Edge states in proximitized graphene ribbons and flakes in a perpendicular magnetic field: emergence of lone pseudohelical pairs and pure spin-current states

Abstract

We investigate the formation of edge states in graphene ribbons and flakes with proximity induced valley-Zeeman and Rashba spin-orbit couplings in the presence of a perpendicular magnetic field $B$. Two types of edges states appear in the spin-orbit gap at the Fermi level at zero field: strongly localized pseudohelical (intervalley) states and weakly localized intravalley states. We show that if the magnetic field is stronger than a crossover field $B_c$, which is a few mT for realistic systems such as graphene/WSe${}_2$, only the pseudohelical edge states remain in zigzag graphene ribbons; the intravalley states disappear. The crossover is directly related to the closing and reopening of the bulk gap formed between nonzero Landau levels. Remarkably, in finite flakes the pseudohelical states undergo perfect reflection at the armchair edges if $B>B_c$, forming standing waves at the zigzag edges. These standing waves comprise two counterpropagating pseudohelical states, so while they carry no charge current, they do carry (pure) spin current.

References in corpus (53)

• Quantum Spin Hall Effect in Graphene
• Graphene Spintronics
• Kwant: a software package for quantum transport
• Van der Waals heterostructures for spintronics and opto-spintronics
• Spin-Orbit Proximity Effect in Graphene
• Colloquium: Spintronics in graphene and other two-dimensional materials
• Strong interface-induced spin-orbit coupling in graphene on WS2
• Graphene on transition-metal dichalcogenides: a platform for proximity spin-orbit physics and optospintronics
• Trivial and inverted Dirac bands, and emergence of quantum spin Hall states in graphene on transition-metal dichalcogenides
• Graphene with Structure-Induced Spin-Orbit Coupling: Spin-Polarized States, Spin Zero Modes, and Quantum Hall Effect
• Room temperature spin Hall effect in graphene/MoS${}_2$ van der Waals heterostructures
• Strongly anisotropic spin relaxation in graphene/transition metal dichalcogenide heterostructures at room temperature
• Charge-to-Spin Conversion by the Rashba-Edelstein Effect in 2D van der Waals Heterostructures up to Room Temperature
• Conductance Quantization in Graphene Nanoribbons
• Spin-orbit driven band inversion in bilayer graphene by van der Waals proximity effect
• Large Proximity-Induced Spin Lifetime Anisotropy in Transition Metal Dichalcogenide/Graphene Heterostructures
• Spin transport in graphene/transition metal dichalcogenide heterostructures
• Spin-orbit coupling in hydrogenated graphene
• Model spin-orbit coupling Hamiltonians for graphene systems
• Tunable spin-orbit coupling and symmetry-protected edge states in graphene/WS${}_2$
• Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides
• Quantum Anomalous Hall Effects in Graphene from Proximity-Induced Uniform and Staggered Spin-Orbit and Exchange Coupling
• Induced spin-orbit coupling in twisted graphene-TMDC heterobilayers: twistronics meets spintronics
• Magnetic proximity in a van der Waals heterostructure of magnetic insulator and graphene
• Spin Proximity Effects in Graphene/Topological Insulator Heterostructures
• Scalable Tight-Binding Model for Graphene
• Twist-angle dependent proximity induced spin-orbit coupling in graphene/transition-metal dichalcogenide heterostructures
• Protected pseudohelical edge states in proximity graphene ribbons and flakes
• Electrical control of valley-Zeeman spin-orbit coupling-induced spin precession at room temperature
• WKB analysis of edge states in graphene in a strong magnetic field
• Spin-Orbit Interaction Induced in Graphene by Transition-Metal Dichalcogenides
• Observation of the spin-orbit gap in bilayer graphene by one-dimensional ballistic transport
• Gate tunability of highly efficient spin-to-charge conversion by spin Hall effect in graphene proximitized with WSe${}_2$
• Edge states in graphene-like systems
• Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field
• Theory of electronic and spin-orbit proximity effects in graphene on Cu(111)
• Mass inversion in graphene by proximity to dichalcogenide monolayer
• Survival of the quantum anomalous Hall effect in orbital magnetic fields as a consequence of the parity anomaly
• Counterintuitive gate dependence of weak antilocalization in bilayer graphene/WSe${}_2$ heterostructures
• Graphene-based heterojunction between two topological insulators
• Manipulation of Spin Transport in Graphene/Transition Metal Dichalcogenide Heterobilayers upon Twisting
• Landau levels, edge states, and strained magnetic waveguides in graphene monolayers with enhanced spin-orbit interaction
• Probing topological transitions in HgTe/CdTe quantum wells by magneto-optical measurements
• Quantum Hall Effect in Graphene with Interface-Induced Spin-Orbit Coupling
• Single and bilayer graphene on the topological insulator Bi${}_2$Se${}_3$: Electronic and spin-orbit properties from first principles
• Transport discovery of emerging robust helical surface states in $Z_2=0$ systems
• Landau levels and magnetic oscillations in gapped Dirac materials with intrinsic Rashba interaction
• Chiral Majorana fermions in graphene from proximity-induced superconductivity
• Spin-orbit-enhanced robustness of supercurrent in graphene/WS${}_2$ Josephson junctions
• Topological edge states of a graphene zigzag nanoribbon with spontaneous edge magnetism
• Proximity induced spin-orbit splitting in graphene nanoribbons on transition metal dichalcogenides
• Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite
• Landau levels in spin-orbit coupling proximitized graphene: bulk states

Cited by in corpus (1)

• Two-dimensional Weyl nodal-line semimetal and antihelical edge states in a modified Kane-Mele model