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Register a new userSystematic treatment of displacements, strains and electric fields in density-functional perturbation theory
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Xifan Wu Department ofn Physics
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The methods of density-functional perturbation theory may be used to calculate various physical response properties of insulating crystals including elastic, dielectric, Born charge, and piezoelectric tensors. These and other important tensors may be defined as second derivatives of the total energy with respect to atomic-displacement, electric-field, or strain perturbations, or as mixed derivatives with respect to two of these perturbations. The resulting tensor quantities tend to be coupled in complex ways in polar crystals, giving rise to a variety of variant definitions. For example, it is generally necessary to distinguish between elastic tensors defined under different electrostatic boundary conditions, and between dielectric tensors defined under different elastic boundary conditions. Here, we describe an approach for computing all of these various response tensors in a unified and systematic fashion. Applications are presented for two materials, wurtzite ZnO and rhombohedral BaTiO3, at zero temperature.
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The direct calculation of the elastic and piezoelectric tensors of solids can be accomplished by treating homogeneous strain within the framework of density-functional perturbation theory. By formulating the energy functional in reduced coordinates, we show that the strain perturbation enters only through metric tensors, and can be treated in a manner exactly paralleling the treatment of other perturbations. We present an analysis of the strain perturbation of the plane-wave pseudopotential functional, including the internal strain terms necessary to treat the atomic-relaxation contributions. Procedures for computationally verifying these expressions by comparison with numerical derivatives of ground-state calculations are described and illustrated.
The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto-)transport properties, or band extrema characteristics yielding carrier densities and density of states. Currently, these masses are usually calculated using finite-difference estimation of density functional theory (DFT) electronic band curvatures. However, finite differences require an additional convergence study and are prone to numerical noise. Moreover, the concept of effective mass breaks down at degenerate band extrema. We assess the former limitation by developing a method that allows to obtain the Hessian of DFT bands directly, using density functional perturbation theory (DFPT). Then, we solve the latter issue by adapting the concept of `transport equivalent effective mass to the $vec{k} cdot hat{vec{p}}$ framework. The numerical noise inherent to finite-difference methods is thus eliminated, along with the associated convergence study. The resulting method is therefore more general, more robust and simpler to use, which makes it especially appropriate for high-throughput computing. After validating the developed techniques, we apply them to the study of silicon, graphane, and arsenic. The formalism is implemented into the ABINIT software and supports the norm-conserving pseudopotential approach, the projector augmented-wave method, and the inclusion of spin-orbit coupling. The derived expressions also apply to the ultrasoft pseudopotential method.
The deviation of the electron density around the nuclei from spherical symmetry determines the electric field gradient (EFG), which can be measured by various types of spectroscopy. Nuclear Quadrupole Resonance (NQR) is particularly sensitive to the EFG. The EFGs, and by implication NQR frequencies, vary dramatically across materials. Consequently, searching for NQR spectral lines in previously uninvestigated materials represents a major challenge. Calculated EFGs can significantly aid at the search inception. To facilitate this task, we have applied high-throughput density functional theory calculations to predict EFGs for 15187 materials in the JARVIS-DFT database. This database, which will include EFG as a standard entry, is continuously increasing. Given the large scope of the database, it is impractical to verify each calculation. However, we assess accuracy by singling out cases for which reliable experimental information is readily available and compare them to the calculations. We further present a statistical analysis of the results. The database and tools associated with our work are made publicly available by JARVIS-DFT ( https://www.ctcms.nist.gov/~knc6/JVASP.html ) and NIST-JARVIS API ( http://jarvis.nist.gov ).
In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. The xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.
We present a constrained density functional perturbation theory scheme for the calculation of structural and harmonic vibrational properties of insulators in the presence of an excited and thermalized electron-hole plasma. The method is ideal to tame ultrafast light induced structural transitions in the regime where the photocarriers thermalize faster than the lattice, the electron-hole recombination time is longer than the phonon period and the photocarrier concentration is large enough to be approximated by an electron-hole plasma. The complete derivation presented here includes total energy, forces and stress tensor, variable cell structural optimization, harmonic vibrational properties and the electron-phonon interaction. We discuss in detail the case of zone center optical phonons not conserving the number of electrons and inducing a Fermi shift in the photo-electron and hole distributions. We validate our implementation by comparing with finite differences in Te and VSe2. By calculating the evolution of the phonon spectrum of Te, Si and GaAs as a function of the fluence of the incoming laser light, we demonstrate that even at low fluences, corresponding to approximately 0.1 photocarriers per cell, the phonon spectrum is substantially modified with respect to the ground state one with new Kohn anomalies appearing and a substantial softening of zone center optical phonons. Our implementation can be efficiently used to detect reversible transient phases and irreversible structural transition induced by ultrafast light absorption.
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