Cheng-Cheng Liu

Quantum spin Hall effect in silicene and two-dimensional germanium.

We investigate the spin-orbit opened energy gap and the band topology in recently synthesized silicene as well as two-dimensional low-buckled honeycomb structures of germanium using first-principles calculations. We demonstrate that silicene with topologically nontrivial electronic structures can realize the quantum spin Hall effect (QSHE) by exploiting adiabatic continuity and the direct calculation of the Z(2) topological invariant. We predict that the QSHE can be observed in an experimentally accessible low temperature regime in silicene with the spin-orbit band gap of 1.55 meV, much higher than that of graphene. Furthermore, we find that the gap will increase to 2.9 meV under certain pressure strain. Finally, we also study germanium with a similar low-buckled stable structure, and predict that spin-orbit coupling opens a band gap of 23.9 meV, much higher than the liquid nitrogen temperature.

Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin

Starting from symmetry considerations and the tight-binding method in combination with first-principles calculation, we systematically derive the low-energy effective Hamiltonian involving spin-orbit coupling (SOC) for silicene. This Hamiltonian is very general because it applies not only to silicene itself but also to the low-buckled counterparts of graphene for the other group-IVA elements Ge and Sn, as well as to graphene when the structure returns to the planar geometry. The effective Hamitonian is the analog to the graphene quantum spin Hall effect (QSHE) Hamiltonian. As in the graphene model, the effective SOC in low-buckled geometry opens a gap at the Dirac points and establishes the QSHE. The effective SOC actually contains the first order in the atomic intrinsic SOC strength xi(0), while this leading-order contribution of SOC vanishes in the planar structure. Therefore, silicene, as well as the low-buckled counterparts of graphene for the other group-IVA elements Ge and Sn, has a much larger gap opened by the effective SOC at the Dirac points than graphene, due to the low-buckled geometry and larger atomic intrinsic SOC strength. Further, the more buckled is the structure, the greater is the gap. Therefore, the QSHE can be observed in low-buckled Si, Ge, and Sn systems in an experimentally accessible temperature regime. In addition, the Rashba SOC in silicene is intrinsic due to its own low-buckled geometry, which vanishes at the Dirac point K, while it has a nonzero value with deviation of (k) over right arrow from the K point. Therefore, the QSHE in silicene is robust against the intrinsic Rashba SOC.

Evidence for Dirac Fermions in a Honeycomb Lattice Based on Silicon

Silicene, a sheet of silicon atoms in a honeycomb lattice, was proposed to be a new Dirac-type electron system similar to graphene. We performed scanning tunneling microscopy and spectroscopy studies on the atomic and electronic properties of silicene on Ag(111). An unexpected √3 × √3 reconstruction was found, which is explained by an extra-buckling model. Pronounced quasiparticle interferences (QPI) patterns, originating from both the intervalley and intravalley scatter, were observed. From the QPI patterns we derived a linear energy-momentum dispersion and a large Fermi velocity, which prove the existence of Dirac fermions in silicene.

Epitaxial growth of single-domain graphene on hexagonal boron nitride

Hexagonal boron nitride (h-BN) has recently emerged as an excellent substrate for graphene nanodevices, owing to its atomically flat surface and its potential to engineer graphenes electronic structure. Thus far, graphene/h-BN heterostructures have been obtained only through a transfer process, which introduces structural uncertainties due to the random stacking between graphene and h-BN substrate. Here we report the epitaxial growth of single-domain graphene on h-BN by a plasma-assisted deposition method. Large-area graphene single crystals were successfully grown for the first time on h-BN with a fixed stacking orientation. A two-dimensional (2D) superlattice of trigonal moiré pattern was observed on graphene by atomic force microscopy. Extra sets of Dirac points are produced as a result of the trigonal superlattice potential and the quantum Hall effect is observed with the 2D-superlattice-related feature developed in the fan diagram of longitudinal and Hall resistance, and the Dirac fermion physics near the original Dirac point is unperturbed. The macroscopic epitaxial graphene is in principle limited only by the size of the h-BN substrate and our synthesis method is potentially applicable on other flat surfaces. Our growth approach could thus open new ways of graphene band engineering through epitaxy on different substrates.

Valley-polarized quantum anomalous Hall effect in silicene.

We find theoretically a new quantum state of matter-the valley-polarized quantum anomalous Hall state in silicene. In the presence of Rashba spin-orbit coupling and an exchange field, silicene hosts a quantum anomalous Hall state with Chern number C=2. We show that through tuning the Rashba spin-orbit coupling, a topological phase transition results in a valley-polarized quantum anomalous Hall state, i.e., a quantum state that exhibits the electronic properties of both the quantum valley Hall state (valley Chern number Cv=3) and quantum anomalous Hall state with C=-1. This finding provides a platform for designing dissipationless valleytronics in a more robust manner.

Low-energy effective Hamiltonian for giant-gap quantum spin Hall insulators in honeycomb X -hydride/halide ( X = N-Bi ) monolayers

Using the tight-binding method in combination with first-principles calculations, we systematically derive a low-energy effective Hilbert subspace and Hamiltonian with spin-orbit coupling for two-dimensional hydrogenated and halogenated group-V monolayers. These materials are proposed to be giant-gap quantum spin Hall insulators with record huge bulk band gaps opened by the spin-orbit coupling at the Dirac points, e.g., from 0.74 to 1.08 eV in Bi\textit{X} (\textit{X} = H, F, Cl, and Br) monolayers. We find that the low-energy Hilbert subspace mainly consists of

Large-Gap Quantum Spin Hall Insulator in Single Layer Bismuth Monobromide Bi4Br4

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Observation of Dirac Cone Warping and Chirality Effects in Silicene

and

Experimental realization of two-dimensional Dirac nodal line fermions in monolayer Cu 2 Si

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Weak Topological Insulators and Composite Weyl Semimetals: β-Bi4X4 (X=Br, I)

orbitals from the group-V elements, and the giant first-order effective intrinsic spin-orbit coupling is from the on-site spin-orbit interaction. These features are quite distinct from those of group-IV monolayers such as graphene and silicene. There, the relevant orbital is