Topological winding properties of spin edge states in Kane-Mele graphene model

Abstract

We study the spin edge states in the quantum spin-Hall (QSH) effect on a single-atomic layer graphene ribbon system with both intrinsic and Rashba spin-orbit couplings. The Harper equation for solving the energies of the spin edge states is derived. The results show that in the QSH phase, there are always two pairs of gapless spin-filtered edge states in the bulk energy gap, corresponding to two pairs of zero points of the Bloch function on the complex-energy Riemann surface (RS). The topological aspect of the QSH phase can be distinguished by the difference of the winding numbers of the spin edge states with different polarized directions cross the holes of the RS, which is equivalent to the Z2 topological invariance proposed by Kane and Mele [Phys. Rev. Lett. 95, 146802 (2005)].

9 pages, 10 figures

References in corpus (15)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Dissipationless Quantum Spin Current at Room Temperature
• 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
• The Quantum Spin Hall Effect: Theory and Experiment
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number
• Topological edge states and quantum Hall effect in the Haldane model
• Edge states and the integer quantum Hall conductance in spin-chiral ferromagnetic kagome lattice

Cited by in corpus (15)

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• High Chern number quantum anomalous Hall phases in graphene ribbons with Haldane orbital coupling
• Topological superconducting states in monolayer FeSe/SrTiO${}_3$
• Intrinsic spin-orbit interactions in flat and curved graphene nanoribbons
• Edge states in a ferromagnetic honeycomb lattice with armchair boundaries
• Quantum spin Hall effect and spin-charge separation in a kagome lattice
• Quantum Spin Hall Effect in Graphene Nanoribbons: Effect of Edge Geometry
• Analytical study of the edge states in the bosonic Haldane model
• Bifurcation of the Edge-State Width in the Two-Dimensional Topological Insulator
• Graphene-based spin switch device via modulated Rashba field and strain
• Explicit derivation of the chiral and (generic) helical edge states for the Kane-Mele model: Closed expressions for the wave function, dispersion relation, and spin rotation
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Spin-polarized currents generated by magnetic Fe atomic chains