Stability of low-dimensionally-confined bipolarons

In the limit of strong electron-phonon coupling, we provide a unified insight into the stability criterion for bipolaron formation in low-dimensionally confined media. The model that we use consists of a pair of electrons immersed in a reservoir of bulk LO phonons and confined within an anisotropic parabolic potential box, whose barrier slopes can be tuned arbitrarily from zero to infinity. Thus, encompassing the bulk and all low-dimensional geometric configurations of general interest, we obtain an explicit tracking of the critical ratio of dielectric constants below which bipolarons can exist. Received 15 September 1999 and Received in final form 20 March 2000     

Hartree-Fock approximation of bipolaron state in quantum dots and wires

The bipolaronic ground state of two electrons in a spherical quantum dot or a quantum wire with parabolic boundaries is studied in the strong electron-phonon coupling regime. We introduce a variational wave function that can conveniently conform to represent alternative ground state configurations of the two electrons, namely, the bipolaronic bound state, the state of two individual polarons, and two nearby interacting polarons confined by the external potential. In the bipolaron state the electrons are found to be separated by a finite distance about a polaron size. We present the formation and stability criteria of bipolaronic phase in confined media. It is shown that the quantum dot confinement extends the domain of stability of the bipolaronic bound state of two electrons as compared to the bulk geometry, whereas the quantum wire geometry aggravates the formation of stable bipolarons.     

The stability of magnetobipolarons in low-dimensional systems

We investigate the stability condition of large bipolarons confined in a parabolic potential containing certain parameters and a uniform magnetic field. The variational wave function is constructed as a product form of electronic parts, consisting of center of mass and internal motion, and a part of coherent phonons generated by Lee-Low-Pines transformation from the vacuum. An analytical expression for the bipolaron energy is found, from which the ground and excited-state energies are obtained numerically by minimization procedure. The bipolaron stability region is determined by comparing the bipolaron energy with those of two separate polarons, which is already calculated within the same approximation. It is shown that the results obtained for the ground state energy of bipolarons reduce to the existing works in zero magnetic field. In the presence of a magnetic field, the stability of bipolarons is examined, for three types of low-dimensional system, as function of certain parameters, such as the magnetic-field, the electron-phonon coupling constant, Coulomb repulsion and the confinement strength. Numerical solutions for the energy levels of the ground and first excited states are examined as functions of the same parameters. Received 7 March 2002 and Received in final form 22 April 2002 Published online 25 June 2002     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. I. The adiabatic limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction , which tends to break them, generates many different ground-states. There are four domains in the phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small , large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large , large g); or 3) be a “quadrisinglet state” which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron. Received 10 December 1998     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. II. Quantum bipolarons

We study the effective mass of the bipolarons and essentially the possibility to get both light and strongly bound bipolarons in the Holstein-Hubbard model and some variations in the vicinity of the adiabatic limit. Several approaches to investigate the quantum mobility of polarons and bipolarons are proposed for this model. First, the quantum fluctuations are treated as perturbations of the mean-field (or adiabatic) approximation of the electron-phonon coupling in order to calculate the bipolaron bands. It is found that the bipolaron mass generally remains very large except in the vicinity of the triple point of the phase diagram (see [1]), where the bipolarons have several degenerate configurations at the adiabatic limit (single site (S0), two sites (S1) and quadrisinglet (QS)), while the polarons are much lighter. This degeneracy reduces the bipolaron mass significantly. Next we improve this result by variational methods (modified Toyozawa Exponential Ansatz or TEA) valid for larger quantum perturbations away from the adiabatic limit. We first test this new method for the single polaron. We find that the triple point of the phase diagram is washed out by the lattice quantum fluctuations which thus suppress the light bipolarons. Further improvements of the method by hybridization of several TEA states do not change this conclusion. Next we show that some model variations, for example a phonon dispersion may increase the stability of the (QS) bipolaron against the quantum lattice fluctuations. We show that the triple point of the phase diagram may be stable to quantum lattice fluctuations and a very sharp mass reduction may occur, leading to bipolaron masses of the order of 100 bare electronic mass for realistic parameters. Thus we argue that such very light bipolarons could condense as a superconducting state at relatively high temperature when their interactions are not too large, that is, their density is small enough. This effect might be relevant for understanding the origin of the high superconductivity of doped cuprates far enough from half filling. Received 15 September 1999     

The ground- and first-excited states of magnetopolarons in two-dimensional quantum dots for all coupling strengths

The ground- and first-excited state energies of a magnetopolaron in a two dimensional parabolic quantum dot are studied within a variational calculation for all coupling strength. The Lee-Low-Pines-Huybrecht variational technique that is developed previously for all coupling strength has been extented for polarons in a magnetic field. The dependence of the polaronic correction on the magnetic field and the confinement length is investigated. The polarization potential and the renormalized cyclotron masses as a function of electron-phonon coupling strength and the strength of both confinement potential and magnetic field are also studied within the same approach. Received 16 December 2002 / Received in final form 14 April 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: kandemir@science.ankara.edu.tr     

Bipolaronic excitations of interacting electron(hole) gas in one-dimensional lattice model

By developing a diagonalization scheme we observe that the dynamics of interacting electrons or holes locally coupled to dispersionless phonon mode in one-dimensional lattice can be mapped into that of paired electron or hole states (bipolaronic states), which then gives a physically appealing picture of excitation modes of the interacting electron or hole gas. As a result, the bipolaronic model of the interacting electron or hole gas, obtained from Holstein–Hubbard Hamiltonian in one-dimensional lattice, exhibits normalization of the hopping terms and leads to a reduced effective mass of the bipolaron, which essentially gives support to the bipolaronic theory of high T_c superconductivity.     

Hierarchies of stability regions for η-pairing superconducting ground states of generalized Hubbard models

For a class of generalized one dimensional Hubbard models, we study the stability region for the superconducting -pairing ground state. We exploit the Optimum Ground State (OGS) approach and the Lanczos diagonalization procedure to derive a sequence of improved bounds. We show that some pieces of the stability boundary are asymptotic, namely independent on the OGS cluster size. The phenomenon is explained by studying the properties of certain exact eigenstates of the OGS Hamiltonians. Received 27 July 1999 and Received in final form 29 September 1999     

Interface polarons in a realistic heterojunction potential

The ground states of interface polarons in a realistic heterojunction potential are investigated by considering the bulk and the interface optical phonon influence. A self-consistent heterojunction potential is used and an LLP-like method is adopted to obtain the polaron effect. The numerical computation has been done for the Zn_1-xCd_xSe/ZnSe system to obtain the polaron ground state energy, self energy and effective mass parallel to the interface. A simplified coherent potential approximation is developed to obtain the parameters of the ternary mixed crystal and the energy band offset of the heterojunction. It is found that at small Cd concentration the bulk longitudinal optical phonons give the main contribution for lower areal electron densities, whereas the interface phonon contribution is dominant for higher areal electron densities. The interface polaron effect is weaker than the effect obtained by the three dimensional bulk phonon and by the two dimensional interface phonon models. Received 17 September 1998     

Spin injection in an organic device with a spin polarized self-assembled monolayer

We propose to achieve spin injection in an organic device by a spin polarized self-assembled monolayer (SPSAM), which is used to tune the spin-dependent coupling between electrode and organic polymer. The results show that spin injection can be realized by both the spin selection and spin manipulation effects of the SPSAM. Interestingly, we found spin polarized wave-packet as a consequence of the spin injection, which is a mix of a normal spin polaron and a spinless bipolaron.     

On the formation and stability of the Fröhlich bipolaron in two- and three-dimensional systems

Summary Within the framework of Rayleigh-Schr?dinger perturbation theory the bound state of two electrons in polar crystals is investigated in various dimensional systems. It is found that Fr?hlich bipolaron can exist in both two and three dimensions in the strong-coupling region, the binding being stronger in the lower dimension. The stability criterion for the formation of the Fr?hlich bipolaron is estimated to yield better results compared to the values quoted in the literature. The author of this paper has agreed to not receive the proofs for correction     

Rayleigh-Schrödinger perturbation theory for electron-phonon interaction in two dimensional quantum dots with asymmetric parabolic potential

Within the framework of the second-order Rayleigh-Schr?dinger perturbation theory, we investigate the effects of the interaction of the electron and longitudinal-optical phonons in two-dimensional semiconductive quantum dots with respect to a general potential. We propose a simple expression for the ground state energy, and compare it with those obtained by Landau-Pekar strong coupling theory. It is shown both analytically and numerically that the results obtained from the second-order Rayleigh-Schr?dinger perturbation theory could be better than those from Landau-Pekar strong coupling theory when the coupling constant is sufficiently small. Moreover, some interesting problems, such as polarons in quasi-one-dimensional quantum wires, and quasi-zero-dimensional asymmetric or symmetric quantum dots can be easily discussed only by taking different limits. After the numerical calculations, we find that there exists a simple dimensional scaling and symmetry relation for the ground state polaron energy. Furthermore, we apply our results to some weak-coupling polar semiconductors such as GaAs, CdS. It is shown that the polaronic effects are found to be quiet appreciable if the confinement lengths and smaller than a few nanometers. Received: 3 December 1997 / Revised: 6 July 1998 / Accepted: 17 September 1998     

Chaotic polaronic and bipolaronic states in the adiabatic Holstein model

A rigorous proof for the existence of bipolaronic states is given for the adiabatic Holstein model for any lattice at any dimension, periodic or not, and for an arbitrary band filling, provided that the electron-phonon coupling (in dimensionless units) is large enough. The existence of mixed polaronic-bipolaronic states is also proven, but for larger electron-phonon coupling. These states consist of arbitrary distributions of bipolarons (or of bipolarons and polarons) localized in real space which can be simply labeled by pseudospin configurations as for a lattice gas model. The theory not only applies to periodic crystals, but also to quasicrystals, amorphous structures, polymer network, etc.When these bipolaronic and mixed polaronic-bipolaronic states exist, it is proven that: (1) These bipolaronic (and mixed polaronic-bipolaronic) states exhibit a nonzero phonon gap with a nonvanishing lower bound and an electronic gap at the Fermi energy. (2) These structures are insulating. The perturbation generated by any local change in the bipolaronic or polaronic distribution or by any charged impurity or defect decays exponentially at long distance. (3) These bipolaronic (and mixed polaronic-bipolaronic) states persist for any uniform magnetic field. (4) For large enough electron-phonon coupling, the ground state of the extended adiabatic Holstein model is a bipolaronic state when there is no uniform magnetic field or when it is small enough. It becomes a mixed polaronic-bipolaronic state for large enough magnetic field (note that the mixed polaronic-bipolaronic states are magnetic).In one-dimensional models, the ground state is an incommensurate (or commensurate) charge density wave (CDW) as predicted by Peierls (this result is not rigorous, but has been confirmed numerically). It is proven that the ground state becomes a bipolaronic charge density wave (BCDW) at large enough electron-phonon coupling. The existence of a transition by breaking of analyticity (TBA), which was numerically observed as a function of the electron-phonon coupling, is then confirmed. In that case, the shape of the effective bipolaron can be numerically calculated. It is observed that its size diverges at the TBA. The physical properties of BCDWs are rather different from those predicted by standard charge density wave theory. Bipolaronic charge density waves can also exist in models which are not only low-dimensional, but purely two- or three-dimensional.The technique for proving these theorems is an application of the concept of anti-integrability initially developed for Hamiltonian dynamical systems. It consists in proving that the eigenstates of the (trivial) Hamiltonian (called antiintegrable) obtained by canceling all electronic and lattice kinetic terms survive as a uniformly continuous function of the electronic kinetic energy terms in the Hamiltonian up to a certain threshold.     

New polaronic excitons in ferroelectric oxides: phenomenological theory

It is shown that three types of new polaronic excitons exist in ferroelectric oxides-charge transfer vibronic excitons (CTVEs). The electron-hole bipolaron pairs are common in all these cases, the difference having to do with the origin of charge transfer-lattice instabilities. These are the cases of the charge transfer and lattice distortions and their vibronic interactions induced in the harmonic (i) and anharmonic (ii) regimes both in the electronic excited state on the one hand, and the (iii) case of the CTVE excited vibronic state induced in the anharmonic regime but related with electronic ground state on the other. All these CTVEs are characterized by strong coupling with good self-localization conditions in separate orientation wells of their multi-well potentials. The relevant phenomenological theory is developed. While the (i) type CTVE is confirmed by luminescence experiments, the (iii) type CTVE with low excitation energy and with metastable intrinsic defect behaviour can be a candidate for the explanation of an order-disorder effect in the classical ferroelectric oxides discovered recently [Phys. Rev. Lett. 90 (2003) 037601].     

Dissociation of bipolaron in non-degenerate polymer chain at high electric fields

We investigate the dynamics of bipolaron in non-degenerate polymer (e.g. PPV) in an external electric field by using a nonadiabatic evolution method, which allows transition between instantaneous electronic states. When the applied electric field exceeds a critical value, a bipolaron is found to dissociate like the case of polaron due to the lattice distortion not being able to follow the fast moving electrons. The critical value is estimated to be of order ¹⁰⁶ V/cm${10}^6\text{ V}/\text{cm}$. This result is consistent with experiment in that a large increase in current in PPV occurs at high fields. At a given electric field, the saturation velocity of bipolaron will decrease with the increase of non-degenerate parameters te$t_e$.     

Mobility of biplasmapolarons and high-T c superconductivity

Summary The mobility of the Fr?hlich bipolarons is a challenging matter for the bipolaronic theory of high-T _c superconductivity. Here we focus our attention on the problem of the effective mass of a bipolaron in a strongly ionic system (like the new H(igh)T _cS(uper)C(onductors) are) and in the presence of an electron gas. We show that there is a sizeable renormalization of the bipolaron mass due to the polarization effects of both the optical phonons and plasmons. Moreover, we show that the effective mass decreases increasing the density of carriers, because the screening effects become more important. In all cases, the values of the bipolaron effective mass are not greater than some tens of electronic masses (m _e).     

Spectroscopic observation of bipolaronic point defects in Ba(1-x)KxBiO3

An infrared-absorption band centered at 0.85 eV, which is below the big optical absorption at the charge-density-wave (CDW) gap energy of 1.85 eV, has been observed for semiconducting single crystalline Ba(1-x)KxBiO3. With substituting K for Ba, the spectral weight of the new band increases with x, while that of the CDW-gap excitation decreases. Since the impurity state with the K substitution is known to be nonmagnetic at low temperatures, Bi3+ the state with 6s2 electrons surrounded by the six Bi5+ ions forms a small bipolaron by losing a pair of electrons in the Rice-Sneddon model. The new band is assigned to a transition from the lower-Peierls band to a state of the bipolaronic point defect.     

对角无序对三重态双极化子系统的超导电性的影响

本文在平均场近似的框架下,对于两δ函数无规分布讨论了对角无序对三重态双极化子系统的影响。得到无序对双极化子密度为半填充附近的影响较显著,超导较变温度严重降低;而当密度较小时,一般的无规能量并不能完全阻碍超导电性的发生,这是由双极化子的隧道运动所导致。因此可以期望在一些无序半导体中可以发现这种类型的超导体。 关键词：     

Optimum ground states of generalized Hubbard models with next-nearest neighbour interaction

We investigate the stability domains of ground states of generalized Hubbard models with next-nearest neighbour interaction using the optimum groundstate approach. We focus on the -pairing state with momentum P=0 and the fully polarized ferromagnetic state at half-filling. For these states exact lower bounds for the regions of stability are obtained in the form of inequalities between the interaction parameters. For the model with only nearest neighbour interaction we show that the bounds for the stability regions can be improved by considering larger clusters. Additional next-nearest neighbour interactions can lead to larger or smaller stability regions depending on the parameter values. Received 30 March 1999 and Received in final form 3 May 1999