224 research outputs found
Auxiliary matrices on both sides of the equator
The spectra of previously constructed auxiliary matrices for the six-vertex
model at roots of unity are investigated for spin-chains of even and odd
length. The two cases show remarkable differences. In particular, it is shown
that for even roots of unity and an odd number of sites the eigenvalues contain
two linear independent solutions to Baxter's TQ-equation corresponding to the
Bethe ansatz equations above and below the equator. In contrast, one finds for
even spin-chains only one linear independent solution and complete strings. The
other main result is the proof of a previous conjecture on the degeneracies of
the six-vertex model at roots of unity. The proof rests on the derivation of a
functional equation for the auxiliary matrices which is closely related to a
functional equation for the eight-vertex model conjectured by Fabricius and
McCoy.Comment: 22 pages; 2nd version: one paragraph added in the conclusion and some
typos correcte
Analytic and geometric properties of photoinduced effects in noncentrosymmetric crystals: photovoltaic current and optical rectification
An original dispersion relation between the stationary coherent nonlinear
optical responses by current and polarisation is obtained. The dispersion
relation provides a new complimentary tool that can be employed to study
light-induced charge transport models and facilitate experimental data
analysis. It is shown that the origin of the coherent current and the
dc-polarisation induced in a noncentrosymmetric crystal under illumination is
related to the theory of the Berry phase and can be represented in terms of the
renormalised geometric potentials. This renormalisation originates from the
extra phase difference acquired by a carrier in the light field on the quantum
transition between the electronic bands. The gauge invariance of the
corresponding expressions for the current and the polarisation is demonstrated.Comment: 7 page
Surface potential at a ferroelectric grain due to asymmetric screening of depolarization fields
Nonlinear screening of electric depolarization fields, generated by a stripe
domain structure in a ferroelectric grain of a polycrystalline material, is
studied within a semiconductor model of ferroelectrics. It is shown that the
maximum strength of local depolarization fields is rather determined by the
electronic band gap than by the spontaneous polarization magnitude.
Furthermore, field screening due to electronic band bending and due to presence
of intrinsic defects leads to asymmetric space charge regions near the grain
boundary, which produce an effective dipole layer at the surface of the grain.
This results in the formation of a potential difference between the grain
surface and its interior of the order of 1 V, which can be of either sign
depending on defect transition levels and concentrations. Exemplary acceptor
doping of BaTiO3 is shown to allow tuning of the said surface potential in the
region between 0.1 and 1.3 V.Comment: 14 pages, 11 figures, submitted to J. Appl. Phy
Bethe roots and refined enumeration of alternating-sign matrices
The properties of the most probable ground state candidate for the XXZ spin
chain with the anisotropy parameter equal to -1/2 and an odd number of sites is
considered. Some linear combinations of the components of the considered state,
divided by the maximal component, coincide with the elementary symmetric
polynomials in the corresponding Bethe roots. It is proved that those
polynomials are equal to the numbers providing the refined enumeration of the
alternating-sign matrices of order M+1 divided by the total number of the
alternating-sign matrices of order M, for the chain of length 2M+1.Comment: LaTeX 2e, 12 pages, minor corrections, references adde
A possible combinatorial point for XYZ-spin chain
We formulate and discuss a number of conjectures on the ground state vectors
of the XYZ-spin chains of odd length with periodic boundary conditions and a
special choice of the Hamiltonian parameters. In particular, arguments for the
validity of a sum rule for the components, which describes in a sense the
degree of antiferromagneticity of the chain, are given.Comment: AMSLaTeX, 15 page
Finite size and intrinsic field effect on the polar-active properties of the ferroelectric-semiconductor heterostructures
Using Landau-Ginzburg-Devonshire approach we calculated the equilibrium
distributions of electric field, polarization and space charge in the
ferroelectric-semiconductor heterostructures containing proper or incipient
ferroelectric thin films. The role of the polarization gradient and intrinsic
surface energy, interface dipoles and free charges on polarization dynamics are
specifically explored. The intrinsic field effects, which originated at the
ferroelectric-semiconductor interface, lead to the surface band bending and
result into the formation of depletion space-charge layer near the
semiconductor surface. During the local polarization reversal (caused by the
inhomogeneous electric field induced by the nanosized tip of the Scanning Probe
Microscope (SPM) probe) the thickness and charge of the interface layer
drastically changes, it particular the sign of the screening carriers is
determined by the polarization direction. Obtained analytical solutions could
be extended to analyze polarization-mediated electronic transport.Comment: 35 pages, 12 figures, 1 table, 2 appendices, to be submitted to Phys.
Rev.
Domain wall conduction in multiaxial ferroelectrics
The conductance of domain wall structures consisting of either stripes or
cylindrical domains in multi-axial ferroelectric-semiconductors is analyzed.
The effects of the domain size, wall tilt and curvature, on charge
accumulation, are analyzed using the Landau-Ginsburg Devonshire (LGD) theory
for polarization combined with Poisson equation for charge distributions. Both
the classical ferroelectric parameters including expansion coefficients in
2-4-6 Landau potential and gradient terms, as well as flexoelectric coupling,
inhomogeneous elastic strains and electrostriction are included in the present
analysis. Spatial distributions of the ionized donors, free electrons and holes
were found self-consistently using the effective mass approximation for the
respective densities of states. The proximity and size effect of the electron
and donor accumulation/depletion by thin stripe domains and cylindrical
nanodomains are revealed. In contrast to thick domain stripes and thicker
cylindrical domains, in which the carrier accumulation (and so the static
conductivity) sharply increases at the domain walls only, small nanodomains of
radius less then 5-10 correlation length appeared conducting across entire
cross-section. Implications of such conductive nanosized channels may be
promising for nanoelectronics.Comment: 39 pages, 11 figures, 3 tables, 4 appendice
Static conductivity of charged domain wall in uniaxial ferroelectric-semiconductors
Using Landau-Ginzburg-Devonshire theory we calculated numerically the static
conductivity of both inclined and counter domain walls in the uniaxial
ferroelectrics-semiconductors of n-type. We used the effective mass
approximation for the electron and holes density of states, which is valid at
arbitrary distance from the domain wall. Due to the electrons accumulation, the
static conductivity drastically increases at the inclined head-to-head wall by
1 order of magnitude for small incline angles theta pi/40 by up 3 orders of
magnitude for the counter domain wall (theta=pi/2). Two separate regions of the
space charge accumulation exist across an inclined tail-to-tail wall: the thin
region in the immediate vicinity of the wall with accumulated mobile holes and
the much wider region with ionized donors. The conductivity across the
tail-to-tail wall is at least an order of magnitude smaller than the one of the
head-to-head wall due to the low mobility of holes, which are improper carries.
The results are in qualitative agreement with recent experimental data for
LiNbO3 doped with MgO.Comment: 20 pages, 6 figures, 1 appendi
Conductivity of twin walls - surface junctions in ferroelastics: interplay of deformation potential, octahedral rotations, improper ferroelectricity and flexoelectric coupling
Electronic and structural phenomena at the twin domain wall-surface junctions
in the ferroelastic materials are analyzed. Carriers accumulation caused by the
strain-induced band structure changes originated via the deformation potential
mechanism, structural order parameter gradient, rotostriction and flexoelectric
coupling is explored. Approximate analytical results show that inhomogeneous
elastic strains, which exist in the vicinity of the twin walls - surface
junctions due to the rotostriction coupling, decrease the local band gap via
the deformation potential and flexoelectric coupling mechanisms. This is the
direct mechanism of the twin walls static conductivity in ferroelastics and, by
extension, in multiferroics and ferroelectrics. On the other hand,
flexoelectric and rotostriction coupling leads to the appearance of the
improper polarization and electric fields proportional to the structural order
parameter gradient in the vicinity of the twin walls - surface junctions. The
"flexo-roto" fields leading to the carrier accumulation are considered as
indirect mechanism of the twin walls conductivity. Comparison of the direct and
indirect mechanisms illustrates complex range of phenomena directly responsible
for domain walls static conductivity in materials with multiple order
parameters.Comment: 35 pages, 11 figures, 3 table, 3 appendices Improved set of
rotostriction coefficients are used in calculation
Piezoresponse Force Spectroscopy of Ferroelectric Materials
Piezoresponse Force Spectroscopy (PFS) has emerged as a powerful technique
for probing highly localized switching behavior and the role of microstructure
and defects on switching. The application of a dc bias to a scanning probe
microscope tip in contact with a ferroelectric surface results in the
nucleation and growth of a ferroelectric domain below the tip, resulting in
changes in local electromechanical response. Resulting hysteresis loops
contains information on local ferroelectric switching behavior. The signal in
PFS is the convolution of the volume of the nascent domain and the probing
volume of the tip. Here, we analyze the signal formation mechanism in PFS by
deriving the main parameters of domain nucleation in a semi-infinite material
and establishing the relationships between domain parameters and PFM signal
using a linear Greens function theory. The effect of surface screening and
finite Debye length on the switching behavior is established. In particular, we
predict that the critical nucleus size in PFM is controlled by the surface
screening mechanism and in the absence of screening, tip-induced switching is
impossible. Future prospects of PFS to study domain nucleation in the vicinity
of defects, local switching centers in ferroelectrics, and unusual polarization
states in low-dimensional ferroelectrics are discussed.Comment: 74 pages, 18 figures, 3 appendices, sent to Phys. Rev.
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