The coupled nonlocal NLS equation is studied by virtue of the $2times2$ Dbar-problem. Two spectral transform matrices are introduced to define two associated Dbar-problems. The relations between the coupled nonlocal NLS potential and the solution of
the Dbar-problem are constructed. The spatial transform method is extended to obtain the coupled nonlocal NLS equation and its conservation laws. The general nonlocal reduction of the coupled nonlocal NLS equation to the nonlocal NLS equation is discussed in detail. The explicit solutions are derived.
The inverse scattering transform is extended to investigate the Tzitz{e}ica equation. A set of sectionally analytic eigenfunctions and auxiliary eigenfunctions are introduced. We note that in this procedure, the auxiliary eigenfunctions play an impor
tant role. Besides, the symmetries of the analytic eigenfunctions and scattering data are discussed. The asymptotic behaviors of the Jost eigenfunctions are derived systematically. A Riemann-Hilbert problem is constructed to study the inverse scattering problem. Lastly, some novel exact solutions are obtained for reflectionless potentials.
There is a large discrepancy between the experimental observations and the theoretical predictions in the morphology of hexagonal boron nitride (h-BN) nanosheets. Theoretically-predicted hexagons terminated by armchair edges are not observed in exper
iments; and experimentally-observed triangles terminated by zigzag edges are found theoretically unstable. There are two key issues in theoretical investigations, namely, an efficient and accurate algorithm of absolute formation energy of h-BN edges, and a good understanding of the role of hydrogen passivation during h-BN growth. Here, we first proposed an efficient algorithm to calculate asymmetric edges with a self-consistent accuracy of about 0.0014 eV/{AA}. This method can also potentially serve as a standard approach for other two-dimensional (2D) compound materials. Then, by using this method, we discovered that only when edges are passivated by hydrogen atoms and temperature effects are taken into account can experimental morphology be explained. We further employed Wulff construction to obtain the equilibrium shapes of H-passivated h-BN nanosheets under its typical growth conditions at T = 1300 K and p = 1 bar, and found out that the equilibrium shapes are sensitive to hydrogen passivation and the growth conditions. Our results resolved long-standing discrepancies between experimental observations and theoretical analysis, explaining the thermodynamic driving force of the triangular, truncated triangular, and hexagonal shapes, and revealing the key role of hydrogen in h-BN growth. These discoveries and the advancement in algorithm may open the gateway towards the realization of 2D electronic and spintronic devices based on h-BN.
A complete knowledge of absolute surface energies with any arbitrary crystal orientation is important for the improvements of semiconductor devices because it determines the equilibrium and nonequilibrium crystal shapes of thin films and nanostructur
es. It is also crucial in the control of thin film crystal growth and surface effect studies in broad research fields. However, obtaining accurate absolute formation energies is still a huge challenge for the semi-polar surfaces of compound semiconductors. It mainly results from the asymmetry nature of crystal structures and the complicated step morphologies and related reconstructions of these surface configurations. Here we propose a general approach to calculate the absolute formation energies of wurtzite semi-polar surfaces by first-principles calculations, taking GaN as an example. We mainly focused on two commonly seen sets of semi-polar surfaces: a-family (11-2X) and m-family (10-1X). For all the semi-polar surfaces that we have calculated in this paper, the self-consistent accuracy is within 1.5 meV/{AA}^2. Our work fills the last technical gap to fully investigate and understand the shape and morphology of compound semiconductors.
InGaN is an ideal alloy system for optoelectronic devices due its tunable band gap. Yet high-quality InGaN requires high In concentration, which is a challenging issue that limits its use in green-light LEDs and other devices. In this paper, we inves
tigated the surfactant effect of Sb on the In incorporation on InGaN (000-1) surface via first-principles approaches. Surface phase diagram was also constructed to determine surface structures under different growth conditions. By analyzing surface stress under different structures, we found that Sb adatom can induce tensile sites in the cation layer, enhancing the In incorporation. These fi ndings may provide fundamental understandings and guidelines for the growth of InGaN with high In concentration.
The concept of quantum stress (QS) is introduced and formulated within density functional theory (DFT), to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QS
(sigma^Q) is derived in relation to deformation potential of electronic states ({Xi}) and variation of electron density ({Delta}n), sigma^Q = {Xi}{Delta}n, as a quantum analog of classical Hooks law. Two distinct QS manifestations are demonstrated quantitatively by DFT 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 QS in some physical phenomena are discussed to underlie its importance.
