1,544 research outputs found
Residual Entropy of the Mott Insulator with No Symmetry Broken
The half-filled ground state of the Hubbard model on the hypercubic lattice
in D dimensions is studied by the Kondo-lattice theory, which is none other
than the 1/D expansion theory, but within the constrained Hilbert subspace
where no symmetry is allowed to be broken. A gap can open in the
single-particle excitation spectrum if and only if the residual entropy or
entropy at T=+0 K is nonzero. The Mott insulator with no symmetry broken, if it
is possible, is characterized by nonzero residual entropy or nonzero entropy at
T=+0 K. This conclusion is consistent with Brinkman and Rice's theory and the
dynamical mean-field theory. According to the well-known argument based on the
Bethe-ansatz solution, on the other hand, the half-filled ground state in one
dimension is the Mott insulator although its residual entropy per unit cell is
vanishing in the thermodynamic limit. Two possible explanations are given for
the contradiction between the present paper and the well-known argument.Comment: 27 page
Frustrated electron liquids in the Hubbard model
The ground state of the Hubbard model is studied within the constrained
Hilbert space where no order parameter exists. The self-energy of electrons is
decomposed into the single-site and multisite self-energies. The calculation of
the single-site self-energy is mapped to a problem of self-consistently
determining and solving the Anderson model. When an electron reservoir is
explicitly considered, it is proved that the single-site self-energy is that of
a normal Fermi liquid even if the multisite self-energy is anomalous. Thus, the
ground state is a normal Fermi liquid in the supreme single-site approximation
(S^3A). In the strong-coupling regime, the Fermi liquid is stabilized by the
Kondo effect in the S^3A and is further stabilized by the Fock-type term of the
superexchange interaction or the resonating-valence-bond (RVB) mechanism beyond
the S^3A. The stabilized Fermi liquid is frustrated as much as an RVB spin
liquid in the Heisenberg model. It is a relevant unperturbed state that can be
used to study a normal or anomalous Fermi liquid and an ordered state in the
whole Hilbert space by Kondo lattice theory. Even if higher-order multisite
terms than the Fock-type term are considered, the ground state cannot be a Mott
insulator. It can be merely a gapless semiconductor even if the multisite
self-energy is so anomalous that it is divergent at the chemical potential. A
Mott insulator is only possible as a high temperature phase.Comment: 11 pages, no figur
Valley Splitting Theory of SiGe/Si/SiGe Quantum Wells
We present an effective mass theory for SiGe/Si/SiGe quantum wells, with an
emphasis on calculating the valley splitting. The theory introduces a valley
coupling parameter, , which encapsulates the physics of the quantum well
interface. The new effective mass parameter is computed by means of a tight
binding theory. The resulting formalism provides rather simple analytical
results for several geometries of interest, including a finite square well, a
quantum well in an electric field, and a modulation doped two-dimensional
electron gas. Of particular importance is the problem of a quantum well in a
magnetic field, grown on a miscut substrate. The latter may pose a numerical
challenge for atomistic techniques like tight-binding, because of its
two-dimensional nature. In the effective mass theory, however, the results are
straightforward and analytical. We compare our effective mass results with
those of the tight binding theory, obtaining excellent agreement.Comment: 13 pages, 7 figures. Version submitted to PR
Rashba spin splitting in biased semiconductor quantum wells
Rashba spin splitting (RSS) in biased semiconductor quantum wells is
investigated theoretically based on the eight-band envelope function model. We
find that at large wave vectors, RSS is both nonmonotonic and anisotropic as a
function of in-plane wave vector, in contrast to the widely used linear and
isotropic model. We derive an analytical expression for RSS, which can
correctly reproduce such nonmonotonic behavior at large wave vectors. We also
investigate numerically the dependence of RSS on the various band parameters
and find that RSS increases with decreasing band gap and subband index,
increasing valence band offset, external electric field, and well width. Our
analytical expression for RSS provides a satisfactory explanation to all these
features.Comment: 5 pages, 4 figures, author names corrected, submitted to Phys. Rev.
Magnetic and charge structures in itinerant-electron magnets: Coexistence of multiple SDW and CDW
A theory of Kondo lattices is applied to studying possible magnetic and
charge structures of itinerant-electron antiferromagnets. Even helical spin
structures can be stabilized when the nesting of the Fermi surface is not sharp
and the superexchange interaction, which arises from the virtual exchange of
pair excitations across the Mott-Hubbard gap, is mainly responsible for
magnetic instability. Sinusoidal spin structures or spin density waves (SDW)
are only stabilized when the nesting of the Fermi surface is sharp enough and a
novel exchange interaction arising from that of pair excitations of
quasi-particles is mainly responsible for magnetic instability. In particular,
multiple SDW are stabilized when their incommensurate ordering wave-numbers
are multiple; magnetizations of different components
are orthogonal to each other in double and triple SDW when magnetic anisotropy
is weak enough. Unless are commensurate, charge density waves
(CDW) with coexist with SDW with . Because the
quenching of magnetic moments by the Kondo effect depends on local numbers of
electrons, the phase of CDW or electron densities is such that magnetic moments
are large where the quenching is weak. It is proposed that the so called stipe
order in cuprate-oxide high-temperature superconductors must be the coexisting
state of double incommensurate SDW and CDW.Comment: 10 pages, no figure
Resonant X-Ray Scattering from the Quadrupolar Ordering Phase of CeB_6
We theoretically investigate the origin of the resonant x-ray scattering
(RXS) signal near the Ce absorption edge in the quadrupolar ordering
phase of CeB, considering the intersite interaction between the
states in the initial state. The anisotropic charge distribution of the
states modulates the states through the intra-atomic Coulomb interaction
and thereby generates a large RXS superlattice intensity. The temperature and
magnetic field dependence indicates that the induced dipolar and octupolar
orders have little influence on the RXS spectra, in good agreement with the
recent experiment.Comment: 4 pages, 4 figure
Size Dependence In The Disordered Kondo Problem
We study here the role randomly-placed non-magnetic scatterers play on the
Kondo effect. We show that spin relaxation effects (with time )in the
vertex corrections to the Kondo self-energy lead to an exact cancellation of
the singular temperature dependence arising from the diffusion poles. For a
thin film of thickness and a mean-free path , disorder provides a
correction to the Kondo resistivity of the form
that explains both the disorder and sample-size depression of the Kondo effect
observed by Blachly and Giordano (PRB {\bf 51}, 12537 (1995)).Comment: 11 pages, LaTeX, 2 Postscript figure
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