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We develop a formalism and a computational method to study polarons in insulators and semi-conductors from first principles. Unlike in standard calculations requiring large supercells, we solve a secular equation involving phonons and electron-phonon matrix elements from density-functional perturbation theory, in a spirit similar to the Bethe-Salpeter equation for excitons. We show that our approach describes seamlessly large and small polarons, and we illustrate its capability by calculating wavefunctions, formation energies, and spectral decomposition of polarons in LiF and Li2O2.
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We present a density functional theory (DFT) based supercell approach for modeling small polarons with proper account for the long-range elastic response of the material. Our analysis of the supercell dependence of the polaron properties (e.g., atomic structure, binding energy, and the polaron level) reveals long-range electrostatic effects and the electron-phonon interaction as the two main contributors. We develop a correction scheme for DFT polaron calculations that significantly reduces the dependence of polaron properties on the DFT exchange-correlation functional and the size of the supercell in the limit of strong electron-phonon coupling. Using our correction approach, we present accurate all-electron full-potential DFT results for small polarons in rocksalt MgO and rutile TiO$_2$.
The equation of state, structural behavior and phase stability of {alpha}-uranium have been investigated up to 1.3 TPa using density functional theory, adopting a simple description of electronic structure that neglects the spin-orbit coupling and strong electronic correlations. The comparison of the enthalpies of Cmcm (alpha-U), bcc, hcp, fcc, and bct predicts that the aplpha-U phase is stable up to a pressure of ~285 GPa, above which it transforms to a bct-U phase. The enthalpy differences between the bct and bcc phase decrease with pressure, but bcc is energetically unfavorable at least up to 1.3 TPa, the upper pressure limit of this study. The enthalpies of the close-packed hcp and fcc phases are 0.7 eV and 1.0 eV higher than that of the stable bct-U phase at a pressure of 1.3 TPa, supporting the wide stability field of the bcc phase. The equation of state, the lattice parameters and the anisotropic compression parameters are in good agreement with experiment up 100 GPa and previous theory. The elastic constants at the equilibrium volume of alpha-U confirm our bulk modulus. This suggests that our simplified description of electronic structure of uranium captures the relevant physics and may be used to describe bonding and other light actinides that show itinerant electronic behavior especially at high pressure.
We have given a summary on our theoretical predictions of three kinds of topological semimetals (TSMs), namely, Dirac semimetal (DSM), Weyl semimetal (WSM) and Node-Line Semimetal (NLSM). TSMs are new states of quantum matters, which are different with topological insulators. They are characterized by the topological stability of Fermi surface, whether it encloses band crossing point, i.e., Dirac cone like energy node, or not. They are distinguished from each other by the degeneracy and momentum space distribution of the nodal points. To realize these intriguing topological quantum states is quite challenging and crucial to both fundamental science and future application. In 2012 and 2013, Na$_3$Bi and Cd$_3$As$_2$ were theoretically predicted to be DSM, respectively. Their experimental verifications in 2014 have ignited the hot and intensive studies on TSMs. The following theoretical prediction of nonmagnetic WSM in TaAs family stimulated a second wave and many experimental works have come out in this year. In 2014, a kind of three dimensional crystal of carbon has been proposed to be NLSM due to negligible spin-orbit coupling and coexistence of time-reversal and inversion symmetry. Though the final experimental confirmation of NLSM is still missing, there have been several theoretical proposals, including Cu$_3$PdN from us. In the final part, we have summarized the whole family of TSMs and their relationship.
We develop a method for calculating the electron-phonon vertex in polar semiconductors and insulators from first principles. The present formalism generalizes the Frohlich vertex to the case of anisotropic materials and multiple phonon branches, and can be used either as a post-processing correction to standard electron-phonon calculations, or in conjunction with {it ab initio} interpolation based on maximally localized Wannier functions. We demonstrate this formalism by investigating the electron-phonon interactions in anatase TiO$_2$, and show that the polar vertex significantly reduces the electron lifetimes and enhances the anisotropy of the coupling. The present work enables {it ab initio} calculations of carrier mobilities, lifetimes, mass enhancement, and pairing in polar materials.
An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic - or higher order - potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated.
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