arXiv subjects
Publications and source records attributed to David Vanderbilt.
We present a novel method for the calculation of the static and electronic dielectric tensor of polar insulating crystals based on concepts from the modern theory of dielectric polarization. As an application, we present the first ab initio calculation of the dielectric constants in the wurtzite III-V nitrides AlN, GaN, and InN.
The spontaneous polarization, dynamical Born charges, and piezoelectric constants of the III-V nitrides AlN, GaN, and InN are studied ab initio using the Berry phase approach to polarization in solids. The piezoelectric constants are found to be up 10 times larger than in conventional III-V's and II-VI's, and comparable to those of ZnO. Further properties at variance with those of conventional III-V compounds are the sign of the piezoelectric constants (positive as in II-VI's) and the very large spontaneous polarization.
We investigate the physics of the core reconstruction and associated structural excitations (reconstruction defects and kinks) of dislocations in silicon, using a linear-scaling density-matrix technique. The two predominant dislocations (the 90-degree and 30-degree partials) are examined, focusing for the 90-degree case on the single-period core reconstruction. In both cases, we observe strongly reconstructed bonds at the dislocation cores, as suggested in previous studies. As a consequence, relatively low formation energies and high migration barriers are generally associated with reconstructed (dangling-bond-free) kinks. Complexes formed of a kink plus a reconstruction defect are found to be strongly bound in the 30-degree partial, while the opposite is true in the case of 90-degree partial, where such complexes are found to be only marginally stable at zero temperature with very low dissociation barriers. For the 30-degree partial, our calculated formation energies and migration barriers of kinks are seen to compare favorably with experiment. Our results for the kink energies on the 90-degree partial are consistent with a recently proposed alternative double-period structure for the core of this dislocation.
We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread sum_n [ _n - _n^2 ] of the Wannier functions in real space, our method proceeds directly from the Bloch functions as represented on a mesh of k-points, and carries out the minimization in a space of unitary matrices U_mn^k describing the rotation among the Bloch bands at each k-point. The method is thus suitable for use in connection with conventional electronic-structure codes. The procedure also returns the total electric polarization as well as the location of each Wannier center. Sample results for Si, GaAs, molecular C2H4, and LiCl will be presented.
We present self-consistent ab-initio total-energy and electronic-structure calculations on stoichiometric and non-stoichiometric TiO2 (110) surfaces. Scanning tunneling microscopy (STM) topographs are simulated by calculating the local electronic density of states over an energy window appropriate for the experimental positive-bias conditions. We find that under these conditions the STM tends to image the undercoordinated Ti atoms, in spite of the physical protrusion of the O atoms, giving an apparent reversal of topographic contrast on the stoichiometric 1x1 or missing-row 2x1 surface. We also show that both the interpretation of STM images and the direct comparison of surface energies favor an added-row structure over the missing-row structure for the oxygen-deficient 2x1 surface.
The theory of the macroscopic field appearing in the Kohn-Sham exchange-correlation potential for dielectric materials, as introduced by Gonze, Ghosez and Godby, is reexamined. It is shown that this Kohn-Sham field cannot be determined from a knowledge of the local state of the material (local crystal potential, electric field, and polarization) alone. Instead, it has an intrinsically nonlocal dependence on the global electrostatic configuration. For example, it vanishes in simple transverse configurations of a polarized dielectric, but not in longitudinal ones.
We suggest that the commonly-accepted core structure of the 90-degree partial dislocation in Si may not be correct, and propose instead a period-doubled structure. We present LDA, tight-binding, and classical Keating-model calculations, all of which indicate that the period-doubled structure is lower in energy. The new structure displays a broken mirror symmetry in addition to the period doubling, leading to a wide variety of possible soliton-like defects and kinks.
A new method is presented for performing first-principles molecular-dynamics simulations of systems with variable occupancies. We adopt a matrix representation for the one-particle statistical operator Gamma, to introduce a ``projected'' free energy functional G that depends on the Kohn-Sham orbitals only and that is invariant under their unitary transformations. The Liouville equation [ Gamma , H ] = 0 is always satisfied, guaranteeing a very efficient and stable variational minimization algorithm that can be extended to non-conventional entropic formulations or fictitious thermal distributions.
We extend our previous first-principles theory for perovskite ferroelectric phase transitions to treat also antiferrodistortive phase transitions. Our approach involves construction of a model Hamiltonian from a Taylor expansion, first-principles calculations to determine expansion parameters, and Monte Carlo simulations to study the resulting system. We apply this approach to three cubic perovskite compounds, SrTiO3, CaTiO3, and NaNbO3, that are known to undergo antiferrodistortive phase transitions. We calculate their transition sequences and transition temperatures at the experimental lattice constants. For SrTiO3, we find our results agree well with experiment. For more complicated compounds like CaTiO3 and NaNbO3, which can have many different structures with very similar energy, the agreement is somewhat less.
We have carried out first-principles total-energy calculations of (001) surfaces of the tetragonal and cubic phases of BaTiO3. Both BaO-terminated (type I) and TiO2-terminated (type II) surfaces are considered, and the atomic configurations have been fully relaxed. We found no deep-gap surface states for any of the surfaces, in agreement with previous theoretical studies. However, the gap is reduced for the type-II surface, especially in the cubic phase. The surface relaxation energies are found to be substantial, i.e., many times larger than the bulk ferroelectric well depth. Nevertheless, the influence of the surface upon the ferroelectric order parameter is modest; we find only a small enhancement of the ferroelectricity near the surface.
The strain induced by lattice mismatch at the interface is responsible for the different value of the band discontinuities observed recently for the AlN/GaN (AlN on GaN) and the GaN/AlN (GaN on AlN) polar (0001) interface. We present a first-principles calculation of valence band offsets, interface dipoles, strain-induced piezoelectric fields, relaxed geometric structure, and formation energies. Our results confirm the existence of a large forward-backward asymmetry for this interface.
Kink defects in the 90-degree partial dislocation in silicon are studied using a linear-scaling density-matrix technique. The asymmetric core reconstruction plays a crucial role, generating at least four distinct kink species as well as soliton defects. The energies and migration barriers of these entities are calculated and compared with experiment. As a result of certain low-energy kinks, a peculiar alternation of the core reconstruction is predicted. We find the solitons to be remarkably mobile even at very low temperature, and propose that they mediate the kink relaxation dynamics.
A first-principles study of the vibrational modes of PbTiO_3 in the ferroelectric tetragonal phase has been performed at all the main symmetry points of the Brillouin zone (BZ). The calculations use the local-density approximation and ultrasoft pseudopotentials with a plane-wave basis, and reproduce well the available experimental information on the modes at the Gamma point, including the LO-TO splittings. The work was motivated in part by a previously reported transition to an orthorhombic phase at low temperatures [(J. Kobayashi, Y. Uesu, and Y. Sakemi, Phys. Rev. B {\bf 28}, 3866 (1983)]. We show that a linear coupling of orthorhombic strain to one of the modes at Gamma plays a role in the discussion of the possibility of this phase transition. However, no mechanical instabilities (soft modes) are found, either at Gamma or at any of the other high-symmetry points of the BZ.
We calculate the transverse effective charges of zincblende compound semiconductors using Harrison's tight-binding model to describe the electronic structure. Our results, which are essentially exact within the model, are found to be in much better agreement with experiment than previous perturbation-theory estimates. Efforts to improve the results by using more sophisticated variants of the tight-binding model were actually less successful. The results underline the importance of including quantities that are sensitive to the electronic wavefunctions, such as the effective charges, in the fitting of tight-binding models.
Using path-integral Monte Carol simulations and an ab initio effective Hamiltonian, we study the effects of quantum fluctuations on structural phase transitions in the cubic perovskite compounds SrTiO3 and BaTiO3. We find quantum fluctuations affect ferroelectric (FE) transitions more strongly than antiferrodistortive (AFD) ones, even though the effective mass of a single FE local mode is larger. For SrTiO3 we find that the quantum fluctuations suppress the FE transition completely, and reduce the AFD transition temperature from 130K to 110K. For BaTiO3, quantum fluctuations do not affect the order of the transition, but do reduce the transition temperature by 35-50 K. The implications of the calculations are discussed.
We present a first-principles study of 180-degree ferroelectric domain walls in tetragonal barium titanate. The theory is based on an effective Hamiltonian that has previously been determined from first-principles ultrasoft-pseudopotential calculations. Statistical properties are investigated using Monte Carlo simulations. We compute the domain-wall energy, free energy, and thickness, analyze the behavior of the ferroelectric order parameter in the interior of the domain wall, and study its spatial fluctuations. An abrupt reversal of the polarization is found, unlike the gradual rotation typical of the ferromagnetic case.
We propose a systematic method of analyzing pseudopotential transferability based on linear-response properties of the free atom, including self-consistent chemical hardness and polarizability. Our calculation of hardness extends the approach of Teter\cite{teter} not only by including self-consistency, but also by generalizing to non-diagonal hardness matrices, thereby allowing us to test for transferability to non-spherically symmetric environments. We apply the method to study the transferability of norm-conserving pseudopotentials for a variety of elements in the Periodic Table. We find that the self-consistent corrections are frequently significant, and should not be neglected. We prove that the partial-core correction improves the pseudopotential hardness of alkali metals considerably. We propose a quantity to represent the average hardness error and calculate this quantity for many representative elements as a function of pseudopotential cutoff radii. We find that the atomic polarizabilities are usually well reproduced by the norm-conserving pseudopotentials. Our results provide useful guidelines for making optimal choices in the pseudopotential generation procedure.
We investigate the energetic ground states of a model two-phase system with 1/r^3 dipolar interactions in two dimensions. The model exhibits spontaneous formation of two kinds of periodic domain structure. A striped domain structure is stable near half filling, but as the area fraction is changed, a transition to a hexagonal lattice of almost-circular droplets occurs. The stability of the equilibrium striped domain structure against distortions of the boundary is demonstrated, and the importance of hexagonal distortions of the droplets is quantified. The relevance of the theory for physical surface systems with elastic, electrostatic, or magnetostatic 1/r^3 interactions is discussed.