Pekar bipolaron and the virial theorem (arbitrary coupling)

The work is devoted to issues related with implementation of the virial theorem for one-center bipolaron. The virial theorem expressions have been obtained for an electron system with Coulomb interactions in the phonon field. It is shown that for the bipolaron functional (one-center configuration) virial theorem holds for arbitrary electron-phonon coupling. As a specific example of the virial theorem for one-center bipolaron configuration, the author adduces numerical calculations of the energy of the ground state and the various contributions (kinetic energy, electron-phonon interaction, electron energy, phonon energy) into the energy of bipolaron, performed within the framework of Buimistrov-Pekar method. It is shown that the virial theorem is fulfilled with high accuracy for the two-electron systems with Coulomb interactions for an arbitrary value electron-phonon coupling. The necessary condition for formation of a bipolaron stable state is accounting electron correlations associated with the direct dependence of the trial electron wave function of the system from the interelectron distance

Polaron effects in exchange clusters (V²⁺ - F⁻ - V²⁺ in KMgF₃)

We have calculated the phonon contribution to the energy of a superexchange. It is shown that the phonon contribution to the exchange interaction is comparable on the order of magnitude with the Coulomb superexchange. The numerical calculations are performed for a molecular cluster consisting of an exchange-coupled pair V ²⁺−F–−V ²⁺ and 10 nearest ions F- in KMgF₃. The distinctions of a temperature dependence of the exchange interaction caused by phonons are discussed. In systems with the close located electronic levels, the account of interaction with a phonon field reduces in occurrence of resonant terms in the exchange interaction of paramagnetic ions. The similar terms result in occurrence of the exponential temperature dependence in an exchange interaction. As an example, the exchange pair of Cu²⁺ ions in K₂CuCl₄ ⋅ 2H₂O ⋅ has been considered. The experimentally observed anomalously strong temperature dependence of the exchange interaction of copper ions in this system can be described by the contribution of the resonant terms caused by a phonon contribution to the exchange interaction. The total exchange can be described by the dependence IΣ = I₀ - I₁(ex -1)⁻¹ where IΣ is the complete exchange interaction in a system including the phonon contribution (the second term) x = δ/k₀T with the parameters I₀ ≅ 0.29 Κ , I₁ ≅ 0.22 Κ , δ ≅ 192 Κ. The parameter δ corresponds to the splitting of a doubly degenerated lowest term of the copper ion in the crystalline field

Theoretical approach to electrodiffusion of shallow donors in semiconductors: I. Stationary limit

Analysis is made for the possibility of redistribution of mobile point defects in a semiconductor after its exposure to the electric field till the stationary conditions in the crystal are reached. Two different ways of applying the voltage are considered: (i) directly to the sample, (ii) to a capacitor, with the sample located between the plates. This model is applicable also to the electric field of any nature, whether external or internal, e.g. that arisning at the metal-semiconductor interface.Дається аналіз можливості розподілу рухомих точкових дефектів в напівпровіднику після дії на нього електричного поля до встановлення стаціонарних умов. Розглядаються два способи прикладання напруги: а) безпосередньо до зразка, б) до обкладинок конденсатора, між якими поміщається зразок. Модель також можна застосовувати для електричних полів будь-якої природи . як зовнішніх так і внутрішніх, що виникають, наприклад, на контакті метал-напівпровідник.Приводится анализ возможности распределения точечных дефектов в полупроводнике после воздействия на него электрического поля до установления стационарных условий. Рассматривается два способа приложения напряжения: а) непосредственно к образцу, б) к обкладкам конденсатора, между которыми помещается образец. Модель также применима для электрических полей любой природы как внешних так и внутренних, возникающих, например, на контакте металл-полупроводник

Bipolarons in anisotropic crystals and low dimensional structures

We consider a simple bipolaron approach to description of anisotropic crystals in the strongcoupling limit. We have taken into account anisotropy of effective band masses and dielectric constants of crystals. The calculations of energy for two - electron system was fulfiled using wave functions chosen as a linear combination of gaussian orbitals, what enables us to easily estimate the electron correlation effects which can play a key role. Bipolaron formation should be quite possible in crystals with hightemperature superconductivity. We have considered an example of La₂CuO₄,, in which there is a great anisotropy of effective masses and dielectric permittivities, where in the limiting case of the maximum anisotropy of effective masses mxy << mz the bipolaron binding energy is 25 % of the polaron energy

Gross–Tulub polaron functional in the region of intermediate and strong coupling

Properties of the polaron functional obtained as a result of averaging the Fröhlich Hamiltonian on the translation-invariant function have been investigated. The polaron functional can be represented in two different forms. It has been shown that the functional of translationally invariant Gross–Tulub polaron cannot be applied in the strong coupling region, where the real part of the complex quantity takes negative values. The function coincides in its structure with the dynamic susceptibility of degenerate electron gas. The necessary condition for obtaining correct results is investigation of the region of admissible values of the Gross–Tulub functional depending on properties of the function , variational parameters, and the electron-phonon interaction parameter α (Fröhlich coupling constant). A simple and exact formula for the recoil energy of the translationally invariant polaron has been derived, which makes it possible to extend the range of admissible values of the parameters of the electron-phonon interaction to the region of extremely strong coupling (α > 10), where . Numerical investigation of different forms of polaron functionals obtained using the field theory methods has been carried out

Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region

The properties of translationally invariant polaron functional have been investigated in the region of strong and extremely strong coupling. It has been shown that the Gross–Tulub polaron functional obtained earlier using the methods of field theory was derived only for the region , where is the Fröhlich constant of the electron-phonon coupling. Various representations of exact and approximate polaron functionals have been considered. Asymptotic dependences of the polaron energy have been obtained using a functional extending the Gross–Tulub functional to the region of extremely strong coupling. The asymptotic dependence of polaron energies for an extremely strong coupling are (for the one-parameter variational function fk), and (for a two-parameter function ). It has been shown that the virial theorem 1:3:4 holds for the two-parameter function . Minimization of the approximate functional obtained by expanding the exact Gross–Tulub functional in a series on leads to a quadratic dependence of the polaron energy. This approximation is justified for . For a two-parameter function , the corresponding dependence has the form . However, the use of approximate functionals, in contrast to the strict variational procedure, when the exact polaron functional varies, does not guarantee obtaining the upper limit for the polaron energy

Condensons and bicondensons in one-dimensional systems

The paper is devoted to simulation of continual strong coupling condensons and bicondensons states in one-dimensional systems by using the Gaussian basis with exponentially correlated multipliers. To determine the accuracy of variational calculations, it has been shown that using the variational function consisting of a sum of 5 Gaussians reproduces the exact value of energy and wave function of the one-dimensional condenson with the accuracy of 7 and 5 significant digits, correspondingly. Analytical expressions for the effective functional of the one-dimensional bicondenson have been obtained. Variational calculations of singlet condenson ground state energy were carried out with simultaneous accounting of single-center correlations and correlations caused by a direct dependence of the bicondenson wave function on the distance between electrons. The graphical dependence of the bicondenson energy on the Coulomb repulsion parameter V C has been represented. The region of existence of bicondenson was determined as a function of electron-electron repulsion parameter V C ≤ V C * ≈ 5 . 4 . The one-center bicondenson model has been considered, and distribution of the two-electron probability density (squared wave function of bicondenson) in the region 2 ≤ V C has two maxima, the distance between which for V C = 2 is R m = 1.8567. This distribution of the probability density is associated with the low dimensionality of the system under consideration

Investigation of electron correlation effect on energy spectrum of two-electron systems in crystals with strong electron-phonon coupling

The influence of electron correlations (direct dependence of electronic wave function on distance between electrons) on energy spectra of two-electron systems (D-, F ', F₂-centers and bipolarons) in polar crystals with strong electron-phonon interaction is investigated. Bipolaron is chosen as the simplest model of two-electron system in the crystal. Bipolaron energy is calculated for various distances between the centers of polarization wells of two polarons with accounting the electron correlations. A singlet bipolaron is stable at rather high energy of ion binding η ≤ ηm ≈ 0,143 (η= ε∞/ η₀). The unique energy minimum corresponds to a one-center bipolaron (an analog of a helium atom). The bipolaron binding energy constitutes up to 25.8% of a double polaron energy at η → 0. A triplet bipolaron (an analog of orthohelium) is energetically disadvantageous. The one-center configuration of a triplet bipolaron corresponds to a maximum on the distance dependence of the total energy JBp(R). The exchange interaction between polarons has antiferromagnetic character. A prediction is made about a possibility of the Wigner crystallization of a polaron gas, which occurs with antiferromagnetic ordering in the polaron system. The examples of energy calculations with accounting the electron correlations of exchanged-coupled pairs, D- and F '-centers in polar crystals are also given

Properties of the shallow D-centers in semiconductors with polar and covalent binding

The theoretical consideration of the energy of the lowest singlet and triplet terms of shallow D¯-centers (two electrons, bound with one-charge Coulomb center) in semiconductors with an ionic and covalent binding has been carried out. The electron-phonon interaction is described by a Frцhlich Hamiltonian. The energy of D¯-center is described with the use of a Buimistrov-Pekar method of canonical transformations for arbitrary electron-phonon coupling. It is shown, that for all area of electron-phonon interaction parameters the Buimistrov-Pekar method yields the lowest values of the ground state energy of D¯-centers and free bipolaron in comparison with the best, for today, numerical calculations of the relevant values which have been carried out within the framework of the direct variation methods. The calculations have shown the lack of the bound metastable triplet states corresponding to the lowest triplet energy term of D¯-center and bipolaron for all the area of electron-phonon interaction parameters, in complete analogy to the Hill theorem about the lack of the bound excited states of H¯ ion. It is shown that the account of interaction with acoustic phonons can produce considerable lowering the ground state energy of D¯-center in comparison with the magnitude 1.0555Ry