Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry

Abstract

We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rocksalt Pb chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb nanogeometry leads to rich band structures, including, in the conduction band, Dirac cones at two distinct energies and nontrivial flat bands and, in the valence band, topological edge states. These edge states are present in several electronic gaps opened in the valence band by the spin-orbit coupling and the quantum confinement in the honeycomb geometry. The lowest Dirac conduction band has S-orbital character and is equivalent to the pi-pi* band of graphene but with renormalized couplings. The conduction bands higher in energy have no counterpart in graphene; they combine a Dirac cone and flat bands because of their P-orbital character. We show that the width of the Dirac bands varies between tens and hundreds of meV. These systems emerge as remarkable platforms for studying complex electronic phases starting from conventional semiconductors. Recent advancements in colloidal chemistry indicate that these materials can be synthesized from semiconductor nanocrystals.

12 pages, 12 figures

References in corpus (10)

• The electronic properties of graphene
• Topological Insulators with Inversion Symmetry
• Nearly-flat bands with nontrivial topology
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
• Engineering artificial graphene in a two-dimensional electron gas
• Influence of trigonal warping on interference effects in bilayer graphene
• Making Massless Dirac Fermions from Patterned Two-Dimensional Electron Gases
• Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
• Delocalized-localized transition in a semiconductor two-dimensional honeycomb lattice

Cited by in corpus (7)

• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Spin-orbit coupling and optical spin Hall effect in photonic graphene
• Scalable Tight-Binding Model for Graphene
• Tight-binding theory of spin-orbit coupling in graphynes
• High-Chern-number bands and tunable Dirac cones in $\beta$-graphyne
• Dynamical competition between Quantum Hall and Quantum Spin Hall effects
• Density-functional investigation of molecular graphene: CO on Cu(111)