Full Tight-binding Calculations Research Articles

Adaptive molecular decomposition: Large-scale quantum chemistry for liquids

We present a linear-scaling method based on self-consistent charge non-orthogonal tight-binding. Linear scaling is achieved using a many-body expansion, which is adjusted dynamically to the instantaneous molecular configuration of a liquid. The method is capable of simulating liquids over large length and time scales, and also handles reactions correctly. Benchmarking on typical carbonate electrolytes used in Li-ion batteries displays excellent agreement with results from full tight-binding calculations. The decomposition slightly breaks the Hellmann-Feynman theorem, which is demonstrated by application to water. However, an additional correction also enables dynamical simulation in this case.

Electronic properties of graphene antidot lattices

Graphene antidot lattices constitute a novel class of nano-engineered graphene devices with controllable electronic and optical properties. An antidot lattice consists of a periodic array of holes that causes a band gap to open up around the Fermi level, turning graphene from a semimetal into a semiconductor. We calculate the electronic band structure of graphene antidot lattices using three numerical approaches with different levels of computational complexity, efficiency and accuracy. Fast finite-element solutions of the Dirac equation capture qualitative features of the band structure, while full tight-binding calculations and density functional theory (DFT) are necessary for more reliable predictions of the band structure. We compare the three computational approaches and investigate the role of hydrogen passivation within our DFT scheme.

Theory of the electronic structure of dilute nitride alloys: beyond the band-anti-crossingmodel

We use an sp3s* tight-binding Hamiltonian to investigate the band-anti-crossing (BAC) model for diluteGaNxAs1−x alloys. The BAC model describes the strong band-gap bowing at low N compositionx in terms of an interaction between the conduction band edge(E−) and a higher-lying band of localized nitrogen resonant states(E+). We demonstratethat the E− level can be described very accurately by the BAC model, in which wetreat the nitrogen levels explicitly using a linear combination of isolatednitrogen resonant states (LCINS). We also use the LCINS results to identifyE+ in the full tight-binding calculations, showing that at low N compositionE+ forms a sharp resonance in the conduction bandΓ-related density of states, which broadens rapidly at higher N composition when theE+ level rises in energy to become degenerate with the larger L-related density of states. Wethen turn to the conduction band dispersion, showing that the two-level BAC modelmust be modified to give a quantitative understanding of the dispersion. Wedemonstrate that the unexpectedly large electron effective mass values observed insome GaNAs samples are due to hybridization between the conduction bandedge and nitrogen states close to the band edge. Finally we show that there isa fundamental connection between the strong composition-dependence of theconduction-band-edge energy and the n-type carrier scattering cross-section inGa(In)NxAs1−x alloys, imposing general limits on the carrier mobility, comparable to the highest measuredmobility in such alloys.

Geometrical perturbation of graphene electronic structure

We discuss low-energy electronic properties of distorted graphene sheets from a local geometric viewpoint, treating curvature and strain as perturbations of a smooth surface. This allows a unified description of the variety of deformations to which carbon nanotubes are susceptible. By using a general symmetry analysis in conjunction with a four-orbital, nonorthogonal tight-binding model, we calculate accurate values of the relevant couplings. Carbon nanotubes 1 have a high Young’s modulus, but are not otherwise mechanically strong, being easily bent, or deformed by van der Waals interactions with a substrate. 2 Hence, the electronic repercussions of mechanical deformations are of interest for both fundamental and device-oriented reasons. Kane and Mele 3 have studied this issue with the aid of a tight-binding model incorporating only p electrons. We use a model-independent group-theoretical analysis to reveal the relevant couplings, which are then evaluated with a fourorbital non-orthogonal tight-binding model that takes into account the strong effects of rehybridization. By expressing curvature and strain as a modification of the Hamiltonian and overlap, we avoid the use of the large unit cells implied by small deformations. The response of electronic structure to curvature and strain is essentially a local coupling, largely independent of boundary conditions or global topology. We therefore isolate the effects of geometric deformation by first studying a single graphene sheet. Although our perturbative approach is in principle limited to gentle distortions, the results are in good agreement with full tight-binding calculations for a radius of curvature as small as two graphene lattice spacings @i.e., a ~12,0! tube#. The conformation of a surface in space ~e.g., a single graphene sheet! is described by a vector-valued embedding function X(x m ), specifying the location of the point with coordinates x m ,m51,2. The pair of vectors tm5]X/]x m ,(m 51,2) provide a basis for the tangent space and determine the metric g mn 5t m it n , which converts coordinate differences into physical distances. If the coordinates are determined relative to a flat unstretched state, the metric carries information about strain. The inverse of this matrix is denoted g ls , so that g lm gmn5d l n . Curvature is detected by second derivatives 4,5 of the embedding function X,

K · P Model of Ordered GaNxAs1—x

We present a three-band k · P Hamiltonian to describe the conduction band dispersion of ordered GaNxAs1—x crystals for low N concentrations (x ≲ 0.05). The model includes interactions between the highest valence band, lowest conduction band and a higher-lying band formed by N resonant states. The k · P conduction band dispersion is in excellent agreement with full tight-binding calculations, and can be used as a basis for a wide range of studies of Ga1—yInyNxAs1—x heterostructures and devices.