Recent years have witnessed great interest [1][2][3][4][5][6] in the quantum spin Hall effect (QSHE) which is a new quantum state of matter with nontrivial topological property due to the scientific importance as a novel quantum state and the technological applications in spintronics. Taking account of Si, Ge significant importance as semiconductor material and intense interest in the realization of QSHE for spintronics, here we investigate the spin-orbit opened energy gap and the band topology in recently synthesized silicene using first-principles calculations. We demonstrate that silicene with topologically nontrivial electronic structures can realize QSHE by exploiting adiabatic continuity and direct calculation of the Z 2 topological invariant. We predict that QSHE in silicene can be observed in an experimentally accessible low temperature regime with the spinorbit band gap of 1.55 meV, much higher than that of graphene due to large spin-orbit coupling and the low-buckled structure. Furthermore, we find that the gap will increase to 2.90 meV under certain pressure strain. Finally, we also study germanium with similar low buckled stable structure, and predict that SOC opens a band gap of 23.9 meV, much higher than the liquid nitrogen temperature.Quantum spin Hall effect (QSHE) with time reversal invariance is gapped in the bulk and conducts charge and spin in gapless edge states without dissipation at the sample boundaries. The existence of QSHE was first proposed in a graphene in which the spin-orbit coupling (SOC) opens a band gap at the Dirac point by Kane and Mele 1 . But the subsequent work found the SOC rather weak, which is in fact a second order process for a flat graphene, so the QSHE in a flat graphene can only occur at unrealistically low temperature 7-9 . So far, there is only one proposal that is able to demonstrate QSHE in a real system, which is in two dimensional mercury telluride-cadmium telluride semiconductor quantum wells 3,4 in despite of some theoretic suggestions 5,6 . Nevertheless, both graphene and HgTe quantum wells are not good enough to be compatible with the present silicon-based electronics industry. As the counterpart of graphene 10 for silicon, silicene has been shown that a low buckled two-dimensional hexagonal structure corresponds to a stable structure, and there are also evidences of graphene-like electronic signature in silicene nanoribbons experimentally 11-13 . Therefore, almost every striking exceptional property of graphene could be transferred to this innovative material with the extra advantage of easily being incorporated into the silicon-based microelectronics industry.The structure of silicene is shown in Fig. 1. We obtain the low-buckled geometry of minimum energy and stability with lattice constant a = 3.86Å and nearest neighbor Si-Si distance d = 2.28Å through structural optimization and calculations of phonon spectrum. The results agree with the previous work 14 . Compared with graphene, the larger Si-Si interatomic distance weakens the π−π overlaps, so it ca...

Starting from the symmetry aspects and tight-binding method in combination with first-principles calculation, we systematically derive the low-energy effective Hamiltonian involving spin-orbit coupling (SOC) for silicene, which is very general because this Hamiltonian applies to not only the silicene itself but also the low-buckled counterparts of graphene for other group IVA elements Ge and Sn, as well as graphene when the structure returns to the planar geometry. The effective Hamitonian is the analogue to the first graphene quantum spin Hall effect (QSHE) Hamiltonian. Similar to graphene model, the effective SOC in low-buckled geometry opens a gap at Dirac points and establishes QSHE. The effective SOC actually contains the first order in the atomic intrinsic SOC strength ξ0, while such leading order contribution of SOC vanishes in planar structure. Therefore, silicene as well as low-buckled counterparts of graphene for other group IVA elements Ge and Sn has much larger gap opened by effective SOC at Dirac points than graphene due to low-buckled geometry and larger atomic intrinsic SOC strength. Further, the more buckled is the structure, the greater is the gap. Therefore, 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 Dirac point K, while it has nonzero value with k deviation from the K point. Therefore, the QSHE in silicene is robust against to the intrinsic Rashba SOC.

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 graphene's 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.