Group theoretical and topological analysis of the quantum spin Hall effect in silicene

Abstract

Silicene consists of a monolayer of silicon atoms in a buckled honeycomb structure. It was recently discovered that the symmetry of such a system allows for interesting Rashba spin-orbit effects. A perpendicular electric field is able to couple to the sublattice pseudospin, making it possible to electrically tune and close the band gap. Therefore, external electric fields may generate a topological phase transition from a topological insulator to a normal insulator (or semimetal) and vice versa. The contribution of the present article to the study of silicene is twofold: First, we perform a group theoretical analysis to systematically construct the Hamiltonian in the vicinity of the $K$ points of the Brillouin zone and discover a new, but symmetry allowed term. Subsequently, we identify a tight binding model that corresponds to the group theoretically derived Hamiltonian near the $K$ points. Second, we start from this tight binding model to analyze the topological phase diagram of silicene by an explicit calculation of the $Z_2$ topological invariant of the band structure. To this end, we calculate the $Z_2$ topological invariant of the honeycomb lattice in a manifestly gauge invariant way which allows us to include $S_z$ symmetry breaking terms -- like Rashba spin orbit interaction -- into the topological analysis. Interestingly, we find that the interplay of two Rashba terms can generate a non-trivial quantum spin Hall phase in silicene. This is in sharp contrast to the more extensively studied honeycomb system graphene where Rashba spin orbit interaction is known to compete with the quantum spin Hall effect in a potentially detrimental way.

24 pages, 6 figures

References in corpus (11)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Andreev reflection and Klein tunneling in graphene
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Computing topological invariants without inversion symmetry
• Spin-orbit coupling in hydrogenated graphene
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Quantum spin Hall effect induced by electric field in silicene
• Topological Phase Transition and Electrically Tunable Diamagnetism in Silicene
• Manifestly gauge independent formulations of the Z2 invariants

Cited by in corpus (17)

• k.p theory for two-dimensional transition metal dichalcogenide semiconductors
• Monolayer Topological Insulators: Silicene, Germanene and Stanene
• Model spin-orbit coupling Hamiltonians for graphene systems
• Tunable Berry curvature, valley and spin Hall effect in Bilayer MoS${}_2$
• Spin-orbit coupling in elemental two-dimensional materials
• Magnetic edge anisotropy in graphene-like honeycomb crystals
• Spin-orbit coupling in fluorinated graphene
• Overcoming Boltzmann's Tyranny in a Transistor via the Topological Quantum Field Effect
• Towards Topological Quasi-Freestanding Stanene via Substrate Engineering
• Topological phases and twisting of graphene on a dichalcogenide monolayer
• Proximity-induced topological phases in bilayer graphene
• Dirac Cone Pairs in Silicene Induced by Interface Si-Ag Hybridization: A First Principles Effective Band Study
• Spin splitting and spin Hall conductivity in buckled monolayers of the group 14: First-principles calculations
• Electromagnetic coupling of spins and pseudospins in bilayer graphene
• Electrically controlled crossover between $2\pi$- and $4\pi$-Josephson effects through topologically-confined channels in silicene
• Topological features of hydrogenated graphene
• Electronic and magnetic properties of honeycomb zigzag nanoribbons in the in-plane transverse electric field using Kane-Mele-Hubbard model