Tight Binding calculations

We propose a tight-binding (TB) model, that includes spin-orbit coupling (SOC), to describe the electronic properties of methyl-substituted germanane (GeCH 3). This model gives an electronic spectrum in agreement with first principle results close to the Fermi level. Using the Z 2 formalism, we show that a topological phase transition from a normal insulator (NI) to a quantum spin Hall (QSH) phase occurs at 11.6% biaxial tensile strain. The sensitivity of the electronic properties of this system on strain, in particular its transition to the topological insulating phase, makes it very attractive for applications in strain sensors and other microelectronic applications.

The local orbital magnetic moments Lδ(i) at different layers i close to the surfaces of Fe, Co, and Ni are determined in the framework of a d-band Hamiltonian, which includes hybridizations, Coulomb interactions, and spin-orbit coupling on the same electronic level. Different directions of the magnetization δ are considered in order to quantify the anisotropy in L. For each δ, the spin-polarized charge distribution and the local densities of states from which L is derived are calculated self-consistently. The role of the local atomic environment is investigated by performing calculations on the (001), (110), and (111) surfaces of the bcc, hcp, and fcc lattices. Lδ(i) is significantly enhanced at surface atoms as compared to the corresponding bulk moment Lδ(bulk). L depends strongly on the local coordination number and is generally larger the more open the surface is. For example, for the Fe(001) surface Lx(1)/Lx(bulk)=2.2 and for the Fe(110) surface Lx(1)/Lx(bulk)=1.3. Lδ(i) decreases abruptly as we move from the uppermost layer (i=1) to the second layer (i=2). After some oscillations, convergence to Lδ(bulk) is reached quite accurately for i>~6. The largest anisotropy in Lδ(i) is found at the hcp (0001) surface of Co (L∥-L⊥≃0.02μB). The orbital moments at pure surfaces are compared with results for deposited films by considering four layers of Co on Pd(111) as a representative example.