arXiv subjects

David Vanderbilt

Publications and source records attributed to David Vanderbilt.

At least 163 records · Page 9Linked to original sources

arXiv2008

First-principles modeling of strain in perovskite ferroelectric thin films

We review the role that first-principles calculations have played in understanding the effects of substrate-imposed misfit strain on epitaxially grown perovskite ferroelectric films. We do so by analyzing the case of BaTiO$_3$, complementing our previous publications on this subject with unpublished data to help explain in detail how these calculations are done. We also review similar studies in the literature for other perovskite ferroelectric-film materials.

cond-mat.mtrl-sci↗

arXiv2008

Dichroic f-sum rule and the orbital magnetization of crystals

We consider the magnetic circular dichroism spectrum of a crystal with broken time-reversal symmetry in the electric-dipole approximation. Using the Kubo-Greenwood formula for the absorptive part of the antisymmetric optical conductivity, its frequency integral is recast as a ground-state property. We show that in insulators this quantity is proportional to the circulation of the occupied Wannier orbitals around their centers (more precisely, to the gauge-invariant part thereof). This differs from the net circulation, or ground state orbital magnetization, which has two additional contributions: (i) the remaining Wannier self-rotation, and (ii) the ``itinerant'' circulation arising from the center-of-mass motion of the Wannier orbitals, both on the surface and in the interior of the sample. Contributions (i) and (ii) are not separately meaningful, since their individual values depend on the particular choice of Wannier functions. Their sum is however gauge-invariant, and can be inferred from a combination of two experiments: a measurement of the magneto-optical spectrum over a sufficiently wide range to evaluate the sum rule, and a gyromagnetic determination of the total orbital magnetization.

cond-mat.mtrl-sci↗

arXiv2007

Fermi-surface calculation of the anomalous Hall conductivity

While the intrinsic anomalous Hall conductivity is normally written in terms of an integral of the electronic Berry curvature over the occupied portions of the Brillouin zone, Haldane has recently pointed out that this quantity (or more precisely, its ``non-quantized part'') may alternatively be expressed as a Fermi-surface property. Here we present an {\it ab-initio} approach for computing the anomalous Hall conductivity that takes advantage of this observation by converting the integral over the Fermi sea into a more efficient integral on the Fermi surface only. First, a conventional electronic-structure calculation is performed with spin-orbit interaction included. Maximally-localized Wannier functions are then constructed by a post-processing step in order to convert the {\it ab-initio} electronic structure around the Fermi level into a tight-binding-like form. Working in the Wannier representation, the Brillouin zone is sampled on a large number of equally spaced parallel slices oriented normal to the total magnetization. On each slice, we find the intersections of the Fermi-surface sheets with the slice by standard contour methods, organize these into a set of closed loops, and compute the Berry phases of the Bloch states as they are transported around these loops. The anomalous Hall conductivity is proportional to the sum of the Berry phases of all the loops on all the slices. Illustrative calculations are performed for Fe, Co and Ni.

cond-mat.mtrl-sci↗

arXiv2007

Ab initio calculations of BaTiO3 and PbTiO3 (001) and (011) surface structure

We present and discuss the results of calculations of surface relaxations and rumplings for the (001) and (011) surfaces of BaTiO3 and PbTiO3, using a hybrid B3PW description of exchange and correlation. On the (001) surfaces, we consider both AO (A = Ba or Pb) and TiO2 terminations. In the former case, the surface AO layer is found to relax inward for both materials, while outward relaxations of all atoms in the second layer are found at both kinds of (001) terminations and for both materials. The surface relaxation energies of BaO and TiO2 terminations on BaTiO3 (001) are found to be comparable, as are those of PbO and TiO2 on PbTiO3 (001), although in both cases the relaxation energy is slightly larger for the TiO2 termination. As for the (011) surfaces, we consider three types of surfaces, terminating on a TiO layer, a Ba or Pb layer, or an O layer. Here, the relaxation energies are much larger for the TiO-terminated than for the Ba or Pb-terminated surfaces. The relaxed surface energy for the O-terminated surface is about the same as the corresponding average of the TiO and Pb-terminated surfaces on PbTiO3, but much less than the average of the TiO and Ba-terminated surfaces on BaTiO3. We predict a considerable increase of the Ti-O chemical bond covalency near the BaTiO3 and PbTiO3 (011) surface as compared to both the bulk and the (001) surface.

cond-mat.mtrl-sci↗

arXiv2007

Theoretical study of ferroelectric potassium nitrate

We present a detailed study of the structural behavior and polarization reversal mechanism in phase III of KNO$_3$, an unusual ferroelectric material in which the nitrate groups rotate during polarization reversal. This material was one of several studied in a previous work [O. Diéguez and D. Vanderbilt, Phys. Rev. Lett. {\bf 96}, 056401 (2006)] where methods were described for computing curves of energy versus electric polarization. In the present work we extend and systematize the previous first-principles calculations on KNO$_3$, and analyze in detail a two-parameter model in which the energy of the system is written as a low-order expansion in the polarization and the nitrate group orientation. We confirm that this model reproduces the first-principles results for KNO$_3$ very well and construct its parameter-space phase diagram, describing regions where unusual triple-well potentials appear. We also present first-principles calculations of KNO$_3$ under pressure, finding that its energy-versus-polarization curves change character by developing a first-derivative discontinuity at zero polarization.

cond-mat.mtrl-sci↗

arXiv2007

Suppressed dependence of polarization on epitaxial strain in highly polar ferroelectrics

A combined experimental and computational investigation of coupling between polarization and epitaxial strain in highly polar ferroelectric PbZr_0.2Ti_0.8O_3 (PZT) thin films is reported. A comparison of the properties of relaxed (tetragonality c/a = 1.05) and highly-strained (c/a = 1.09) epitaxial films shows that polarization, while being amongst the highest reported for PZT or PbTiO_3 in either film or bulk forms (P_r = 82 microC/cm^2), is almost independent of the epitaxial strain. We attribute this behavior to a suppressed sensitivity of the A-site cations to epitaxial strain in these Pb-based perovskites, where the ferroelectric displacements are already large, contrary to the case of less polar perovskites, such as BaTiO_3. In the latter case, the A-site cation (Ba) and equatorial oxygen displacements can lead to substantial polarization increases.

cond-mat.mtrl-sci↗

arXiv2007

Spectral and Fermi surface properties from Wannier interpolation

We present an efficient first-principles approach for calculating Fermi surface averages and spectral properties of solids, and use it to compute the low-field Hall coefficient of several cubic metals and the magnetic circular dichroism of iron. The first step is to perform a conventional first-principles calculation and store the low-lying Bloch functions evaluated on a uniform grid of k-points in the Brillouin zone. We then map those states onto a set of maximally-localized Wannier functions, and evaluate the matrix elements of the Hamiltonian and the other needed operators between the Wannier orbitals, thus setting up an ``exact tight-binding model.'' In this compact representation the k-space quantities are evaluated inexpensively using a generalized Slater-Koster interpolation. Because of the strong localization of the Wannier orbitals in real space, the smoothness and accuracy of the k-space interpolation increases rapidly with the number of grid points originally used to construct the Wannier functions. This allows k-space integrals to be performed with ab-initio accuracy at low cost. In the Wannier representation, band gradients, effective masses, and other k-derivatives needed for transport and optical coefficients can be evaluated analytically, producing numerically stable results even at band crossings and near weak avoided crossings.

cond-mat.mtrl-sci↗

arXiv2007

Theoretical phase diagram of ultrathin films of incipient ferroelectrics

We have used a first-principles-based scheme to compute the temperature-versus-misfit strain ``Pertsev'' phase diagram of ultrathin films of {\sl incipient} ferroelectric KTaO$_3$. Our results suggest that, at variance with the bulk material, KTaO$_3$ ultrathin films cannot be described as quantum paraelectrics. Rather, the behavior of the films is largely determined by surface/interface effects that favor ferroelectricity and the imperfect screening of the depolarizing fields. This leads to Pertsev phase diagrams that are qualitatively similar to those of {\sl normal} ferroelectrics such as BaTiO$_3$.

cond-mat.mtrl-sci↗

arXiv2006

First-principles perturbative computation of dielectric and Born charge tensors in finite electric fields

We present a perturbative treatment of the response properties of insulating crystals under a dc bias field, and use this to study the effects of such bias fields on the Born effective charge tensor and dielectric tensor of insulators. We start out by expanding a variational field-dependent total-energy functional with respect to the electric field within the framework of density-functional perturbation theory. The second-order term in the expansion of the total energy is then minimized with respect to the first-order wave functions, from which the Born effective charge tensor and dielectric tensor are easily computed. We demonstrate an implementation of the method and perform illustrative calculations for the III-V semiconductors AlAs and GaAs under finite bias field.

cond-mat.mtrl-sci↗

arXiv2006

Nonlinear optics of III-V semiconductors in the terahertz regime: an ab-initio study

We compute from first principles the infrared dispersion of the nonlinear susceptibility $χ^{(2)}$ in zincblende semiconductors. At terahertz frequencies the nonlinear susceptibility depends not only on the purely electronic response $χ^{(2)}_{\infty}$, but also on three other parameters $C_1$, $C_2$ and $C_3$ describing the contributions from ionic motion. They relate to the TO Raman polarizability, the second-order displacement-induced dielectric polarization, and the third-order lattice potential. Contrary to previous theory, we find that mechanical anharmonicity ($C_3$) dominates over electrical anharmonicity ($C_2$), which is consistent with recent experiments on GaAs. We predict that the sharp minimum in the intensity of second-harmonic generation recently observed for GaAs between $ω_{\rm TO}/2$ and $ω_{\rm TO}$ does not occur for several other III-V compounds.

cond-mat.mtrl-sci↗

arXiv2006

First-principles study of polarization in ZnMgO

Wurtzite ZnO can be substituted with up to ~30% MgO to form a metastable ZnMgO alloy while still retaining the wurtzite structure. Because this alloy has a larger band gap than pure ZnO, ZnMgO/ZnO quantum wells and superlattices are of interest as candidates for applications in optoelectronic and electronic devices. Here, we report the results of an ab-initio study of the spontaneous polarization of ZnMgO alloys as a function of their composition. We perform calculations of the crystal structure based on density-functional theory in the local-density approximation, and the polarization is calculated using the Berry-phase approach. We decompose the changes in polarization into purely electronic, lattice-displacement mediated, and strain mediated components, and quantify the relative importance of these contributions. We consider both free-stress and epitaxialstrain elastic boundary conditions, and show that our results can be fairly well reproduced by a simple model in which the piezoelectric response of pure ZnO is used to estimate the polarization change of the ZnMgO alloy induced by epitaxial strain.

cond-mat.other↗

arXiv2006

The insulator/Chern-insulator transition in the Haldane model

We study the behavior of several physical properties of the Haldane model as the system undergoes its transition from the normal-insulator to the Chern-insulator phase. We find that the density matrix has exponential decay in both insulating phases, while having a power-law decay, more characteristic of a metallic system, precisely at the phase boundary. The total spread of the maximally-localized Wannier functions is found to diverge in the Chern-insulator phase. However, its gauge-invariant part, related to the localization length of Resta and Sorella, is finite in both insulating phases and diverges as the phase boundary is approached. We also clarify how the usual algorithms for constructing Wannier functions break down as one crosses into the Chern-insulator region of the phase diagram.

cond-mat.mes-hall↗

arXiv2006

Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation

The intrinsic anomalous Hall effect in ferromagnets depends on subtle spin-orbit-induced effects in the electronic structure, and recent ab-initio studies found that it was necessary to sample the Brillouin zone at millions of k-points to converge the calculation. We present an efficient first-principles approach for computing the anomalous Hall conductivity. We start out by performing a conventional electronic-structure calculation including spin-orbit coupling on a uniform and relatively coarse k-point mesh. From the resulting Bloch states, maximally-localized Wannier functions are constructed which reproduce the ab-initio states up to the Fermi level. The Hamiltonian and position-operator matrix elements, needed to represent the energy bands and Berry curvatures, are then set up between the Wannier orbitals. This completes the first stage of the calculation, whereby the low-energy ab-initio problem is transformed into an effective tight-binding form. The second stage only involves Fourier transforms and unitary transformations of the small matrices set up in the first stage. With these inexpensive operations, the quantities of interest are interpolated onto a dense k-point mesh and used to evaluate the anomalous Hall conductivity as a Brillouin zone integral. The present scheme, which also avoids the cumbersome summation over all unoccupied states in the Kubo formula, is applied to bcc Fe, giving excellent agreement with conventional, less efficient first-principles calculations. Remarkably, we find that more than 99% of the effect can be recovered by keeping a set of terms depending only on the Hamiltonian matrix elements, not on matrix elements of the position operator.

cond-mat.mtrl-sci↗

arXiv2006

Wannier-based definition of layer polarizations in perovskite superlattices

In insulators, the method of Marzari and Vanderbilt [Phys. Rev. B {\bf 56}, 12847 (1997)] can be used to generate maximally localized Wannier functions whose centers are related to the electronic polarization. In the case of layered insulators, this approach can be adapted to provide a natural definition of the local polarization associated with each layer, based on the locations of the nuclear charges and one-dimensional Wannier centers comprising each layer. Here, we use this approach to compute and analyze layer polarizations of ferroelectric perovskite superlattices, including changes in layer polarizations induced by sublattice displacements (i.e., layer-decomposed Born effective charges) and local symmetry breaking at the interfaces. The method provides a powerful tool for analyzing the polarization-related properties of complex layered oxide systems.

cond-mat.mtrl-sci↗

arXiv2006

Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals

We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern number, vanishes). Following the approach used recently to develop the single-band formalism [T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. {\bf 95}, 137205 (2005)], we work in the Wannier representation and find that the magnetization is comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior and an unexpected one arising from net currents carried by Wannier functions near the surface. Unlike the single-band case, where each of these contributions is separately gauge-invariant, in the multi-band formulation only the \emph{sum} of both terms is gauge-invariant. Our final expression for the orbital magnetization can be rewritten as a bulk property in terms of Bloch functions, making it simple to implement in modern code packages. The reciprocal-space expression is evaluated for 2d model systems and the results are verified by comparing to the magnetization computed for finite samples cut from the bulk. Finally, while our formal proof is limited to normal insulators, we also present a heuristic extension to Chern insulators (having nonzero Chern invariant) and to metals. The validity of this extension is again tested by comparing to the magnetization of finite samples cut from the bulk for 2d model systems. We find excellent agreement, thus providing strong empirical evidence in favor of the validity of the heuristic formula.

cond-mat.mtrl-sci↗

arXiv2006

Structural and dielectric properties of amorphous ZrO2 and HfO2

Zirconia (ZrO2) and hafnia (HfO2) are leading candidates for replacing SiO2 as the gate insulator in CMOS technology. Amorphous versions of these materials (a-ZrO2 and a-HfO2)) can be grown as metastable phases on top of a silicon buffer; while they tend to recrystallize during subsequent annealing steps, they would otherwise be of considerable interest because of the promise they hold for improved uniformity and electrical passivity. In this work, we report our theoretical studies of a-ZrO2 and a-HfO2 by first-principles density-functional methods. We construct realistic amorphous models using the ``activation-relaxation'' technique (ART) of Barkema and Mousseau. The structural, vibrational, and dielectric properties of the resulting models are analyzed in detail. The overall average dielectric constant is computed and found to be comparable to that of the monoclinic phase.

cond-mat.mtrl-sci↗

arXiv2006

First-Principles Perturbative Computation of Phonon Properties of Insulators in Finite Electric Fields

We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

cond-mat.mtrl-sci↗

arXiv2006

Importance of second-order piezoelectric effects in zincblende semiconductors

We show that the piezoelectric effect that describes the emergence of an electric field in response to a crystal deformation in III-V semiconductors such as GaAs and InAs has strong contributions from second-order effects that have been neglected so far. We calculate the second-order piezoelectric tensors using density functional theory and obtain the piezoelectric field for [111]-oriented In$_x$Ga$_{1-x}$As quantum wells of realistic dimensions and concentration $x$. We find that the linear and the quadratic piezoelectric coefficients have the opposite effect on the field, and for large strains the quadratic terms even dominate. Thus, the piezoelectric field turns out to be a rare example of a physical quantity for which the first- and second-order contributions are of comparable magnitude.

cond-mat.mtrl-sci↗