Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form ${\mathcal H}\psi=E {\mathcal P}\psi$, with Hermitian tight-binding operators ${\mathcal H}$, ${\mathcal P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.Comment: 16 pages, 3 figure

Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling

I. Introduction II. Two-dimensional lattice fermions III. Methods to avoid fermion doubling (sine dispersion, sine plus cosine dispersion, staggered lattice dispersion, linear sawtooth dispersion, tangent dispersion) IV. Topologically protected Dirac cone V. Application: Klein tunneling (tangent fermions on a space-time lattice, wave packet propagation) VI. Application: Strong antilocalization (transfer matrix of tangent fermions, topological insulator versus graphene) VII. Application: Anomalous quantum Hall effect (gauge invariant tangent fermions, topologically protected zeroth Landau level) VIII. Application: Majorana metal (Dirac versus Majorana fermions, phase diagram) IX. OutlookComment: review article, 26 pages, 13 figures; V2: added three appendices, and provided code for the various implementation

Magnetic breakdown spectrum of a Kramers-Weyl semimetal

We calculate the Landau levels of a Kramers-Weyl semimetal thin slab in a perpendicular magnetic field $B$. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band width that oscillates periodically in $1/B$. We interpret the spectrum in terms of a one-dimensional superlattice induced by magnetic breakdown at Weyl points. The band width oscillations may be observed as $1/B$-periodic magnetoconductance oscillations, at weaker fields and higher temperatures than the Shubnikov-de Haas oscillations due to Landau level quantization. No such spectrum appears in a generic Weyl semimetal, the Kramers degeneracy at time-reversally invariant momenta is essential.Comment: 13 pages, 18 figure

Localization landscape for Dirac fermions

In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for the scalar wave equation in a random potential, or equivalently for the Schr\"{o}dinger equation of spinless electrons. Here we generalize the concept to the Dirac equation, which includes the effects of spin-orbit coupling and allows to study quantum localization in graphene or in topological insulators and superconductors. The landscape function $u(r)$ is defined on a lattice as a solution of the differential equation $\overline{{H}}u(r)=1$, where $\overline{{H}}$ is the Ostrowsky comparison matrix of the Dirac Hamiltonian. Random Hamiltonians with the same (positive definite) comparison matrix have localized states at the same positions, defining an equivalence class for Anderson localization. This provides for a mapping between the Hermitian and non-Hermitian Anderson model.Comment: 6 pages, 6 figure

Facetted patchy particles through entropy-driven patterning of mixed ligand SAMS

We present a microscopic theory that describes the ordering of two distinct ligands on the surface of a faceted nanoparticle. The theory predicts that when one type of ligand is significantly bulkier than all others, the larger ligands preferentially align themselves along the edges and vertices of the nanoparticle. Monte Carlo simulations confirm these predictions. We show that the intrinsic conformational entropy of the ligands stabilizes this novel edge-aligned phase.Comment: 11 pages, 10 figure

Direct evidence of ZnO morphology modification via the selective adsorption of ZnO-binding peptides

Biomolecule-mediated ZnO synthesis has great potential for the tailoring of ZnO morphology for specific application in biosensors, window materials for display and solar cells, dye-sensitized solar cells (DSSCs), biomedical materials, and photocatalysts due to its specificity and multi-functionality. In this contribution, the effect of a ZnO-binding peptide (ZnO-BP, G-12: GLHVMHKVAPPR) and its GGGC-tagged derivative (GT-16: GLHVMHKVAPPRGGGC) on the growth of ZnO crystals expressing morphologies dependent on the relative growth rates of (0001) and (10 (1) over bar0) planes of ZnO have been studied. The amount of peptide adsorbed was determined by a depletion method using oriented ZnO films grown by Atomic Layer Deposition (ALD), while the adsorption behavior of G-12 and GT-16 was investigated using XPS and a computational approach. Direct evidence was obtained to show that (i) both the ZnO-BP identified by phage display and its GGGC derivative (GT-16) are able to bind to ZnO and modify crystal growth in a molecule and concentration dependent fashion, (ii) plane selectivity for interaction with the (0001) versus the (10 (1) over bar0) crystal planes is greater for GT-16 than G-12; and (iii) specific peptide residues interact with the crystal surface albeit in the presence of charge compensating anions. To our knowledge, this is the first study to provide unambiguous and direct quantitative experimental evidence of the modification of ZnO morphology via (selective and nonselective) adsorption-growth inhibition mechanisms mediated by a ZnO-BP identified from phage display libraries

Experimental and theoretical investigation of ligand effects on the synthesis of ZnO nanoparticles

ZnO nanoparticles with highly controllable particle sizes(less than 10 nm) were synthesized using organic capping ligands in Zn(Ac)2 ethanolic solution. The molecular structure of the ligands was found to have significant influence on the particle size. The multi-functional molecule tris(hydroxymethyl)-aminomethane (THMA) favoured smaller particle distributions compared with ligands possessing long hydrocarbon chains that are more frequently employed. The adsorption of capping ligands on ZnnOn crystal nuclei (where n = 4 or 18 molecular clusters of(0001) ZnO surfaces) was modelled by ab initio methods at the density functional theory (DFT) level. For the molecules examined, chemisorption proceeded via the formation of Zn...O, Zn...N, or Zn...S chemical bonds between the ligands and active Zn2+ sites on ZnO surfaces. The DFT results indicated that THMA binds more strongly to the ZnO surface than other ligands, suggesting that this molecule is very effective at stabilizing ZnO nanoparticle surfaces. This study, therefore, provides new insight into the correlation between the molecular structure of capping ligands and the morphology of metal oxide nanostructures formed in their presence

Selective Synthesis of Fe2O3 and Fe3O4 Nanowires Via a Single Precursor: A General Method for Metal Oxide Nanowires

Hematite (α-Fe2O3) and magnetite (Fe3O4) nanowires with the diameter of about 100 nm and the length of tens of micrometers have been selectively synthesized by a microemulsion-based method in combination of the calcinations under different atmosphere. The effects of the precursors, annealing temperature, and atmosphere on the morphology and the structure of the products have been investigated. Moreover, Co3O4 nanowires have been fabricated to confirm the versatility of the method for metal oxide nanowires