No Arabic abstract
A generalized tight-binding model, which is based on the subenvelope functions of the different sublattices, is developed to explore the novel magnetic quantization in monolayer gray tin. The effects due to the $sp^{3}$ bonding, the spin-orbital coupling, the magnetic field and the electric field are simultaneously taken into consideration. The unique magneto-electronic properties lie in two groups of low-lying Landau levels, with different orbital components, localization centers, state degeneracy, spin configurations, and magnetic- and electric-field dependences. The first and second groups mainly come from the $5p_{z}$ and ($5p_{x}$,$5p_{y}$) orbitals, respectively. Their Landau-level splittings are, respectively, induced by the electric field and spin-orbital interactions. The intragroup anti-crossings are only revealed in the former. The unique tinene Landau levels are absent in graphene, silicene and germanene.
Monolayer tinene presents rich absorption spectra in electric fields. There are three kinds of special structures, namely shoulders, logarithmically symmetric peaks and asymmetric peaks in the square-root form, corresponding to the optical excitations of the extreme points, saddle points and constant-energy loops. With the increasing field strength, two splitting shoulder structures, which are dominated by the parabolic bands of ${5p_z}$ orbitals, come to exist because of the spin-split energy bands. The frequency of threshold shoulder declines to zero and then linearly grows. The third shoulder at ${0.75 sim 0.85}$ eV mainly comes from (${5p_x,5p_y}$) orbitals. The former and the latter orbitals, respectively, create the saddle-point symmetric peaks near the M point, while they hybridize with one another to generate the loop-related asymmetric peaks. Tinene quite differs from graphene, silicene, and germanene. The special relationship among the multi-orbital chemical bondings, spin-orbital couplings and Coulomb potentials accounts for the feature-rich optical properties.
We identify by ab initio calculations a new type of three-dimensional carbon allotropes constructed by inserting acetylenic or diacetylenic bonds into a body-centered cubic C$_8$ lattice. The resulting $sp+sp^3$-hybridized cubane-yne and cubane-diyne structures consisting of C$_8$ cubes can be characterized as a cubic crystalline modification of linear carbon chains, but energetically more favorable than the simplest linear carbyne chain and the cubic tetrahedral diamond and yne-diamond consisting of C$_4$ tetrahedrons. Electronic band calculations indicate that these new carbon allotropes are semiconductors with an indirect band gap of 3.08 eV for cubane-yne and 2.53 eV for cubane-diyne. The present results establish a new type of carbon phases consisting of C$_8$ cubes and offer insights into their outstanding structural and electronic properties.
Using density-functional calculations, we study the effect of sp$^3$-type defects created by different covalent functionalizations on the electronic and magnetic properties of graphene. We find that the induced magnetic properties are {it universal}, in the sense that they are largely independent on the particular adsorbates considered. When a weakly-polar single covalent bond is established with the layer, a local spin-moment of 1.0 $mu_B$ always appears in graphene. This effect is similar to that of H adsorption, which saturates one $p_z$ orbital in the carbon layer. The magnetic couplings between the adsorbates show a strong dependence on the graphene sublattice of chemisorption. Molecules adsorbed at the same sublattice couple ferromagnetically, with an exchange interaction that decays very slowly with distance, while no magnetism is found for adsorbates at opposite sublattices. Similar magnetic properties are obtained if several $p_z$ orbitals are saturated simultaneously by the adsorption of a large molecule. These results might open new routes to engineer the magnetic properties of graphene derivatives by chemical means.
The generalized tight-binding model, being based on the spin-dependent sublattices, is developed to explore the magnetic quantization of monolayer bismuthene. The sp$^{3}$ orbital hybridizations, site energies, nearest and next-nearest hopping integrals, spin-orbital interactions and magnetic field (${B_{z}}$ ${hat{z}}$) are taken into account simultaneously. There exist three groups of low-lying Landau levels (LLs), in which they are mainly from the (6p$_{x}$,6p$_{y}$,6p$_{z}$) orbitals, and only the first group belongs to the unoccupied conduction states. Furthermore, each group is further split into the spin-up- and spin-down-dominated subgroups. The six subgroups present the rich and unique $B_{z}$-dependent LL energy spectra, covering the specific or arc-shaped $% B_{z}$-dependences, the normal/irregular spin-split energies, and the non-crossing/crossing/anti-crossing behaviors. Specially, the second group of valence LLs near the Fermi level can create the frequent inter-subgroup LL anti-crossings since the main and side modes are comparable. The main features of energy spectra can create the special structures in density of states.
Local energy extrema of the bands in momentum space, or valleys, can endow electrons in solids with pseudo-spin in addition to real spin. In transition metal dichalcogenides this valley pseudo-spin, like real spin, is associated with a magnetic moment which underlies the valley-dependent circular dichroism that allows optical generation of valley polarization, intervalley quantum coherence, and the valley Hall effect. However, magnetic manipulation of valley pseudospin via this magnetic moment, analogous to what is possible with real spin, has not been shown before. Here we report observation of the valley Zeeman splitting and magnetic tuning of polarization and coherence of the excitonic valley pseudospin, by performing polarization-resolved magneto-photoluminescence on monolayer WSe2. Our measurements reveal both the atomic orbital and lattice contributions to the valley orbital magnetic moment; demonstrate the deviation of the band edges in the valleys from an exact massive Dirac fermion model; and reveal a striking difference between the magnetic responses of neutral and charged valley excitons which is explained by renormalization of the excitonic spectrum due to strong exchange interactions.