Quantum Spin Hall Effect in Graphene Nanoribbons: Effect of Edge Geometry

Abstract

There has been tremendous recent progress in realizing topological insulator initiated by the proposal of Kane and Mele for the graphene system. They have suggested that the odd $Z_2$ index for the graphene manifests the spin filtered edge states for the graphene nanoribbons, which lead to the quantum spin Hall effect(QSHE). Here we investigate the role of the spin-orbit interaction both for the zigzag and armchair nanoribbons with special care in the edge geometry. For the pristine zigzag nanoribbons, we have shown that one of the $\sigma$ edge bands located near E=0 lifts up the energy of the spin filtered chiral edge states at the zone boundary by warping the $\pi$-edge bands, and hence the QSHE does not occur. Upon increasing the carrier density above a certain critical value, the spin filtered edge states are formed leading to the QSHE. We suggest that the hydrogen passivation on the edge can recover the original feature of the QSHE. For the armchair nanoribbon, the QSHE is shown to be stable. We have also derived the real space effective hamiltonian, which demonstrates that the on-site energy and the effective spin orbit coupling strength are strongly enhanced near the ribbon edges. We have shown that the steep rise of the confinement potential thus obtained is responsible for the warping of the $\pi$-edge bands.

20 pages, 6 figures

References in corpus (14)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Spin-orbit gap of graphene: First-principles calculations
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Dynamical polarization, screening, and plasmons in gapped graphene
• Charge and spin Hall conductivity in metallic graphene
• Spin orbit in curved graphene ribbons
• Unscreened Coulomb interactions and quantum spin Hall phase in neutral zigzag graphene ribbons
• Intrinsic spin Hall effect in graphene: Numerical calculations in a multi-orbital mode

Cited by in corpus (4)

• Interference of Topologically Protected Edge States in Silicene Nanoribbons
• Influence of electric and magnetic fields and $\sigma$-edge bands on the electronic and optical spectra of graphene nanoribbons
• Quantum spin Hall phase in multilayer graphene
• Fundamental properties of Alkali-intercalated bilayer graphene nanoribbons