86 research outputs found
Signatures of Discontinuity in the Exchange-Correlation Energy Functional Derived from the Subband Electronic Structure of Semiconductor Quantum Wells
The discontinuous character of the exact exchange-correlation energy
functional of Density Functional Theory is shown to arise naturally in the
subband spectra of semiconductor quantum wells. Using an \emph{ab-initio}
functional, including exchange exactly and correlation in an exact partial way,
a discontinuity appears in the potential, each time a subband becomes
slightly occupied. Exchange and correlation give opposite contributions to the
discontinuity, with correlation overcoming exchange. The jump in the
intersubband energy is in excellent agreement with experimental data.Comment: 5 pages, 3 figure
Pseudospin anisotropy of trilayer semiconductor quantum Hall ferromagnets
When two Landau levels are brought to a close coincidence between them and
with the chemical potential in the Integer Quantum Hall regime, the two Landau
levels can just cross or collapse while the external or pseudospin field that
induces the alignment changes. In this work, all possible crossings are
analyzed theoretically for the particular case of semiconductor trilayer
systems, using a variational Hartree-Fock approximation. The model includes
tunneling between neighboring layers, bias, intra-layer and inter-layer Coulomb
interaction among the electrons. We have found that the general pseudospin
anisotropy classification scheme used in bilayers applies also to the trilayer
situation, with the simple crossing corresponding to an easy-axis ferromagnetic
anisotropy analogy, and the collapse case corresponding to an easy-plane
ferromagnetic analogy. An isotropic case is also possible, with the levels just
crossing or collapsing depending on the filling factor and the quantum numbers
of the two nearby levels. While our results are valid for any integer filling
factor (=1,2,3,...), we have analyzed in detail the crossings at
and , and we have given clear predictions that will help in their
experimental search. In particular, the present calculations suggest that by
increasing the bias, the trilayer system at these two filling factors can be
driven from an easy-plane anisotropy regime to an easy-axis regime, and then
can be driven back to the easy-plane regime. This kind of reentrant behavior is
an unique feature of the trilayers, compared with the bilayers
Coulomb and tunneling coupled trilayer systems at zero magnetic field
The ground-state electronic configuration of three coupled bidimensional
electron gases has been determined using a variational Hartree-Fock approach,
at zero magnetic field. The layers are Coulomb coupled, and tunneling is
present between neighboring layers. In the limit of small separation between
layers, the tunneling becomes the dominant energy contribution, while for large
distance between layers the physics is driven by the Hartree electrostatic
energy. Transition from tunneling to hartree dominated physics is shifted
towards larger layer separation values as the total bidimensional density of
the trilayers decreases. The inter-layer exchange helps in stabilize a
"balanced" configuration, where the three layers are approximately equally
occupied; most of the experiments are performed in the vicinity of this
balanced configuration. Several ground-state configurations are consequence of
a delicate interplay between tunneling and inter-subband exchange
Position-dependent exact-exchange energy for slabs and semi-infinite jellium
The position-dependent exact-exchange energy per particle
(defined as the interaction between a given electron at and its
exact-exchange hole) at metal surfaces is investigated, by using either jellium
slabs or the semi-infinite (SI) jellium model. For jellium slabs, we prove
analytically and numerically that in the vacuum region far away from the
surface , {\it
independent} of the bulk electron density, which is exactly half the
corresponding exact-exchange potential [Phys.
Rev. Lett. {\bf 97}, 026802 (2006)] of density-functional theory, as occurs in
the case of finite systems. The fitting of
to a physically motivated image-like expression is feasible, but the resulting
location of the image plane shows strong finite-size oscillations every time a
slab discrete energy level becomes occupied. For a semi-infinite jellium, the
asymptotic behavior of is somehow different.
As in the case of jellium slabs has
an image-like behavior of the form , but now with a
density-dependent coefficient that in general differs from the slab universal
coefficient 1/2. Our numerical estimates for this coefficient agree with two
previous analytical estimates for the same. For an arbitrary finite thickness
of a jellium slab, we find that the asymptotic limits of
and only
coincide in the low-density limit (), where the
density-dependent coefficient of the semi-infinite jellium approaches the slab
{\it universal} coefficient 1/2.Comment: 26 pages, 7 figures, to appear in Phys. Rev.
Kohn-Sham Exchange Potential for a Metallic Surface
The behavior of the surface barrier that forms at the metal-vacuum interface
is important for several fields of surface science. Within the Density
Functional Theory framework, this surface barrier has two non-trivial
components: exchange and correlation. Exact results are provided for the
exchange component, for a jellium metal-vacuum interface, in a slab geometry.
The Kohn-Sham exact-exchange potential has been generated by using
the Optimized Effective Potential method, through an accurate numerical
solution, imposing the correct boundary condition. It has been proved
analytically, and confirmed numerically, that ; this conclusion is not affected by the inclusion of correlation
effects. Also, the exact-exchange potential develops a shoulder-like structure
close to the interface, on the vacuum side. The issue of the classical image
potential is discussed.Comment: Phys. Rev. Lett. (to appear
Universal correction for the Becke-Johnson exchange potential
The Becke-Johnson exchange potential [J. Chem. Phys. 124, 221101 (2006)] has
been successfully used in electronic structure calculations within
density-functional theory. However, in its original form the potential may
dramatically fail in systems with non-Coulombic external potentials, or in the
presence of external magnetic or electric fields. Here, we provide a
system-independent correction to the Becke-Johnson approximation by (i)
enforcing its gauge invariance and (ii) making it exact for any single-electron
system. The resulting approximation is then better designed to deal with
current-carrying states, and recovers the correct asymptotic behavior for
systems with any number of electrons. Tests of the resulting corrected exchange
potential show very good results for a Hydrogen chain in an electric field and
for a four-electron harmonium in a magnetic field
- …