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Register a new userAccurate Complex Scaling of Three Dimensional Numerical Potentials
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The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schroedinger operator. Whenever it is desirable to apply the complex scaling to investigate resonances in physical systems defined on numerical discrete grids, the most direct approach relies on the application of a similarity transformation to the original, unscaled Hamiltonian. We show that such an approach can be conveniently implemented in the Daubechies wavelet basis set, featuring a very promising level of generality, high accuracy, and no need for artificial convergence parameters. Complex scaling of three dimensional numerical potentials can be efficiently and accurately performed. By carrying out an illustrative resonant state computation in the case of a one-dimensional model potential, we then show that our wavelet-based approach may disclose new exciting opportunities in the field of computational non-Hermitian quantum mechanics.
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The discovery of two-dimensional (2D) ferroelectrics with switchable out-of-plane polarization such as monolayer $alpha$-In$_2$Se$_3$ offers a new avenue for ultrathin high-density ferroelectric-based nanoelectronics such as ferroelectric field effect transistors and memristors. The functionality of ferroelectrics depends critically on the dynamics of polarization switching in response to an external electric/stress field. Unlike the switching dynamics in bulk ferroelectrics that have been extensively studied, the mechanisms and dynamics of polarization switching in 2D remain largely unexplored. Molecular dynamics (MD) using classical force fields is a reliable and efficient method for large-scale simulations of dynamical processes with atomic resolution. Here we developed a deep neural network-based force field of monolayer In$_2$Se$_3$ using a concurrent learning procedure that efficiently updates the first-principles-based training database. The model potential has accuracy comparable with density functional theory (DFT), capable of predicting a range of thermodynamic properties of In$_2$Se$_3$ polymorphs and lattice dynamics of ferroelectric In$_2$Se$_3$. Pertinent to the switching dynamics, the model potential also reproduces the DFT kinetic pathways of polarization reversal and 180$^circ$ domain wall motions. Moreover, isobaric-isothermal ensemble MD simulations predict a temperature-driven $alpha rightarrow beta$ phase transition at the single-layer limit, as revealed by both local atomic displacement and Steinhardts bond orientational order parameter $Q_4$. Our work paves the way for further research on the dynamics of ferroelectric $alpha$-In$_2$Se$_3$ and related systems.
Graphite, with many industrial applications, is one of the widely sought-after allotropes of carbon. The sp2 hybridized and thermodynamically stable form of carbon forms a layered structure with strong in-plane carbon bonds and weak inter-layer van der Waals bonding. Graphite is also a high-temperature ceramic, and shaping them into complex geometries is challenging, given its limited sintering behavior even at high temperatures. Although the geometric design of the graphite structure in many of the applications could dictate its precision performance, conventional synthesis methods for formulating complex geometric graphite shapes are limited due to the intrinsic brittleness and difficulties of high-temperature processing. Here, we report the development of colloidal graphite ink from commercial graphite powders with reproducible rheological behavior that allows the fabrication of any complex architectures with tunable geometry and directionality via 3D printing at room temperature. The method is enabled via using small amounts of clay, another layered material, as an additive, allowing the proper design of the graphene ink and subsequent binding of graphite platelets during printing. Sheared layers of clay are easily able to flow, adapt, and interface with graphite layers forming strong binding between the layers and between particles that make the larger structures. The direct ink printing of complex 3D architectures of graphite without further heat treatments could lead to easy shape engineering and related applications of graphite at various length scales, including complex graphite molds or crucibles. The 3D printed complex graphitic structures exhibit excellent thermal, electrical, and mechanical properties, and the clay additive does not seem to alter these properties due to the excellent inter-layer dispersion and mixing within the graphite material.
We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II su- perconductors, magnetic materials and aspects of cosmology. We characterise the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully-packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls-off algebraically and we associate it to a geometric percolation transition that we characterise in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermo- dynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach towards a state that, within numerical accuracy, shares many features with the one at the percolation threshold, a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops, and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length-scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.
The reliability of kinetic Monte Carlo (KMC) simulations depends on accurate transition rates. The self-learning KMC method (Trushin et al 2005 Phys. Rev. B 72 115401) combines the accuracy of rates calculated from a realistic potential with the efficiency of a rate catalog, using a pattern recognition scheme. This work expands the original two-dimensional method to three dimensions. The concomitant huge increase in the number of rate calculations on the fly needed can be avoided by setting up an initial database, containing exact activation energies calculated for processes gathered from a simpler KMC model. To provide two representative examples, the model is applied to the diffusion of Ag monolayer islands on Ag(111), and the homoepitaxial growth of Ag on Ag(111) at low temperatures.
Identification and design of defects in two-dimensional (2D) materials as promising single photon emitters (SPE) requires a deep understanding of underlying carrier recombination mechanisms. Yet, the dominant mechanism of carrier recombination at defects in 2D materials has not been well understood, and some outstanding questions remain: How do recombination processes at defects differ between 2D and 3D systems? What factors determine defects in 2D materials as excellent SPE at room temperature? In order to address these questions, we developed first-principles methods to accurately calculate the radiative and non-radiative recombination rates at defects in 2D materials, using h-BN as a prototypical example. We reveal the carrier recombination mechanism at defects in 2D materials being mostly dominated by defect-defect state recombination in contrast to defect-bulk state recombination in most 3D semiconductors. In particular, we disentangle the non-radiative recombination mechanism into key physical quantities: zero-phonon line (ZPL) and Huang-Rhys factor. At the end, we identified strain can effectively tune the electron-phonon coupling at defect centers and drastically change non-radiative recombination rates. Our theoretical development serves as a general platform for understanding carrier recombination at defects in 2D materials, while providing pathways for engineering of quantum efficiency of SPE.
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