Recently, there have been intense efforts in searching for new topological insulator materials. Based on first-principles calculations, we find that all the ultrathin Bi (111) films are characterized by a nontrivial $Z_2$ number independent of the film thickness, without the odd-even oscillation of topological triviality as commonly perceived. The stable nontrivial $Z_2$ topology is retained by the concurrent band gap inversions at multiple time-reversal-invariant $k$ points with the increasing film thickness and associated with the intermediate interbilayer coupling of the Bi film. Our calculations further indicate that the presence of metallic surface states in thick Bi (111) films can be effectively removed by surface adsorption.

Topological insulators are a recently discovered class of materials having insulating bulk electronic states but conducting boundary states distinguished by nontrivial topology. So far, several generations of topological insulators have been theoretically predicted and experimentally confirmed, all based on inorganic materials. Here, based on first-principles calculations, we predict a family of two-dimensional organic topological insulators made of organometallic lattices. Designed by assembling molecular building blocks of triphenyl-metal compounds with strong spin-orbit coupling into a hexagonal lattice, this new classes of organic topological insulators are shown to exhibit nontrivial topological edge states that are robust against significant lattice strain. We envision that organic topological insulators will greatly broaden the scientific and technological impact of topological insulators.

When the dimension of a solid structure is reduced, there will be two emerging effects, quantum confinement and surface effect, which dominate at nanoscale. Based on first-principles calculations, we demonstrate that due to an intriguing interplay between these two dominating effects, the topological and electronic (topoelectronic) properties of Sb (111) nanofilms undergo a series of transitions as a function of the reducing film thickness: transforming from a topological semimetal to a topological insulator at 7.8 nm (22 bilayer), then to a quantum spin Hall (QSH) phase at 2.7 nm (8 bilayer), and finally, to a normal (topological trivial) semiconductor at 1.0 nm (3 bilayer). Our theoretical findings identify the existence of the QSH in the Sb (111) nanofilms within a narrow range of thickness and suggest that the Sb (111) nanofilms provide an ideal test bed for experimental study of topoelectronic phase transitions.

Graphene is known as the strongest 2D material in nature, yet we show that moderate charge doping of either electrons or holes can further enhance its ideal strength by up to $\sim 17\%$, based on first-principles calculations. This unusual electronic enhancement, versus conventional structural enhancement, of the material’s strength is achieved by an intriguing physical mechanism of charge doping counteracting the strain induced enhancement of the Kohn anomaly, which leads to an overall stiffening of the zone boundary $K_1$ phonon mode whose softening under strain is responsible for graphene failure. Electrons and holes work in the same way due to the high electron-hole symmetry around the Dirac point of graphene, while overdoping may weaken the graphene by softening other phonon modes. Our findings uncover another fascinating property of graphene with broad implications in graphene-based electromechanical devices.

The evidence that the band gap of Si changes significantly with strain suggests that by alternating regions of strained and unstrained Si one creates a single-element electronic heterojunction superlattice (SL), with the carrier confinement defined by strain rather than by the chemical differences in conventional compositional SLs. Using first-principles calculations, we map out the electronic phase diagram of a one-dimensional pure-silicon SL. It exhibits a high level of phase tunability, e.g., tuning from type~I to type~II. Our theory rationalizes a recent observation of a strain SL in a Si nanowire and provides general guidance for the fabrication of single-element strain SLs.

The concept of quantum electronic stress (QES) is introduced and formulated within density functional theory to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QES (${\sigma }^{\mathrm{QE}}$) is derived in relation to deformation potential of electronic states ($\Xi$) and variation of electron density ($\Delta n$), ${\sigma }^{\mathrm{QE}}=\Xi \Delta n$ as a quantum analog of classical Hooke’s law. Two distinct QES manifestations are demonstrated quantitatively by density functional theory calculations: (1) in the form of bulk stress induced by charge carriers and (2) in the form of surface stress induced by quantum confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.