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Register a new userComparison of analytic and numerical bond-order potentials for W and Mo
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Thomas Hammerschmidt
Publication date
2016
fields
Physics
and research's language is
English
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Bond-order potentials (BOPs) are derived from the tight-binding (TB) approximation and provide a linearly-scaling computation of the energy and forces for a system of interacting atoms. While the numerical BOPs involve the numerical integration of the response (Greens) function, the expressions for the energy and interatomic forces are analytical within the formalism of the analytic BOPs. In this paper we present a detailed comparison of numerical and analytic BOPs. We use established parametrisations for the bcc refractory metals W and Mo and test structural energy differences; tetragonal, trigonal, hexagonal and orthorhombic deformation paths; formation energies of point defects as well as phonon dispersion relations. We find that the numerical and analytic BOPs generally are in very good agreement for the calculation of energies. Different from the numerical BOPs, the forces in the analytic BOPs correspond exactly to the negative gradients of the energy. This makes it possible to use the analytic BOPs in dynamical simulations and leads to improved predictions of defect energies and phonons as compared to the numerical BOPs.
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In a joint theoretical and experimental investigation we show that a series of transition metals with strained body-centered cubic lattice ---W, Ta, Nb, and Mo--- host surface states that are topologically protected by mirror symmetry. Our finding extends the class of topologically nontrivial systems by topological crystalline transition metals. The investigation is based on independent calculations of the electronic structures and of topological invariants, the results of which agree with established properties of the Dirac-type surface state in W(110). To further support our prediction, we investigate both experimentally by spin-resolved inverse photoemission and theoretically an unoccupied topologically nontrivial surface state in Ta(110).
In recent years, transition metal dichalcogenides (TMDs) have garnered great interest as topological materials -- monolayers of centrosymmetric $beta$-phase TMDs have been identified as 2D topological insulators (TIs), and bulk crystals of noncentrosymmetric $gamma$-phase MoTe$_2$ and WTe$_2$ have been identified as type-II Weyl semimetals. However, ARPES and STM probes of these TMDs have revealed huge, arc-like surface states that overwhelm, and are sometimes mistaken for, the much smaller topological surface Fermi arcs of bulk type-II Weyl points. In this letter, we use first-principles calculations and (nested) Wilson loops to analyze the bulk and surface electronic structure of both $beta$- and $gamma$-MoTe$_2$, finding that $beta$-MoTe$_2$ ($gamma$-MoTe$_2$ gapped with symmetry-preserving distortion) is an inversion-symmetry-indicated $mathbb{Z}_{4}$-nontrivial ($noncentrosymmetric, non$-$symmetry$-$indicated$) higher-order TI (HOTI) driven by double band inversion. Both structural phases of MoTe$_2$ exhibit the same surface features as WTe$_2$, revealing that the large Fermi arcs are in fact not topologically trivial, but are rather the characteristic split and gapped fourfold surface states of a HOTI. We also show that, when the effects of SOC are neglected, $beta$-MoTe$_2$ is a nodal-line semimetal with $mathbb{Z}_{2}$-nontrivial monopole nodal lines (MNLSM). This finding confirms that MNLSMs driven by double band inversion are the weak-SOC limit of HOTIs, implying that MNLSMs are higher-order topological $semimetals$ with flat-band-like hinge states, which we find to originate from the corner modes of 2D fragile TIs.
We study the two dimensional XY-model with high precision Monte Carlo techniques and investigate the continuum approach of the step-scaling function of its finite volume mass gap. The continuum extrapolated results are found consistent with analytic predictions for the finite volume energy spectrum based on the equivalence with sine-Gordon theory. To come to this conclusion it was essential to use an also predicted form of logarithmic decay of lattice artifacts for the extrapolation.
Interatomic potentials (IPs) are reduced-order models for calculating the potential energy of a system of atoms given their positions in space and species. IPs treat atoms as classical particles without explicitly modeling electrons and thus are computationally far less expensive than first-principles methods, enabling molecular simulations of significantly larger systems over longer times. Developing an IP is a complex iterative process involving multiple steps: assembling a training set, designing a functional form, optimizing the function parameters, testing model quality, and deployment to molecular simulation packages. This paper introduces the KIM-based learning-integrated fitting framework (KLIFF), a package that facilitates the entire IP development process. KLIFF supports both analytic and machine learning IPs. It adopts a modular approach whereby various components in the fitting process, such as atomic environment descriptors, functional forms, loss functions, optimizers, quality analyzers, and so on, work seamlessly with each other. This provides a flexible framework for the rapid design of new IP forms. Trained IPs are compatible with the Knowledgebase of Interatomic Models (KIM) application programming interface (API) and can be readily used in major materials simulation packages compatible with KIM, including ASE, DL_POLY, GULP, LAMMPS, and QC. KLIFF is written in Python with computationally intensive components implemented in C++. It is parallelized over data and supports both shared-memory multicore desktop machines and high-performance distributed memory computing clusters. We demonstrate the use of KLIFF by fitting an analytic Stillinger--Weber potential and a machine learning neural network potential for silicon. The KLIFF package, together with its documentation, is publicly available at: https://github.com/openkim/kliff.
Motived by experimentally synthesized $mathrm{MoSi_2N_4}$ (textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020})), the intrinsic piezoelectricity in monolayer $mathrm{XSi_2N_4}$ (X=Ti, Zr, Hf, Cr, Mo and W) are studied by density functional theory (DFT). Among the six monolayers, the $mathrm{CrSi_2N_4}$ has the best piezoelectric strain coefficient $d_{11}$ of 1.24 pm/V, and the second is 1.15 pm/V for $mathrm{MoSi_2N_4}$. Taking $mathrm{MoSi_2N_4}$ as a example, strain engineering is applied to improve $d_{11}$. It is found that tensile biaxial strain can enhance $d_{11}$ of $mathrm{MoSi_2N_4}$, and the $d_{11}$ at 4% can improve by 107% with respect to unstrained one. By replacing the N by P or As in $mathrm{MoSi_2N_4}$, the $d_{11}$ can be raise substantially. For $mathrm{MoSi_2P_4}$ and $mathrm{MoSi_2As_4}$, the $d_{11}$ is as high as 4.93 pm/V and 6.23 pm/V, which is mainly due to smaller $C_{11}-C_{12}$ and very small minus or positive ionic contribution to piezoelectric stress coefficient $e_{11}$ with respect to $mathrm{MoSi_2N_4}$. The discovery of this piezoelectricity in monolayer $mathrm{XSi_2N_4}$ enables active sensing, actuating and new electronic components for nanoscale devices, and is recommended for experimental exploration.
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