphene
• Transport through quantum spin Hall insulator/metal junctions in graphene ribbons
• Spin Hall effect at interfaces between HgTe/CdTe quantum wells and metals
• Gate-induced carrier density modulation in bulk graphene: Theories and electrostatic simulation using Matlab pdetool