1,621 research outputs found
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.Comment: 12 pages, 9 figure
Density-functional investigation of the rhombohedral to simple cubic phase transition of arsenic
We report on our investigation of the crystal structure of arsenic under
compression, focusing primarily on the pressure-induced A7 to simple cubic (sc)
phase transition. The two-atom rhombohedral unit cell is subjected to pressures
ranging from 0 GPa to 200 GPa; for each given pressure, cell lengths and
angles, as well as atomic positions, are allowed to vary until the fully
relaxed structure is obtained. We find that the nearest and next-nearest
neighbor distances give the clearest indication of the occurrence of a
structural phase transition. Calculations are performed using the local density
approximation (LDA) and the PBE and PW91 generalized gradient approximations
(GGA-PBE and GGA-PW91) for the exchange-correlation functional. The A7 to sc
transition is found to occur at 21+/-1 GPa in the LDA, at 28+/-1 GPa in the
GGA-PBE and at 29+/-1 GPa in the GGA-PW91; no volume discontinuity is observed
across the transition in any of the three cases. We use k-point grids as dense
as 66X66X66 to enable us to present reliably converged results for the A7 to sc
transition of arsenic.Comment: To be published in Physical Review B; material supplementary to this
article is available at arXiv:0810.169
6 SCIENTIFIC HIGHLIGHT OF THE MONTH: ”First principles calculation of Solid-State NMR parameters” First principles calculation of Solid-State NMR parameters
The past decade has seen significant advances in the technique of nuclear magnetic resonance as applied to condensed phase systems. This progress has been driven by the development of sophisticated radio-frequency pulse sequences to manipulate nuclear spins, and by the availability of high-field spectrometers. During this period it has become possible to predict the major NMR observables using periodic first-principles techniques. Such calculations are now widely used in the solid-state NMR community. In this short article we aim to provide an overview of the capability and challenges of solid-state NMR. We summarise the key NMR parameters and how they may be calculated from first principles. Finally we outline the advantages of a joint experimental and computational approach to solid-state NMR.
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.Comment: 16 pages, 7 figure
A First Principles Theory of Nuclear Magnetic Resonance J-Coupling in solid-state systems
A method to calculate NMR J-coupling constants from first principles in
extended systems is presented. It is based on density functional theory and is
formulated within a planewave-pseudopotential framework. The all-electron
properties are recovered using the projector augmented wave approach. The
method is validated by comparison with existing quantum chemical calculations
of solution-state systems and with experimental data. The approach has been
applied to verify measured J-coupling in a silicophosphate structure,
Si5O(PO4)6Comment: 9 page
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 in zincblende semiconductors. At terahertz
frequencies the nonlinear susceptibility depends not only on the purely
electronic response , but also on three other parameters
, and 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 () dominates over
electrical anharmonicity (), 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 and
does not occur for several other III-V compounds.Comment: 9 pages, 3 figures; updated bibliograph
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.Comment: 12 pages, 7 figure
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