DL_MG : A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution

The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential—a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson–Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10^9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein–ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver

Simultaneous Prediction of the Magnetic and Crystal Structure of Materials Using a Genetic Algorithm

We introduce a number of extensions and enhancements to a genetic algorithm for crystal structure prediction, to make it suitable to study magnetic systems. The coupling between magnetic properties and crystal structure means that it is essential to take a holistic approach, and we present for the first time, a genetic algorithm that performs a simultaneous global optimisation of both magnetic structure and crystal structure. We first illustrate the power of this approach on a novel test system—the magnetic Lennard–Jones potential—which we define. Then we study the complex interface structures found at the junction of a Heusler alloy and a semiconductor substrate as found in a proposed spintronic device and show the impact of the magnetic interface structure on the device performance

Cr2AlN and the search for the highest temperature superconductor in the M2AX family

We have developed a high-throughput computational method to predict the superconducting transition temperature in stable hexagonal M 2AX phases, and applied it to all the known possible choices for M (M: Sc, Ti, V, Cr, Mn, Fe, Y, Zr, Nb, Mo, Lu, Hf and Ta). We combine this with the best candidates for A (A: Al, Cu, Ge and Sn ) and X (X: C and N) from our previous work, and predict T c for 60 M2AX-phase materials, 53 of which have never been studied before. From all of these, we identify Cr2AlN as the best candidate for the highest T c , and confirm its high T c with more detailed density functional theory electron-phonon coupling calculations. Our detailed calculations predict Tc = 14.8 K for Cr2AlN, which is significantly higher than any Tc value known or predicted for any material in the M2AX family to date

Huge power factor in p-type half-Heusler alloys NbFeSb and TaFeSb

NbFeSb is a promising thermoelectric material which according to experimental and theoretical studies exhibits a high power factor of up to 10 mW/(m.K^2) at room temperature and ZT of 1 at 1000 K. In all previous theoretical studies, κ_latt is calculated using simplified models, which ignore structural defects. In this work, we calculate κ_latt by solving the Boltzmann Transport Equation and subsequently including the contributions of grain boundaries, point defects and electron-phonon interaction. The results for κ_latt and ZT are in excellent agreement with experimental measurements. In addition, we investigate theoretically the thermoelectric properties of TaFeSb. The material has recently been synthesised experimentally, thus conrming the theoretical hypothesis for its stability. This encourages a full-scale computation of its thermoelectric performance.Our results show that TaFeSb is indeed an excellent thermoelectric material which has an unprecedentedly high power factor of 16 mW/(m.K^2) at room temperature and ZT of 1.5 at 1000 K

Significant improvement of the Seebeck coefficient of Fe2VAl with antisite defects

In this work we present first principles study of the effect of stoichiometric pairs of antisite defects, V occupying Al site (VAl) and Al occupying V site (AlV), on the electronic structure and Seebeck coefficient of the Fe2VAlHeusler alloy. We show that introduction of these defects opens the bandgap of Fe2VAl, changing it from semi-metal to semiconductor, which results in an increase of the Seebeck coefficient for a range of doping concentrations and temperatures. We calculated Seebeck coefficients at different doping concentrations and temperatures shows good agreement with experimental data

Nanoscale Si fishbone structures for manipulating heat transport using phononic resonators for thermoelectric applications

Thermoelectric materials have the potential to convert waste heat into electricity, but their thermoelectric efficiency must be improved before they are effective and economically viable. One promising route to improving thermoelectric efficiency in thin-film thermoelectric materials is to reduce the material’s thermal conductivity through nanopatterning the surface. In this work nanoscale phononic resonators are introduced to the surface, and their potential to reduce thermal conductivity is explored via coupled experimental and theoretical techniques. Atomistic modelling is used to predict the dependence of the thermal conductivity on different design parameters and used to guide the design and fabrication of silicon fishbone nanostructures. The nanostructure design incorporates a variation on design parameters such as barb length, width and spacing along the shaft length to enable correlation with changes in thermal conductivity. The thermal characteristics of the nanostructures are investigated experimentally using the spatial resolution of scanning thermal microscopy to correlate changes in thermal conductivity with the changes in the structure parameters. The method developed uses a microheater to establish a temperature gradient along the structure which will be affected by any local variations in thermal conductivity. The impact on the thermal gradient and consequently on the tip temperature is modelled using finite element computer simulations. Experimental changes as small as 7.5% are shown to be detectable in this way. Despite the experimental technique being shown to be able to detect thermal changes far smaller than those predicted by the modelling, no modifications of the thermal conductivity are detected. It is concluded that in order to realise the effects of phononic resonators to reduce thermal conductivity, that much smaller structures with a greater ratio of resonator to shaft will be needed

Controlling the half-metallicity of Heusler/Si(1 1 1) interfaces by a monolayer of Si–Co–Si

By using first-principles calculations we show that the spin-polarization reverses its sign at atomically abrupt interfaces between the half-metallic Co₂ (Fe,Mn)(Al,Si) and Si(1 1 1). This unfavourable spin-electronic configuration at the Fermi-level can be completely removed by introducing a Si–Co–Si monolayer at the interface. In addition, this interfacial monolayer shifts the Fermi-level from the valence band edge close to the conduction band edge of Si. We show that such a layer is energetically favourable to exist at the interface. This was further confirmed by direct observations of CoSi₂ nano-islands at the interface, by employing atomic resolution scanning transmission electron microscopy

The role of chemical structure on the magnetic and electronic properties of Co2FeAl0.5Si0.5/Si(111) interface

We show that Co2FeAl0.5Si0.5 film deposited on Si(111) has a single crystal structure and twin related epitaxial relationship with the substrate. Sub-nanometer electron energy loss spectroscopy shows that in a narrow interface region there is a mutual inter-diffusion dominated by Si and Co. Atomic resolution aberration-corrected scanning transmission electron microscopy reveals that the film has B2 ordering. The film lattice structure is unaltered even at the interface due to the substitu- tional nature of the intermixing. First-principles calculations performed using structural models based on the aberration corrected electron microscopy show that the increased Si incorporation in the film leads to a gradual decrease of the magnetic moment as well as significant spin-polarization reduction. These effects can have significant detrimental role on the spin injection from the Co2FeAl0.5Si0.5 film into the Si substrate, besides the structural integrity of this junction

Theory of momentum-resolved magnon electron energy loss spectra: The case of Yttrium Iron Garnet

We explore the inelastic spectra of electrons impinging in a magnetic system. The methodology here presented is intended to highlight the charge-dependent interaction of the electron beam in a STEM-EELS experiment, and the local vector potential generated by the magnetic lattice. This interaction shows an intensity $10^{-2}$ smaller than the purely spin interaction, which is taken to be functionally the same as in the inelastic neutron experiment. On the other hand, it shows a strong scattering vector dependence ($\kappa^{-4}$) and a dependence with the relative orientation between the probe wavevector and the local magnetic moments of the solid. We present YIG as a case study due to its high interest by the community