3,655 research outputs found
The institutional embeddedness of social capital: a multilevel investigation across 24 European countries
Theory of spin-orbit coupling in bilayer graphene
Theory of spin-orbit coupling in bilayer graphene is presented. The
electronic band structure of the AB bilayer in the presence of spin-orbit
coupling and a transverse electric field is calculated from first-principles
using the linearized augmented plane wave method implemented in the WIEN2k
code. The first-principles results around the K points are fitted to a
tight-binding model. The main conclusion is that the spin-orbit effects in
bilayer graphene derive essentially from the single-layer spin-orbit coupling
which comes almost solely from the d orbitals. The intrinsic spin-orbit
splitting (anticrossing) around the K points is about 24\mu eV for the
low-energy valence and conduction bands, which are closest to the Fermi level,
similarly as in the single layer graphene. An applied transverse electric field
breaks space inversion symmetry and leads to an extrinsic (also called
Bychkov-Rashba) spin-orbit splitting. This splitting is usually linearly
proportional to the electric field. The peculiarity of graphene bilayer is that
the low-energy bands remain split by 24\mu eV independently of the applied
external field. The electric field, instead, opens a semiconducting band gap
separating these low-energy bands. The remaining two high-energy bands are
spin-split in proportion to the electric field; the proportionality coefficient
is given by the second intrinsic spin-orbit coupling, whose value is 20\mu eV.
All the band-structure effects and their spin splittings can be explained by
our tight-binding model, in which the spin-orbit Hamiltonian is derived from
symmetry considerations. The magnitudes of intra- and interlayer
couplings---their values are similar to the single-layer graphene ones---are
determined by fitting to first-principles results.Comment: 16 pages, 13 figures, 5 tables, typos corrected, published versio
Measurement of Electron-Optical Parameters for High-Resolution Electron Microscopy Image Interpretation
A method is presented to measure various electron-optical parameters needed for high-resolution electron microscopy image interpretation with high accuracy. The method is based on the measurement of a series of beam-tilt induced image displacements. The displacements are calculated via cross-correlation of the images, and subsequently fitted to a third-order polynomal in the beam tilt. From two series of images (using the x and y beam tilt coils), the spherical aberration constant of the microscope can be measured, as well as the current values of defocus, beam tilt and astigmatism. The spherical aberration constant of three Philips microscopes is measured with a precision better than 1 %, apart from calibration errors.The misalignment in the reference image (i.e. without induced beam tilt) can be measured with an absolute accuracy of 0.05 mrad, while the accuracy in the measured defocus value is 5 nm (at a magnification of 250,000). A computer is used to direct the experiments via remote control of the microscope and perform fast image processing to calculate the cross-correlations
Tetrahedral Symmetry in Ground- and Low-Lying States of Exotic A ~ 110 Nuclei
Recent theoretical calculations predict a possible existence of nuclei with
tetrahedral symmetry: more precisely, the mean-field hamiltonians of such
nuclei are symmetric with respect to double point-group Td. In this paper, we
focus on the neutron-rich Zirconium isotopes as an example and present
realistic mean-field calculations which predict tetrahedral ground-state
configurations in 108,110Zr and low-lying excited states of tetrahedral
symmetry in a number of N > 66 isotopes. The motivations for focusing on these
nuclei, as well as a discussion of the possible experimental signatures of
tetrahedral symmetry are also presented.Comment: Accepted in Phys. Rev. C - Rapid Communication
Nuclear Tetrahedral Symmetry: Possibly Present Throughout the Periodic Table
More than half a century after the fundamental, spherical shell structure in
nuclei has been established, theoretical predictions indicate that the
shell-gaps comparable or even stronger than those at spherical shapes may
exist. Group-theoretical analysis supported by realistic mean-field
calculations indicate that the corresponding nuclei are characterized by the
('double-tetrahedral') group of symmetry, exact or approximate. The
corresponding strong shell-gap structure is markedly enhanced by the existence
of the 4-dimensional irreducible representations of the group in question and
consequently it can be seen as a geometrical effect that does not depend on a
particular realization of the mean-field. Possibilities of discovering the
corresponding symmetry in experiment are discussed.Comment: 4 pages in LaTeX and 4 figures in eps forma
Invariant expansion for the trigonal band structure of graphene
We present a symmetry analysis of the trigonal band structure in graphene,
elucidating the transformational properties of the underlying basis functions
and the crucial role of time-reversal invariance. Group theory is used to
derive an invariant expansion of the Hamiltonian for electron states near the K
points of the graphene Brillouin zone. Besides yielding the characteristic
k-linear dispersion and higher-order corrections to it, this approach enables
the systematic incorporation of all terms arising from external electric and
magnetic fields, strain, and spin-orbit coupling up to any desired order.
Several new contributions are found, in addition to reproducing results
obtained previously within tight-binding calculations. Physical ramifications
of these new terms are discussed.Comment: 10 pages, 1 figure; expanded version with more details and additional
result
Effective calculation of LEED intensities using symmetry-adapted functions
The calculation of LEED intensities in a spherical-wave representation can be substantially simplified by symmetry relations. The wave field around each atom is expanded in symmetry-adapted functions where the local point symmetry of the atomic site applies. For overlayer systems with more than one atom per unit cell symmetry-adapted functions can be used when the division of the crystal into monoatomic subplanes is replaced by division into subplanes containing all symmetrically equivalent atomic positions
Spin Density Matrix of Spin-3/2 Hole Systems
For hole systems with an effective spin j=3/2, we present an invariant
decomposition of the spin density matrix that can be interpreted as a multipole
expansion. The charge density corresponds to the monopole moment and the spin
polarization due to a magnetic field corresponds to a dipole moment while heavy
hole-light hole splitting can be interpreted as a quadrupole moment. For quasi
two-dimensional hole systems in the presence of an in-plane magnetic field B
the spin polarization is a higher-order effect that is typically much smaller
than one even if the minority spin subband is completely depopulated. On the
other hand, the field B can induce a substantial octupole moment which is a
unique feature of j=3/2 hole systems.Comment: 8 pages, 1 figure, 3 table
Steady-state spin densities and currents
This article reviews steady-state spin densities and spin currents in
materials with strong spin-orbit interactions. These phenomena are intimately
related to spin precession due to spin-orbit coupling which has no equivalent
in the steady state of charge distributions. The focus will be initially on
effects originating from the band structure. In this case spin densities arise
in an electric field because a component of each spin is conserved during
precession. Spin currents arise because a component of each spin is continually
precessing. These two phenomena are due to independent contributions to the
steady-state density matrix, and scattering between the conserved and
precessing spin distributions has important consequences for spin dynamics and
spin-related effects in general. In the latter part of the article extrinsic
effects such as skew scattering and side jump will be discussed, and it will be
shown that these effects are also modified considerably by spin precession.
Theoretical and experimental progress in all areas will be reviewed
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