Local-density-functional calculations are used to study the change of work functions induced by a layer of adsorbates. We investigated and compared the work function of a monolayer of Mo, Ag, Au, Fe, Co, Ni, Nb, Li, N, and O on W͑100͒, W͑110͒, W͑211͒, and W͑111͒ surfaces. While many systems obey the commonly accepted rule that electronegative adsorbates increase the work function of the surface, we find some exceptions. For example, overlayers of Fe, Co, and Ni increase the work function of W͑100͒, W͑211͒, and W͑111͒, but decrease the work function of the W͑110͒ surface, although the charge transfer is the same in all orientations. We found that even a layer of oxygen can decrease the work function of W͑100͒, although there are always electrons transferred from the W substrate to the oxygen adsorbates. In order to understand these results, we established the relationship between surface dipole density and work function within the framework of local-density formalism. It turns out that subtle details of the charge transfer can determine the sign and magnitude of surface dipole change, leading to a strong dependence on the orientation of the substrate, with the consequence that the work-function changes are not always governed by the sign and quantity of adsorbate induced charge transfer.

Carbon nanotubes can be viewed as rolled-up graphene sheets. As such, their work functions should be closely related to those of graphene due to geometric and structural similarities. In this paper, we have systematically investigated the work functions of single-walled and multiwalled carbon nanotubes by density functional calculations. The work functions of single-walled carbon nanotubes ͑SWCNTs͒ are very close to those of graphene in the armchair conformation, while for the zigzag and chiral conformations, the work functions are close to those of graphene as the diameter is larger than a certain threshold. When the diameter of the tube is smaller than 10 Å, the work functions of zigzag and chiral tubes increase dramatically as the diameter decreases. The deviation in the work function from that of graphene for small tubes can be explained and qualitatively estimated by the downshift of the Fermi level due to the curvature effect. For multiwalled carbon nanotubes ͑MWCNTs͒, we only consider zigzag and armchair MWCNTs. We find that the work functions of all armchair and zigzag MWCNTs with inner tube diameters larger than 10 Å are very close to those of graphene. The work functions of zigzag MWCNTs with inner tube diameters smaller than 10 Å exhibit significant variations depending on the diameters of the inner and outer tubes. Using a very simple model, we find that the work functions of MWCNTs can be successfully estimated from the work functions and electronic structures of the constituent SWCNTs.

We have investigated topological electronic properties of freestanding bilayers of group IV (C, Si, Ge, Sn, and, Pb) and V (As, Sb, and, Bi) elements of the periodic table in the buckled and planar honeycomb structures under isotropic strain using first-principles calculations. Our focus is on mapping strain driven phase diagrams and identifying topological phase transitions therein as a pathway for guiding search for suitable substrates to grow two-dimensional (2D) topological insulators (TIs) films. Bilayers of group IV elements, excepting Pb, generally transform from trivial metal → topological metal → TI → topological metal → trivial metal phase with increasing strain from negative (compressive) to positive (tensile) values. Similarly, among the group V elements, As and Sb bilayers transform from trivial metal → trivial insulator → TI phase, while Bi transforms from a topological metal to TI phase. The band gap of 0.5 eV in the TI phase of Bi is the largest we found among all bilayers studied, with the band gap increasing further under tensile strain. Differences in the topological Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. characteristics of bilayers of group V elements reflect associated differences in the strength of the spin-orbit coupling (SOC). We show, in particular, that the topological band structure of Sb bilayer becomes similar to that of a Bi bilayer when the strength of the SOC in Sb is artificially enhanced by a factor of 4. This study provides the first report that As can be a 2D TI under tensile strain. Notably, we found the existence of TI phases in all elemental bilayers we studied, except Pb.