Interaction of polarons in two and three dimensions

Two-dimensional and three-dimensional bipolarons of large radius, symmetrized with respect to the coordinate parts of the two-center wave functions, are investigated in the adiabatic approximation with allowance for dynamic interelectronic correlations. The adiabatic potential lines are plotted. It is shown that the quasimolecular configuration appearing in the Hartree-Fock approximation is unstable in both the two-dimensional and the three-dimensional cases. The ground state is a one-center configuration. Estimates are given for the binding energy and the heat of dissociation of a bipolaron. Fiz. Tverd. Tela (St. Petersburg) 39, 441–443 (March 1997)     

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     

聚对苯撑[poly(p-phenylene)]的基态、极化子和双极化子激发态

本文在紧束缚模型基础上,对聚对苯撑类材料提出一简单的哈密顿量,并计算了系统的能带结构,给出基态、极化子、双极化子激发态,得到了双极化子比两个单极化子更容易激发这一重要结论。在能带中除发现能隙内的两个极化子定域能级外,还发现导带和价带都要发生二劈裂,带边上出现浅能级,它们对应的电子态均是定域的。 关键词：     

Ground state and polaron and bipolaron excited states in polydiacetylene

The electronic properties of ground state and charged excited states of non-degenerate polydiacetylene were investigated by means of a tight-binding model. The parameters of the model were obtained by comparison of the experimental and other theoretical results. It was found that there is a stable dimerized structure of polydiacetylene in ground state and the doping induces the nonlinear excitations, such as polarons and bipolarons. In order to compare the stability of polaron and bipolaron, the creation energy and binding energy were separately defined. By neglecting the electron-electron Coulomb interaction, a bipolaron is more stable than two independent polarons.     

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     

Soliton-Like Bipolaron in Two-Dimensional Deformable Electron-Phonon System

Based on Emin's idea of deformation potential in deformable continuum, a bipolaron Hamiltonian is generalized to two-dimensional deformable electron-phonon system with the assumption of localized deformation potential of δ function. The dynamic properties of bipolaron are studied in the framework of Davydov's soliton theory, and a nonlinear Schrodinger equation is derived using the principle of least action. By function-series method, an exact two-dimensional (2D) soliton solution is obtained. We find that the center-of-mass motion of bipolaron is shown in a solitary wave form, and its relative motion is a harmonic one.     

Comments on “Translation-invariant bipolarons and the problem of high-temperature superconductivity”

We comment on the recent results of Refs. [1], [2] on the bipolaron problem derived using an approximation of Gross–Tulub. It is proved that, contrary to the claim made in Refs. [1], [2], the bipolaron ground-state energy calculated there in the strong-coupling approximation has not been shown to constitute a variational upper bound.     

基态非简并聚合物中的极化子和双极化子的动力学(Ⅰ)--弱电场下研究

文中模拟了在基态非简并聚合物中的极化子和双极化子在弱电场中的运动,研究了在不同简并参数的系统中极化子和双极化子的动力学稳定性,发现在同一个系统中,双极化子比极化子的运动速度慢,晶格振荡小; 在简并参数大的系统中,极化子和双极化子的运动速度都变慢.极化子和双极化子在弱电场下都存在饱和速度,达到饱和速度后, 电场的能量发生了转换.     

Linear screening effects on large bipolarons

Summary The screening effects of the formation of large bipolarons have been studied. It is shown that the dependence of the bipolaron binding energy on the electron density does not change qualitatively by using different dielectric functions for describing electron screening. The same result is found if the electron system is described as a bipolaron gas (charged bosons).     

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).     

Bipolarons in a KCl melt

A theory of two excess electrons in alkali halide melts is developed using variational estimates of path integrals. As a result of the strong screening, the average field generated by the ions has little influence on the electrons and the problem reduces to a study of a bipolaron type of free energy functional. The behavior of this functional is determined as a function of the thermodynamic and structural characteristics of the melt. Variational bipolaron calculations are made using the approximation of uncorrelated electrons and using Kohn-Sham theory to allow for electron-electron correlations. The results of the calculations using Kohn-Sham theory agree with the data obtained by quantum molecular dynamics and show that a correct choice of trial wave function which allows explicitly for the correlation of two electrons is required to obtain a correct estimate of bipolaron stability.     

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     

Al_xGa_(1-x)As:Si中DX中心的双极化子机制及统计分析

基于极化子和双极化子的物理图像,采用无拟合参数的巨正则统计方法计算了Si掺杂的AlxGa1-xAs的导带载流子浓度,计算得到的理论结果从高温到低温都与实验结果定量一致.计算证实了AlxGa1-xAs:Si中的DX中心的基态DX-是电子-晶格相互作用产生的负电双极化子.处于热平衡状态时,施主Si在AlxGa1-xAs中除了电离状态,处于不同晶格构型的单、双极化子态共存,低温时双极化子态被冻结;光照下发生持续光电导时,双极化子态变成单极化子态同时向导带释放一个电子,此过程伴随着进一步的晶格弛豫.理论与实验的对照说明单电子局域的DX0态在热平衡时并不能稳定存在,这和提出的双极化子机制是完全一致的.     

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：     

共轭高分子链中大极化子与小极化子的弹性碰撞

基于Su-Schrieffer-Heeger(SSH)模型,考虑电子-电子相互作用,以及在哈密顿量中引入Brazovskii-Kivova对称破缺项,采用动力学演化的方法研究了在外电场作用下共轭高聚物分子链中大极化子与小极化子之间的弹性散射过程.研究发现,载流子的载荷性质不但决定大小极化子之间的相互作用性质,也深刻地影响了其发生散射后的载流子输运性质.在较低电场的作用下,当两载流子电性相同时,发生碰撞后,小极化子将推动着大极化子一起运动;而当两者电性相反时,碰撞后,大极化子将拖曳着小极化子一起运动.当电场强度超过临界值时,将产生量子隧穿效应,即,大小极化子相互迅速穿透,且不受载流子的载荷影响.     

导电聚合物P3MT的光调制反射谱

本文报道了导电聚合物光调制反射光谱的研究工作。实验观察到聚三甲基噻吩的带间跃迁和与双极化子态有关的跃迁,并且观察了谱结构随掺杂浓度、温度以及调制光强度的变化。实验结果证明,光子能量大于禁带宽度E_g的光可在聚合物分子链中诱导产生双极化子。虽然双极化子可以由光诱导产生,也可以由杂质诱导产生,但它本身是不依赖于诱导方式的聚合物分子链的本征元激发态。荷电的双极化子可受离化杂质的库仑吸引,产生钉扎效应,并使禁闭参数变大。 关键词：     

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.     

Fe:Mg:LiNbO3晶体电子结构和吸收光谱的第一性原理研究

基于密度泛函理论的第一性原理, 研究了LiNbO₃晶体以及不同Mg浓度的Fe:Mg:LiNbO₃晶体的电子结构和吸收光谱. 研究结果显示: 掺铁铌酸锂晶体的杂质能级由Fe 的3d轨道和O的2p轨道贡献, 禁带宽度为2.845 eV; 对于Mg, Fe共掺样品, Mg的浓度小于或等于阈值时, 禁带宽度分别为2.901 和2.805 eV; 掺铁铌酸锂晶体的吸收谱在2.3和2.6 eV处分别存在一个吸收峰, 其强度因Mg的浓度不同而发生变化. 研究结果还表明, 不同浓度的Mg对晶体内Fe²⁺和Fe³⁺的浓度以及占位产生了不同的影响. 还提出了光电子的形成不应单独考虑铁的轨道电子态, 而应同时考虑与铁成键的氧的轨道电子态的观点.     

Organic electroluminescence channel avoiding triplet excitons

Polarons and bipolarons are main carriers in conducting polymers. It is shown that a bipolaron can open a channel of electroluminescence, which does not involve a triplet exciton, and can enhance the efficiency of electroluminescence. The dynamics of this channel is simulated.