Tzanko Ivanov

Quadrupole terms in the Maxwell equations: Born energy, partial molar volume, and entropy of ions.

A new equation of state relating the macroscopic quadrupole moment density Q to the gradient of the field ∇E in an isotropic fluid is derived: Q = αQ(∇E - U∇·E/3), where the quadrupolarizability αQ is proportional to the squared molecular quadrupole moment. Using this equation of state, a generalized expression for the Born energy of an ion dissolved in quadrupolar solvent is obtained. It turns out that the potential and the energy of a point charge in a quadrupolar medium are finite. From the obtained Born energy, the partial molar volume and the partial molar entropy of a dissolved ion follow. Both are compared to experimental data for a large number of simple ions in aqueous solutions. From the comparison the value of the quadrupolar length LQ is determined, LQ = (αQ/3ɛ)(1/2) = 1-4 Å. Data for ion transfer from aqueous to polar oil solution are analyzed, which allowed for the determination of the quadrupolarizability of nitrobenzene.

The polarized interface between quadrupolar insulators: Maxwell stress tensor, surface tension, and potential.

The quadrupolar Maxwell electrostatic equations predict several qualitatively different results compared to Poissons classical equation in their description of the properties of a dielectric interface. All interfaces between dielectrics possess surface dipole moment which results in a measurable surface potential jump. The surface dipole moment is conjugated to the bulk quadrupole moment density (the quadrupolarization) similarly to Gausss relation between surface charge and bulk polarization. However, the classical macroscopic Maxwell equations completely neglect the quadrupolarization of the medium. Therefore, the electrostatic potential distribution near an interface of intrinsic dipole moment can be correctly described only within the quadrupolar macroscopic equations of electrostatics. They predict that near the polarized interface a diffuse dipole layer exists, which bears many similarities to the diffuse charge layer near a charged surface, in agreement with existing molecular dynamics simulation data. It turns out that when the quadrupole terms are kept in the multipole expansion of the laws of electrostatics, the solutions for the potential and the electric field are continuous functions at the surface. A well-defined surface electric field exists, interacting with the adsorbed dipoles. This allows for a macroscopic description of the surface dipole-surface dipole and the surface dipole-bulk quadrupole interactions. They are shown to have considerable contribution to the interfacial tension-of the order of tens of mN/m! To evaluate it, the Maxwell stress tensor in quadrupolar medium is deduced, including the electric field gradient action on the quadrupoles, as well as quadrupolar image force and quadrupolar electrostriction. The dependence of the interfacial tension on the external normal electric field (the dielectrocapillary curve) is predicted and the dielectric susceptibility of the dipolar double layer is related to the quadrupolarizabilities of the bulk phases and the intrinsic polarization of the interface. The coefficient of the dielectro-Marangoni effect (surface flow due to gradient of the normal electric field) is found. A model of the Langevin type for the surface dipole moment and the intrinsic surface polarizability is presented.

Effect of the surface polarizability on electrostatic screening in semiconductors

Following the Gibbs approach a general electrostatic model of heterogeneous systems with non-homogeneous interfaces is proposed. The intrinsic surface polarization is taken into account through the introduction of a surface dielectric constant and the electrostatic boundary conditions are generalized as two-dimensional Poisson equations. This model is applied to analysis of the electrostatic potential of charged defects on a semiconductor surface. As a result, a good theoretical fit of the experimental data is obtained. The fitting value of the surface dielectric constant is in good agreement with its theoretical estimation in the framework of the Gibbs approach.

t-J model in slave fermion formulation-holon-holon interactions

Abstract The slave fermion formulation of the t-J model is studied. The effective interaction between the fermionic holons, mediated by the bosonic spinons, is calculated. This interaction is attractive for the holon Cooper pairs and can lead to superconductivity with charged spinless fermions as current carriers.

A spherical cavity model for quadrupolar dielectrics

The dielectric properties of a fluid composed of molecules possessing both dipole and quadrupole moments are studied based on a model of the Onsager type (molecule in the centre of a spherical cavity). The dielectric permittivity ε and the macroscopic quadrupole polarizability αQ of the fluid are related to the basic molecular characteristics (molecular dipole, polarizability, quadrupole, quadrupolarizability). The effect of αQ is to increase the reaction field, to bring forth reaction field gradient, to decrease the cavity field, and to bring forth cavity field gradient. The effects from the quadrupole terms are significant in the case of small cavity size in a non-polar liquid. The quadrupoles in the medium are shown to have a small but measurable effect on the dielectric permittivity of several liquids (Ar, Kr, Xe, CH4, N2, CO2, CS2, C6H6, H2O, CH3OH). The theory is used to calculate the macroscopic quadrupolarizabilities of these fluids as functions of pressure and temperature. The cavity radii are also determined for these liquids, and it is shown that they are functions of density only. This extension of Onsagers theory will be important for non-polar solutions (fuel, crude oil, liquid CO2), especially at increased pressures.

The nonlinear response of a quantum dot in a time-dependent field

We calculate the rectification coefficient and the second-harmonic generation coefficient for a quantum dot biased with an ac field. The coefficients are calculated as functions of the gate voltage (i.e. the positions of the resonant levels) and the frequency of the applied field. The rectification coefficient has a peaked dependence on the gate voltage with one central (negative) and two side (positive) peaks around the voltage at which the corresponding energy level for interacting electrons is equal to the collector electrode chemical potential. The peak heights are related to the average number of electrons in the dot - a feature which is a direct consequence of the electron interactions. The second-harmonic generation coefficient has similar behaviour for low frequencies ( at zero frequency). The frequency dependence of the rectification coefficient has features resulting from the photon-assisted tunnelling through the dot. The resonant-like enhancement of the rectification coefficient cannot be attributed to the photon-assisted transitions between different resonant levels in the dot.

Linear response spin admittance of a quantum dot subject to a spin bias

We compute the linear response spin admittance of a non-equilibrium quantum dot subject to a spin bias and an ac charge bias with small amplitude. As a function of the position of the resonant level (i.e. the gate voltage) the spin admittance shows a set of two peaks around the gate voltage at which the resonant or the upper level of the dot is in the vicinity of the equilibrium Fermi level in the leads. The peak heights can be related to the average number of quantum dot electrons. The frequency dependence of the spin admittance shows features resulting from the photon-assisted tunneling through the dot.

Normal metal to ferromagnetic superconductor tunnelling

We study the point-contact tunnelling between a normal metal and a ferromagnetic superconductor. In the case of magnon-induced pairing the tunnelling conductance is a continuous and smooth function of the applied voltage. For small values of the applied voltage the Ohm law holds. We show that one can obtain the magnetization and the superconducting order parameter from the tunnelling conductance. In the case of paramagnon-induced superconductivity the tunnelling does not depend on the magnetization. We argue that the tunnelling experiment can unambiguously determine the correct pairing mechanism in the ferromagnetic superconductors.

Holon effective mass in the slave fermion treatment of the t-J model

Abstract In terms of slave fermion representation of the t-J model the effect of the holon-spinon interactions on the holon effective mass is investigated. It is shown that the presence of the bose-condensed spinons in the ground state strongly enhances the holon mass.