Quantum spin Hall phase in multilayer graphene
arXiv:1503.06736 · doi:10.1103/PhysRevB.91.235451
Abstract
The so called quantum spin Hall phase is a topologically non trivial insulating phase that is predicted to appear in graphene and graphene-like systems. In this work we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four orbital tight-binding model that includes the full atomic spin-orbit coupling and we calculate the topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all the possible stackings, only those with odd number of layers host gapless edge states while those with even number of layers are trivial insulators. For the heterostructures where graphene is encapsulated by trivial insulators, it turns out that the interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.
7 pages, 6 figures
References in corpus (41)
- Van der Waals heterostructures
- Quantum Spin Hall Effect in Graphene
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Topological Insulators with Inversion Symmetry
- Landau level degeneracy and quantum Hall effect in a graphite bilayer
- Germanene: a novel two-dimensional Germanium allotrope akin to Graphene and Silicene
- Substrate-induced bandgap in graphene on hexagonal boron nitride
- Epitaxial Growth of a Silicene Sheet
- Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
- Low-energy effective Hamiltonian involving spin-orbit coupling in Silicene and Two-Dimensional Germanium and Tin
- The electronic properties of bilayer graphene
- Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
- Spin-orbit gap of graphene: First-principles calculations
- Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
- Band-structure topologies of graphene: spin-orbit coupling effects from first principles
- Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
- Spin-Orbit Proximity Effect in Graphene
- Electronic properties of the MoS2-WS2 heterojunction
- Band Structure of ABC-Stacked Graphene Trilayers
- One-dimensional Topological Edge States of Bismuth Bilayers
- Quantum spin Hall effect in three dimensional materials: Lattice computation of Z topological invariants and its application to Bi and Sb
- Two-Dimensional Topological Insulator State and Topological Phase Transition in Bilayer Graphene
- Spontaneously gapped ground state in suspended bilayer graphene
- Electronic structure of multilayer graphene
- Theory of spin-orbit coupling in bilayer graphene
- Proximity effect in graphene-topological insulator heterostructures
- Topologically protected quantum transport in locally exfoliated bismuth at room temperature
- Spin-orbit coupling in a graphene bilayer and in graphite
- Revealing the electronic band structure of trilayer graphene on SiC: An angle-resolved photoemission study
- Band topology and quantum spin Hall effect in bilayer graphene
- Quantum spin Hall states in graphene interacting with WS or WSe
- Quantum Spin Hall and Quantum Anomalous Hall States Realized in Junction Quantum Wells
- Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene
- Topological edge states in single- and multi-layer BiBr
- Spin-orbit coupling and broken spin degeneracy in multilayer graphene
- Anisotropic intrinsic spin relaxation in graphene due to flexural distortions
- Spin orbit in curved graphene ribbons
- Topological insulating phases in mono and bilayer graphene
- Distinct Competing Ordered ν=2 States in Bilayer Graphene
- Intrinsic and substrate induced spin-orbit interaction in chirally stacked trilayer graphene
- Quantum Spin Hall Effect in Graphene Nanoribbons: Effect of Edge Geometry