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Register a new userEnergy density in density functional theory: Application to crystalline defects and surfaces
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We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.
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We present a real-space formulation and implementation of Kohn-Sham Density Functional Theory suited to twisted geometries, and apply it to the study of torsional deformations of X (X = C, Si, Ge, Sn) nanotubes. Our formulation is based on higher order finite difference discretization in helical coordinates, uses ab intio pseudopotentials, and naturally incorporates rotational (cyclic) and screw operation (i.e., helical) symmetries. We discuss several aspects of the computational method, including the form of the governing equations, details of the numerical implementation, as well as its convergence, accuracy and efficiency properties. The technique presented here is particularly well suited to the first principles simulation of quasi-one-dimensional structures and their deformations, and many systems of interest can be investigated using small simulation cells containing just a few atoms. We apply the method to systematically study the properties of single-wall zigzag and armchair group-IV nanotubes, as they undergo twisting. For the range of deformations considered, the mechanical behavior of the tubes is found to be largely consistent with isotropic linear elasticity, with the torsional stiffness varying as the cube of the nanotube radius. Furthermore, for a given tube radius, this quantity is seen to be highest for carbon nanotubes and the lowest for those of tin, while nanotubes of silicon and germanium have intermediate values close to each other. We also describe different aspects of the variation in electronic properties of the nanotubes as they are twisted. In particular, we find that akin to the well known behavior of armchair carbon nanotubes, armchair nanotubes of silicon, germanium and tin also exhibit bandgaps that vary periodically with imposed rate of twist, and that the periodicity of the variation scales in an inverse quadratic manner with the tube radius.
The electronic structure of surfaces plays a key role in the properties of quantum devices. However, surfaces are also the most challenging to simulate and engineer. Here, we study the electronic structure of InAs(001), InAs(111), and InSb(110) surfaces using a combination of density functional theory (DFT) and angle-resolved photoemission spectroscopy (ARPES). We were able to perform large-scale first principles simulations and capture effects of different surface reconstructions by using DFT calculations with a machine-learned Hubbard U correction [npj Comput. Mater. 6, 180 (2020)]. To facilitate direct comparison with ARPES results, we implemented a bulk unfolding scheme by projecting the calculated band structure of a supercell surface slab model onto the bulk primitive cell. For all three surfaces, we find a good agreement between DFT calculations and ARPES. For InAs(001), the simulations clarify the effect of the surface reconstruction. Different reconstructions are found to produce distinctive surface states. For InAs(111) and InSb(110), the simulations help elucidate the effect of oxidation. Owing to larger charge transfer from As to O than from Sb to O, oxidation of InAs(111) leads to significant band bending and produces an electron pocket, whereas oxidation of InSb(110) does not. Our combined theoretical and experimental results may inform the design of quantum devices based on InAs and InSb semiconductors, e.g., topological qubits utilizing the Majorana zero modes.
A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a gradient of density is zero. As the gradient increases, the energy is diminished by a gradient suppressing factor, designed to attenuate the energy from its maximum value similar to the shape of a bell curve. Based on this behavior, we constructed a very simple mathematical formula that predicted the correlation energy of atoms and molecules. Combined with our proposed exchange energy functional, we calculated the correlation energies, the total energies, and the ionization energies of test atoms and molecules; and despite the unique simplicities, the functionals accuracies are in the top tier performance, competitive to the B3LYP, BLYP, PBE, TPSS, and M11. Therefore, we propose that, as guided by the simplicities and supported by the accuracies, the correlation energy is the energy that locally tends to drive the system toward the uniform electron gas.
We propose a new method for accurately calculating electrical transport properties of a lightly-doped thermoelectric material from density functional theory (DFT) calculations, based on experimental data and density functional theory results for the corresponding undoped material. We employ this approach because hybrid DFT calculations are prohibitive for the large supercells required to model low dopant concentrations comparable to those achieved experimentally for high-performing thermoelectrics. Using zinc antimonide as our base material, we find that the electrical transport properties calculated with DFT and Boltzmann transport theory exhibit the same trends with changes in chemical potential as those computed with hybrid DFT, and propose a fitting algorithm that involves adjusting the computed Fermi energy so that the resulting Seebeck coefficient trends with temperature match experimental trends. We confirm the validity of this approach in reproducing the experimental trends in electrical conductivity and Seebeck coefficient versus temperature for Bi-doped $beta-$Zn$_4$Sb$_3$. We then screen various transition metal cation dopants, including copper and nickel, and find that a Cu dopant concentration of 2.56% in Zn$_{39}$Sb$_{30}$ exhibited a 14% increase in the thermoelectric power factor for temperatures between 300-400 K. We thus propose that transition metal dopants may significantly improve the thermoelectric performance of the host material, compared to heavy and/or rare-earth dopants.
A magnetic skyrmion observed experimentally in chiral magnets is a topologically protected spin texture. For their unique properties, such as high mobility under current drive, skyrmions have huge potential for applications in next-generation spintronic devices. Defects naturally occurring in magnets have profound effects on the static and dynamical properties of skyrmions. In this work, we study the effect of an atomic defect on a skyrmion using the first-principles calculations within the density functional theory, taking MnSi as an example. By substituting one site of Mn or Si with different elements, we can tune the pinning energy. The effects of pinning by an atomic defect can be understood qualitatively within a phenomenological model.
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