Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

At the atomic-cluster scale, pure boron is markedly similar to carbon, forming simple planar molecules and cage-like fullerenes. Theoretical studies predict that two-dimensional (2D) boron sheets will adopt an atomic configuration similar to that of boron atomic clusters. We synthesized atomically thin, crystalline 2D boron sheets (i.e., borophene) on silver surfaces under ultrahigh-vacuum conditions. Atomic-scale characterization, supported by theoretical calculations, revealed structures reminiscent of fused boron clusters with multiple scales of anisotropic, out-of-plane buckling. Unlike bulk boron allotropes, borophene shows metallic characteristics that are consistent with predictions of a highly anisotropic, 2D metal.

Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs

The celebrated electronic properties of graphene(1,2) have opened the way for materials just one atom thick(3) to be used in the post-silicon electronic era(4). An important milestone was the creation of heterostructures based on graphene and other two-dimensional crystals, which can be assembled into three-dimensional stacks with atomic layer precision(5-7). Such layered structures have already demonstrated a range of fascinating physical phenomena(8-71), and have also been used in demonstrating a prototype field-effect tunnelling transistor(12), which is regarded to be a candidate for post-CMOS (complementary metal-oxide semiconductor) technology. The range of possible materials that could be incorporated into such stacks is very large. Indeed, there are many other materials with layers linked by weak van der Waals forces that can be exfoliated(3,13) and combined together to create novel highly tailored heterostructures. Here, we describe a new generation of field-effect vertical tunnelling transistors where two-dimensional tungsten disulphide serves as an atomically thin barrier between two layers of either mechanically exfoliated or chemical vapour deposition-grown graphene. The combination of tunnelling (under the barrier) and thermionic (over the barrier) transport allows for unprecedented current modulation exceeding 1 x 10(6) at room temperature and very high ON current. These devices can also operate on transparent and flexible substrates.

Vertical field-effect transistor based on graphene?WS2 heterostructures for flexible and transparent electronics

We present a new scheme to extract numerically optimal interatomic potentials from large amounts of data produced by first-principles calculations. The method is based on fitting the potential to ab initio atomic forces of many atomic configurations, including surfaces, clusters, liquids and crystals at finite temperature. The extensive data set overcomes the difficulties encountered by traditional fitting approaches when using rich and complex analytic forms, allowing to construct potentials with a degree of accuracy comparable to that obtained by ab initio methods. A glue potential for aluminium obtained with this method is presented and discussed.

https://iopscience.iop.org/article/10.1209/0295-5075/26/8/005/pdf

Interatomic Potentials from First-Principles Calculations: The Force-Matching Method

A 2D metastable carbon allotrope, penta-graphene, composed entirely of carbon pentagons and resembling the Cairo pentagonal tiling, is proposed. State-of-the-art theoretical calculations confirm that the new carbon polymorph is not only dynamically and mechanically stable, but also can withstand temperatures as high as 1000 K. Due to its unique atomic configuration, penta-graphene has an unusual negative Poisson’s ratio and ultrahigh ideal strength that can even outperform graphene. Furthermore, unlike graphene that needs to be functionalized for opening a band gap, penta-graphene possesses an intrinsic quasi-direct band gap as large as 3.25 eV, close to that of ZnO and GaN. Equally important, penta-graphene can be exfoliated from T12-carbon. When rolled up, it can form pentagon-based nanotubes which are semiconducting, regardless of their chirality. When stacked in different patterns, stable 3D twin structures of T12-carbon are generated with band gaps even larger than that of T12-carbon. The versatility of penta-graphene and its derivatives are expected to have broad applications in nanoelectronics and nanomechanics.

/pdf/penta-graphene-a-new-carbon-allotrope-2o4wkb0gwj.pdf

Penta-graphene: A new carbon allotrope

We present an equation of state (EOS) that describes how the hydrostatic change in surface area is related to two-dimensional in-plane pressure ($\mathcal{F}$) and yields the measure of a material's resilience to isotropic stretching (the layer modulus $\ensuremath{\gamma}$) as one of its fit parameters. We give results for the monolayer systems of graphene and boronitrene, and we also include results for Si, Ge, GeC, and SiC in the isostructural honeycomb structure for comparison. Our results show that, of the honeycomb structures, graphene is the most resilient to stretching with a value of ${\ensuremath{\gamma}}_{\text{C}}$ = $206.6$ N m${}^{\ensuremath{-}1}$, second is boronitrene with ${\ensuremath{\gamma}}_{\text{BN}}$ = $177.0$ N m${}^{\ensuremath{-}1}$, followed by ${\ensuremath{\gamma}}_{\text{SiC}}$ = 116.5 N m${}^{\ensuremath{-}1}$, ${\ensuremath{\gamma}}_{\text{GeC}}$ = 101.0 N m${}^{\ensuremath{-}1}$, ${\ensuremath{\gamma}}_{\text{Si}}$ = 44.5 N m${}^{\ensuremath{-}1}$, and ${\ensuremath{\gamma}}_{\text{Ge}}$ = 29.6 N m${}^{\ensuremath{-}1}$. We calculate the Young's and shear moduli from the elastic constants and find that, in general, they rank according to the layer modulus. We also find that the calculated layer modulus matches the one obtained from the EOS. We use the EOS to predict the isotropic intrinsic strength of the various systems and find that, in general, the intrinsic stresses also rank according to the layer modulus. Graphene and boronitrene have comparable strengths with intrinsic stresses of 29.4 and 26.0 N m${}^{\ensuremath{-}1}$, respectively. We considered four graphene allotropes including pentaheptite and graphdiyne and find that pentaheptite has a value for $\ensuremath{\gamma}$ comparable to graphene. We find a phase transition from graphene to graphdiyne at $\mathcal{F}$ = $\ensuremath{-}7.0$ N m${}^{\ensuremath{-}1}$. We also consider bilayer, trilayer, and four-layered graphene and find that the addition of extra layers results in a linear dependence of $\ensuremath{\gamma}$ with $\mathcal{F}$.

Mechanical properties of graphene and boronitrene

Density-functional theory has been successfully applied in solid-state calculations where it has been customary to extract a single number, the total energy. Within this formalism, we show that one can, in addition, define a local energy density scrE(r) which is a sum of kinetic, Maxwell, exchange-correlation, and other contributions that depend on the external potential. Despite the inherent nonuniqueness of scrE(r), we show that it can be used to calculate well-defined energies from integrals over regions, e.g., at surfaces. We present explicit calculations for the Si(111) ideal surface as a test case and we demonstrate the power and efficiency of the method by determining energies of two inequivalent GaAs(100) surfaces from a single calculation.

First-principles energy density and its applications to selected polar surfaces.

The energetics of various low-energy intrinsic, extrinsic, and twinlike stacking fault configurations in hexagonal-close-packed magnesium are determined from first-principles calculations. To zeroth-order, the ordering of the energies can be understood in terms of the number of fcc-like planes in the sequence of close-packed planes. However, such a simple model fails to quantitatively reproduce the calculated energies of the faults. We propose a model based on a local bond orientation scheme which reproduces the calculated results and is able to accurately predict the energies of arbitrary stacking sequences. This model has only two independent parameters, the energy of the intrinsic ${I}_{1}$ stacking fault and the energy difference between hcp and fcc Mg. Both energy and entropy considerations suggest that isolated ${I}_{1}$ stacking faults should predominate.

Stacking faults in magnesium

GaAs (111) and (1'-.2m''.3m'̄ '.2m''-.3m' 1'-.2m''.3m'̄ '.2m''-.3m' 1'-.2m''.3m'̄ '.2m''-.3m' ) surfaces and the GaAs/AlAs (111) heterojunction studied using a local energy density

The vacancy formation energies and (Mg, Al, and Si) impurity heats of solution are calculated for Al and Mg using a first-principles pseudopotential approach and large supercells. While the interaction of the defects considered here are already negligible for reasonably small unit cells, adequate sampling of the Brillouin zone is found to be essential for these metallic systems, even for systems containing more than 100 atoms per unit cell; e.g., the vacancy formation energy of Al for 108 atoms per cell has the incorrect sign if only the \ensuremath{\Gamma} point is sampled. When the volume and structural relaxations are treated consistently, heats of formation and solution and relaxation volumes are obtained that are in good agreement with the available experimental data. Simple trends in the relaxations around the impurities in the various materials can be understood in terms of the size of the impurities compared with the host atoms. Contrary to some commonly used models, the energetics of the impurities are found to be dominated by electronic, rather than elastic, contributions. The defect-induced changes to the local electronic structure are also discussed.

Nithaya Chetty

Papers

Mechanical properties of graphene and boronitrene

First-principles energy density and its applications to selected polar surfaces.

Stacking faults in magnesium

GaAs (111) and (1'-.2m''.3m'̄ '.2m''-.3m' 1'-.2m''.3m'̄ '.2m''-.3m' 1'-.2m''.3m'̄ '.2m''-.3m' ) surfaces and the GaAs/AlAs (111) heterojunction studied using a local energy density

Vacancies and impurities in aluminum and magnesium