skip to main content

Title: Ab initio electron-defect interactions using Wannier functions

Computing electron–defect (e–d) interactions from first principles has remained impractical due to computational cost. Here we develop an interpolation scheme based on maximally localized Wannier functions (WFs) to efficiently computee–d interaction matrix elements. The interpolated matrix elements can accurately reproduce those computed directly without interpolation and the approach can significantly speed up calculations ofe–d relaxation times and defect-limited charge transport. We show example calculations of neutral vacancy defects in silicon and copper, for which we compute thee–d relaxation times on fine uniform and random Brillouin zone grids (and for copper, directly on the Fermi surface), as well as the defect-limited resistivity at low temperature. Our interpolation approach opens doors for atomistic calculations of charge carrier dynamics in the presence of defects.

; ; ;
Award ID(s):
1642443 1750613
Publication Date:
Journal Name:
npj Computational Materials
Nature Publishing Group
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The interactions between solute atoms and crystalline defects such as vacancies, dislocations, and grain boundaries are essential in determining alloy properties. Here we present a general linear correlation between two descriptors of local electronic structures and the solute-defect interaction energies in binary alloys of body-centered-cubic (bcc) refractory metals (such as W and Ta) with transition-metal substitutional solutes. One electronic descriptor is the bimodality of thed-orbital local density of states for a matrix atom at the substitutional site, and the other is related to the hybridization strength between the valancesp-andd-bands for the same matrix atom. For a particular pair of solute-matrix elements, this linear correlation is valid independent of types of defects and the locations of substitutional sites. These results provide the possibility to apply local electronic descriptors for quantitative and efficient predictions on the solute-defect interactions and defect properties in alloys.

  2. Abstract

    As the use of spectral/hpelement methods, and high-order finite element methods in general, continues to spread, community efforts to create efficient, optimized algorithms associated with fundamental high-order operations have grown. Core tasks such as solution expansion evaluation at quadrature points, stiffness and mass matrix generation, and matrix assembly have received tremendous attention. With the expansion of the types of problems to which high-order methods are applied, and correspondingly the growth in types of numerical tasks accomplished through high-order methods, the number and types of these core operations broaden. This work focuses on solution expansion evaluation at arbitrary points within an element. This operation is core to many postprocessing applications such as evaluation of streamlines and pathlines, as well as to field projection techniques such as mortaring. We expand barycentric interpolation techniques developed on an interval to 2D (triangles and quadrilaterals) and 3D (tetrahedra, prisms, pyramids, and hexahedra) spectral/hpelement methods. We provide efficient algorithms for their implementations, and demonstrate their effectiveness using the spectral/hpelement libraryNektar++by running a series of baseline evaluations against the ‘standard’ Lagrangian method, where an interpolation matrix is generated and matrix-multiplication applied to evaluate a point at a given location. We present results from a rigorous seriesmore »of benchmarking tests for a variety of element shapes, polynomial orders and dimensions. We show that when the point of interest is to be repeatedly evaluated, the barycentric method performs at worst$$50\%$$50%slower, when compared to a cached matrix evaluation. However, when the point of interest changes repeatedly so that the interpolation matrix must be regenerated in the ‘standard’ approach, the barycentric method yields far greater performance, with a minimum speedup factor of$$7\times $$7×. Furthermore, when derivatives of the solution evaluation are also required, the barycentric method in general slightly outperforms the cached interpolation matrix method across all elements and orders, with an up to$$30\%$$30%speedup. Finally we investigate a real-world example of scalar transport using a non-conformal discontinuous Galerkin simulation, in which we observe around$$6\times $$6×speedup in computational time for the barycentric method compared to the matrix-based approach. We also explore the complexity of both interpolation methods and show that the barycentric interpolation method requires$${\mathcal {O}}(k)$$O(k)storage compared to a best case space complexity of$${\mathcal {O}}(k^2)$$O(k2)for the Lagrangian interpolation matrix method.

    « less
  3. Abstract

    Objective.Combined proton–photon treatments, where most fractions are delivered with photons and only a few are delivered with protons, may represent a practical approach to optimally use limited proton resources. It has been shown that, when organs at risk (OARs) are located within or near the tumor, the optimal multi-modality treatment uses protons to hypofractionate parts of the target volume and photons to achieve near-uniform fractionation in dose-limiting healthy tissues, thus exploiting the fractionation effect. These plans may be sensitive to range and setup errors, especially misalignments between proton and photon doses. Thus, we developed a novel stochastic optimization method to directly incorporate these uncertainties into the biologically effective dose (BED)-based simultaneous optimization of proton and photon plans.Approach.The method considers the expected valueEband standard deviationσbof the cumulative BEDbin every voxel of a structure. For the target, a piecewise quadratic penalty function of the formbminEb2σb+2is minimized, aiming for plans in which the expected BED minus two times the standard deviation exceeds the prescribed BEDbmin.Analogously,more »close=')' open='(' separators=''>Eb+2σbbmax+2is considered for OARs.Main results.Using a spinal metastasis case and a liver cancer patient, it is demonstrated that the novel stochastic optimization method yields robust combined treatment plans. Tumor coverage and a good sparing of the main OARs are maintained despite range and setup errors, and especially misalignments between proton and photon doses. This is achieved without explicitly considering all combinations of proton and photon error scenarios.Significance.Concerns about range and setup errors for safe clinical implementation of optimized proton–photon radiotherapy can be addressed through an appropriate stochastic planning method.

    « less
  4. Abstract

    In insulating crystals, it was previously shown that defects with two fewer dimensions than the bulk can bind topological electronic states. We here further extend the classification of topological defect states by demonstrating that the corners of crystalline defects with integer Burgers vectors can bind 0D higher-order end (HEND) states with anomalous charge and spin. We demonstrate that HEND states are intrinsic topological consequences of the bulk electronic structure and introduce new bulk topological invariants that are predictive of HEND dislocation states in solid-state materials. We demonstrate the presence of first-order 0D defect states in PbTe monolayers and HEND states in 3D SnTe crystals. We relate our analysis to magnetic flux insertion in insulating crystals. We find thatπ-flux tubes in inversion- and time-reversal-symmetric (helical) higher-order topological insulators bind Kramers pairs of spin-charge-separated HEND states, which represent observable signatures of anomalous surface half quantum spin Hall states.

  5. Abstract

    In the field of beam physics, two frontier topics have taken center stage due to their potential to enable new approaches to discovery in a wide swath of science. These areas are: advanced, high gradient acceleration techniques, and x-ray free electron lasers (XFELs). Further, there is intense interest in the marriage of these two fields, with the goal of producing a very compact XFEL. In this context, recent advances in high gradient radio-frequency cryogenic copper structure research have opened the door to the use of surface electric fields between 250 and 500 MV m−1. Such an approach is foreseen to enable a new generation of photoinjectors with six-dimensional beam brightness beyond the current state-of-the-art by well over an order of magnitude. This advance is an essential ingredient enabling an ultra-compact XFEL (UC-XFEL). In addition, one may accelerate these bright beams to GeV scale in less than 10 m. Such an injector, when combined with inverse free electron laser-based bunching techniques can produce multi-kA beams with unprecedented beam quality, quantified by 50 nm-rad normalized emittances. The emittance, we note, is the effective area in transverse phase space (x,px/mec) or (y,py/mec) occupied by the beam distribution, and it is relevant tomore »achievable beam sizes as well as setting a limit on FEL wavelength. These beams, when injected into innovative, short-period (1–10 mm) undulators uniquely enable UC-XFELs having footprints consistent with university-scale laboratories. We describe the architecture and predicted performance of this novel light source, which promises photon production per pulse of a few percent of existing XFEL sources. We review implementation issues including collective beam effects, compact x-ray optics systems, and other relevant technical challenges. To illustrate the potential of such a light source to fundamentally change the current paradigm of XFELs with their limited access, we examine possible applications in biology, chemistry, materials, atomic physics, industry, and medicine—including the imaging of virus particles—which may profit from this new model of performing XFEL science.

    « less