Twist-angle dependent proximity induced spin-orbit coupling in graphene/transition-metal dichalcogenide heterostructures

Abstract

We investigate the proximity-induced spin-orbit coupling in heterostructures of twisted graphene and monolayers of transition-metal dichalcogenides (TMDCs) MoS${}_2$, WS${}_2$, MoSe${}_2$, and WSe${}_2$ from first principles. We identify strain, which is necessary to define commensurate supercells, as the key factor affecting the band offsets and thus magnitudes of the proximity couplings. We establish that for biaxially strained graphene the band offsets between the Dirac point and conduction (valence) TMDC bands vary linearly with strain, regardless of the twist angle. This relation allows to identify the apparent zero-strain band offsets and find a compensating transverse electric field correcting for the strain. The resulting corrected band structure is then fitted around the Dirac point to an established spin-orbit Hamiltonian. This procedure yields the dominant, valley-Zeeman and Rashba spin-orbit couplings. The magnitudes of these couplings do not vary much with the twist angle, although the valley-Zeeman coupling vanishes for 30${}^{\circ }$ and Mo-based heterostructures exhibit a maximum of the coupling at around 20${}^{\circ }$. The maximum for W-based stacks is at 0${}^{\circ }$. The Rashba coupling is in general weaker than the valley-Zeeman coupling, except at angles close to 30${}^{\circ }$. We also identify the Rashba phase angle which measures the deviation of the in-plane spin texture from tangential, and find that this angle is very sensitive to the applied transverse electric field. We further discuss the reliability of the supercell approach with respect to atomic relaxation (rippling of graphene), relative lateral shifts of the atomic layers, and transverse electric field.

14 pages, 9 figures, 7 tables

References in corpus (19)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Graphene Spintronics
• Quantum Anomalous Hall Effect in Graphene from Rashba and Exchange Effects
• Van der Waals heterostructures for spintronics and opto-spintronics
• Spin-Orbit Proximity Effect in Graphene
• Twistronics: Manipulating the Electronic Properties of Two-dimensional Layered Structures through their Twist Angle
• 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
• Tunable spin-orbit coupling and symmetry-protected edge states in graphene/WS${}_2$
• Proximity effects in bilayer graphene on monolayer WSe${}_2$: Field-effect spin-valley locking, spin-orbit valve, and spin transistor
• Interlayer interaction in general incommensurate atomic layers
• 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
• Twistronics: A turning point in 2D quantum materials
• Magnetotransport in heterostructures of transition metal dichalcogenides and graphene
• Graphene-WS${}_2$ heterostructures for tunable spin injection and spin transport
• Gate tunability of highly efficient spin-to-charge conversion by spin Hall effect in graphene proximitized with WSe${}_2$
• Spin transport in high-mobility graphene on WS${}_2$ substrate with electric-field tunable proximity spin-orbit interaction
• Electric-field-tunable valley Zeeman effect in bilayer graphene heterostructures: Realization of the spin-orbit valve effect

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• Tunable superconductivity and Möbius Fermi surfaces in an inversion-symmetric twisted van der Waals heterostructure
• Impurity-induced excitations in a topological two-dimensional ferromagnet/superconductor van der Waals moiré heterostructure
• Proximity-enhanced valley Zeeman splitting at the WS${}_2$/graphene interface
• Edge states in proximitized graphene ribbons and flakes in a perpendicular magnetic field: emergence of lone pseudohelical pairs and pure spin-current states
• Charge quenching at defect states in transition metal dichalcogenide-graphene van der Waals heterobilayers
• Electrical and thermal transport in a twisted heterostructure of transition metal dichalcogenide and CrI${}_3$ connected to a superconductor