Topological states in multi-orbital HgTe honeycomb lattices

Abstract

Research on graphene has revealed remarkable phenomena arising in the honeycomb lattice. However, the quantum spin Hall effect predicted at the K point could not be observed in graphene and other honeycomb structures of light elements due to an insufficiently strong spin–orbit coupling. Here we show theoretically that 2D honeycomb lattices of HgTe can combine the effects of the honeycomb geometry and strong spin–orbit coupling. The conduction bands, experimentally accessible via doping, can be described by a tight-binding lattice model as in graphene, but including multi-orbital degrees of freedom and spin–orbit coupling. This results in very large topological gaps (up to 35 meV) and a flattened band detached from the others. Owing to this flat band and the sizable Coulomb interaction, honeycomb structures of HgTe constitute a promising platform for the observation of a fractional Chern insulator or a fractional quantum spin Hall phase.

Photonic versus electronic quantum anomalous Hall effect

“…In the large Rashba SOC limit, this description was found to converge towards an extended Haldane model [14]. Another field, which has considerably grown these last years, is the emulation of such topological insulators with different types of particles, such as fermions (either charged, as electrons in nanocrystals [17,18], or neutral, such as fermionic atoms in optical lattices [19,20]) and bosons (atoms, photons, or mixed light-matter quasiparticles) [21][22][23][24][25][26][27][28][29]. The main advantage of artificial analogs is the possibility to tune the parameters [30], to obtain inaccessible regimes, and to measure quantities out of reach in the original systems.…”

Self-Assembly of Cubes into 2D Hexagonal and Honeycomb Lattices by Hexapolar Capillary Interactions

“…These interactions can be tuned by varying, e.g., the particle shape and chemistry [10,[19][20][21], or the curvature of the fluidfluid interface [22][23][24]. Very recent experiments [25][26][27] have shown that adsorbed nanocubes with truncated corners can assemble into graphenelike honeycomb and hexagonal lattices. The origin of these structures is unknown, although ligand adsorption and van der Waals forces between specific facets of the truncated cubes have been suggested [25].…”

Robustness of states at the interface between topological insulators of opposite spin Chern number

“…This model describes the p sector of systems in which the sp hybridization is weak, i.e., when the s-p coupling is small compared to the difference between p and s on-site energies. This is found for example in honeycomb lattices of semiconductor nanocrystals [35,36] or in 2D organometallic frameworks [37].…”

“…The Hamiltonian is written as [5,36,38] (1) where i, j represent lattice sites, i, j nearest-neighbor sites (connecting vector r ij ), α, β spin (↑, ↓), and b, b orbitals. The first term in eq.…”

“…The last term (∝ γ i,b;j,b ) in the form of a nearestneighbor hopping is the Rashba SOC which appears when the mirror symmetry (z → −z) is broken, for example by a perpendicular electric field or by interaction with a substrate. An interesting specificity of this p-orbital model is its intrinsic SOC encoded as a large on-site (intra-atomic) term whereas, in the Kane-Mele model, the SOC is at the level of much smaller second-nearest-neighbor highorder perturbation terms [36,38]. Another advantage of the p-orbital model is that the on-site terms remain well defined at the two sides of a heterojunction, which is not the case for second-nearest-neighbor terms.…”