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 forming 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 rock-salt 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 nano-geometry leads to rich band structures including, in the conduction band, Dirac cones at two distinct energies and non-trivial 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 π − π ⋆ 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.

Tight-binding theory of spin-orbit coupling in graphynes

“…On the other hand, this created a lot of activity towards the tailoring of artificial structures exhibiting Dirac cones and strong SOC. Some of the so far proposed systems include self-assembled honeycomb arrays of CdSe and PbSe semiconducting nanocrystals [3], patterned quantum dots [4], and molecular graphene [5]. Yet another interesting class of Dirac materials in this respect consists of graphynes.…”

Orbital Edge States in a Photonic Honeycomb Lattice

“…Edge states in MoS 2 flakes have been observed [24], and recent works aim at quantifying their impact in the transport properties [25]. Edge states in orbital modes have also been studied theoretically in connection to d-wave superconductivity [11,26] and spin-orbit coupling in superlattices of nanocrystals [27], systems very hard to realize experimentally with tuneable parameters. A photonic simulator of orbital bands, would open the door to the study of the microscopic properties of orbital edge states [28] and the connection to the topological properties of orbital bulk bands.…”

Spin-Orbit Coupling and the Optical Spin Hall Effect in Photonic Graphene

“…In graphene, the situation is even worse, since the spin-orbit coupling is extremely weak. Deposition of adatoms has been proposed to increase the spinorbit coupling [10], and it allowed the recent observation of the SHE [11], but associated with a very short spin relaxation length, of the order of 1 µm.On the other hand, artificial honeycomb lattices for atomic Bose Einstein Condensates (BEC) [12] and photons [13][14][15][16][17] have been realized. These systems are gaining a lot of attention due to the large possible control over the system parameters, up to complete Hamiltonian engineering [18,19].…”

“…On the other hand, artificial honeycomb lattices for atomic Bose Einstein Condensates (BEC) [12] and photons [13][14][15][16][17] have been realized. These systems are gaining a lot of attention due to the large possible control over the system parameters, up to complete Hamiltonian engineering [18,19].…”