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.