1,873 research outputs found
The quantum-mechanical position operator and the polarization problem
The position operator (defined within Schroedinger representation as usual)
becomes meaningless when the usual Born-von Karman periodic boundary conditions
are adopted: this fact is at the root of the polarization problem. I show how
to define the position expectation value by means of rather peculiar many-body
(multiplicative) operator acting on the wavefunction of the extended system.
This definition can be regarded as the generalization of a precursor work,
apparently unrelated to the polarization problem. For uncorrelated electrons,
the present finding coincides with the so-called "single-point Berry phase"
formula, which can hardly be regarded as the approximation of a continuum
integral, and is computationally very useful for disordered systems.
Simulations which are based on this concept are being performed by several
groups.Comment: 10 pages, 1 embedded figure (in two panels). Presented at the Fifth
Williamsburg Workshop on First-Principles Calculations for Ferroelectric
First-principles modeling of electrostatically doped perovskite systems
Macroscopically, confined electron gases at polar oxide interfaces are
rationalized within the simple "polar catastrophe" model. At the microscopic
level, however, many other effects such as electric fields, structural
distortions and quantum-mechanical interactions enter into play. Here we show
how to bridge the gap between these two length scales, by combining the
accuracy of first-principles methods with the conceptual simplicity of model
Hamiltonian approaches. To demonstrate our strategy, we address the equilibrium
distribution of the compensating free carriers at polar LaAlO3/SrTiO3
interfaces. Remarkably, a model including only calculated bulk properties of
SrTiO3 and no adjustable parameters accurately reproduces our full
first-principles results. Our strategy provides a unified description of charge
compensation mechanisms in SrTiO3-based systems.Comment: 4 pages, 4 figures. Supplementary notes:
http://www.icmab.es/dmmis/leem/stengel/supp.pd
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
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
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
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
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