1,406 research outputs found
Orbital magnetization and Chern number in a supercell framework: Single k-point formula
The key formula for computing the orbital magnetization of a crystalline
system has been recently found [D. Ceresoli, T. Thonhauser, D. Vanderbilt, R.
Resta, Phys. Rev. B {\bf 74}, 024408 (2006)]: it is given in terms of a
Brillouin-zone integral, which is discretized on a reciprocal-space mesh for
numerical implementation. We find here the single -point limit, useful
for large enough supercells, and particularly in the framework of
Car-Parrinello simulations for noncrystalline systems. We validate our formula
on the test case of a crystalline system, where the supercell is chosen as a
large multiple of the elementary cell. We also show that--somewhat
counterintuitively--even the Chern number (in 2d) can be evaluated using a
single Hamiltonian diagonalization.Comment: 4 pages, 3 figures; appendix adde
Towards a bulk theory of flexoelectricity
Flexoelectricity is the linear response of polarization to a strain gradient.
Here we address the simplest class of dielectrics, namely elemental cubic
crystals, and we prove that therein there is no extrinsic (i.e. surface)
contribution to flexoelectricity in the thermodynamic limit. The flexoelectric
tensor is expressed as a bulk response of the solid, manifestly independent of
surface configurations. Furthermore, we prove that the flexoelectric responses
induced by a long-wavelength phonon and by a uniform strain gradient are
identical.Comment: 5 pages, 1 figure (2 panels
The Quantum-Mechanical Position Operator in Extended Systems
The position operator (defined within the Schroedinger representation in the
standard way) becomes meaningless when periodic boundary conditions are adopted
for the wavefunction, as usual in condensed matter physics. We show how to
define the position expectation value by means of a simple many-body operator
acting on the wavefunction of the extended system. The relationships of the
present findings to the Berry-phase theory of polarization are discussed.Comment: Four pages in RevTe
Electron Localization in the Insulating State
The insulating state of matter is characterized by the excitation spectrum,
but also by qualitative features of the electronic ground state. The insulating
ground wavefunction in fact: (i) sustains macroscopic polarization, and (ii) is
localized. We give a sharp definition of the latter concept, and we show how
the two basic features stem from essentially the same formalism. Our approach
to localization is exemplified by means of a two--band Hubbard model in one
dimension. In the noninteracting limit the wavefunction localization is
measured by the spread of the Wannier orbitals.Comment: 5 pages including 3 figures, submitted to PR
Density-functional theory of polar insulators
We examine the density-functional theory of macroscopic insulators, obtained in the large-cluster limit or under periodic boundary conditions. For polar crystals, we find that the two procedures are not equivalent. In a large-cluster case, the exact exchange-correlation potential acquires a homogeneous ``electric field'' which is absent from the usual local approximations, and the Kohn-Sham electronic system becomes metallic. With periodic boundary conditions, such a field is forbidden, and the polarization deduced from Kohn-Sham wavefunctions is incorrect even if the exact functional is used
Theory of Orbital Magnetization in Solids
In this review article, we survey the relatively new theory of orbital
magnetization in solids-often referred to as the "modern theory of orbital
magnetization"-and its applications. Surprisingly, while the calculation of the
orbital magnetization in finite systems such as atoms and molecules is straight
forward, in extended systems or solids it has long eluded calculations owing to
the fact that the position operator is ill-defined in such a context.
Approaches that overcome this problem were first developed in 2005 and in the
first part of this review we present the main ideas reaching from a Wannier
function approach to semi-classical and finite-temperature formalisms. In the
second part, we describe practical aspects of calculating the orbital
magnetization, such as taking k-space derivatives, a formalism for
pseudopotentials, a single k-point derivation, a Wannier interpolation scheme,
and DFT specific aspects. We then show results of recent calculations on Fe,
Co, and Ni. In the last part of this review, we focus on direct applications of
the orbital magnetization. In particular, we will review how properties such as
the nuclear magnetic resonance shielding tensor and the electron paramagnetic
resonance g-tensor can elegantly be calculated in terms of a derivative of the
orbital magnetization
Orbital magnetization in periodic insulators
Working in the Wannier representation, we derive an expression for the
orbital magnetization of a periodic insulator. The magnetization is shown to be
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.
Each contribution can be expressed as a bulk property in terms of Bloch
functions in a gauge-invariant way. Our expression is verified by comparing
numerical tight-binding calculations for finite and periodic samples.Comment: submitted to PRL; signs corrected in Eqs. (11), (12), (19), and (20
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.Comment: 14 pages, 8 figures. Fixed a typo in appendix
Strong-correlation effects in Born effective charges
Large values of Born effective charges are generally considered as reliable
indicators of the genuine tendency of an insulator towards ferroelectric
instability. However, these quantities can be very much influenced by strong
electron correlation and metallic behavior, which are not exclusive properties
of ferroelectric materials. In this paper we compare the Born effective charges
of some prototypical ferroelectrics with those of magnetic, non-ferroelectric
compounds using a novel, self-interaction free methodology that improves on the
local-density approximation description of the electronic properties. We show
that the inclusion of strong-correlation effects systermatically reduces the
size of the Born effective charges and the electron localization lengths.
Furthermore we give an interpretation of the Born effective charges in terms of
band energy structure and orbital occupations which can be used as a guideline
to rationalize their values in the general case.Comment: 10 pages, 4 postscript figure
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